V prostranstvenno-gruppovom podkhode volnovaya funktsiya singletnoi (tripletnoi) kuperovskoi pary stroitsya kak simmetrizovannyi (antisimmetrizovannyi) kronekerovskii kvadrat NP (neprivodimogo predstavleniya) prostranstvennoi gruppy. V obshchei tochke ZB (zony Brillyuena) rezul'taty etogo podkhoda sovpadayut s rezul'tatami podkhoda Andersona, a v simmetrichnykh tochkakh ZB vozmozhnye simmetrii pary zavisyat ot tret'ego kvantovogo chisla – NP prostranstvennoi gruppy i okazyvayutsya razlichnymi dlya simmorfnykh i nesimmorfnykh prostranstvennykh grupp. Poluchaemaya v takom podkhode struktura nulei pary dlya odnomernykh NP sovpadaet s rezul'tatami fenomenologicheskikh podkhodov, a dlya dvumernykh NP vvoditsya chetvertoe kvantovoe chislo – indeks NP promezhutochnoi gruppy.

Rassmatrivaetsya svyaz' NP tochechnoi gruppy s vozmozhnymi momentami v teorii Ginzburga-Landau. V takom podkhode topologicheskaya faza «namatyvaetsya» v bazisnoi ZB i rasprostranyaetsya na ostal'nye ee chasti operatsiyami tochechnoi gruppy. Pokazano, chto simmetriya tripletnoi pary s kompleksnoi volnovoi funktsiei v UTe2 opisyvaetsya shubnikovskoi gruppoi mm’m’ i postroeny bazisnye funktsii. Dlya Sr2RuO4 pokazano, chto teoreticheskaya struktura nulei pary simmetrii Eg sootvetstvuet vsem eksperimentam, a polukvantovanie potoka v prisutstvii vneshnego polya ob'yasneno simmetriino. Tri fazy UPt3 opisany v terminakh dopolnitel'nykh kvantovykh chisel.

The widely accepted Chalker-Coddington model of IQHE has the problem of inconsistency between numerical and experimental values of localization length exponent. Recently it was shown that taking into account the random geometrical structure of the scattering network itself alongside U(1) phase disorder has the capability of fixing the discrepancy. The geometrical randomness is introduced through specific parametrized modification of the regular network model. A correspondence between the created structure to the real-life potential based scattering network structure is established through curvature distribution analysis, a connection between random network parameters and experimentally measurable compensation parameter is predicted. The issue of reliability of numerical calculations is addressed by introducing a more robust and faster technique, namely the S-matrix approach. New calculations verify the previously known results and provide better precision.

Two-dimensional semiconductor-superconductor heterostructures form the foundation of numerous nanoscale physical systems. However, measuring the properties of such heterostructures, and characterizing the semiconductor in-situ is challenging. A recent experimental study [arXiv:2107.03695] was able to probe the semiconductor within the heterostructure using microwave measurements of the superfluid density. This work revealed a rapid depletion of superfluid density in semiconductor, caused by the in-plane magnetic field which in presence of spin-orbit coupling creates so-called Bogoliubov Fermi surfaces. The experimental work used a simplified theoretical model that neglected the presence of non-magnetic disorder in the semiconductor, hence describing the data only qualitatively. Motivated by experiments, we introduce a theoretical model describing a disordered semiconductor with strong spin-orbit coupling that is proximitized by a superconductor. Our model provides specific predictions for the density of states and superfluid density. Presence of disorder leads to the emergence of a gapless superconducting phase, that may be viewed as a manifestation of Bogoliubov Fermi surface. When applied to real experimental data, our model showcases excellent quantitative agreement, enabling the extraction of material parameters such as mean free path and mobility, and estimating g-tensor after taking into account the orbital contribution of magnetic field. Our model can be used to probe in-situ parameters of other superconductor-semiconductor heterostructures and can be further extended to give access to transport properties.

https://arxiv.org/abs/2311.09347

V khode doklada budut obsuzhdat'sya rezul'taty dvukh rabot 2312.04138 i 2312.04139.

Pervaya rabota posvyashchena issledovaniyu dinamicheskikh effektov vzaimodeistviya izgibnykh i vnutriploskostnykh fononov v dvumernykh kristallicheskikh membranakh. Otsutstvie logarifmicheskikh raskhodimostei v dinamicheskikh vkladakh pozvolyaet opredelit' skeiningovyi vid i asimptotiki sobstvenno-energeticheskoi chasti kak funktsii chastoty. Takzhe udaetsya naiti dinamicheskie indeksy v dlinnovolnovom predele dlya izgibnykh i ploskostnykh fononov.

Vtoraya rabota rassmatrivaet vliyanie konechnogo natyazheniya na vremya zhizni kvazichastits. V etom sluchae proiskhodit parametricheskoe suzhenie spektral'nykh linii izgibnykh fononov. My polagaem, chto eto mozhet posluzhit' prichinoi vysokoi dobrotnosti mekhanicheskikh nanorezonatorov na osnove dvumernykh kristallicheskikh membran.

The superconducting diode effects refers to supercurrent flow only along one direction, but not in the opposite one. We review this phenomenon and describe our recent theory [1,2] of voltage-biased Josephson diodes in junctions of superconductors with finite-momentum Cooper pairing. For a short weak link, this problem can be solved by scattering theory, taking into account multiple Andreev reflections to all orders. We find rich subharmonic structure with highly efficient rectification at subgap voltages and large junction transparency.

[1] A. Zazunov, J. Rech, T. Jonckheere, B. Gremaud, T. Martin, and R. Egger, arXiv:2307.14698. [2] A. Zazunov, J. Rech, T. Jonckheere, B. Gremaud, T. Martin, and R. Egger, arXiv:2307.15386.

Rassmatrivaetsya odnochastichnaya zadacha o dinamike sostoyanii v poluprovodnikovoi dvoinoi kvantovoi tochke v ramkakh odnomernoi modeli s sil'nym spin-orbital'nym vzaimodeistviem, postoyannym magnitnym i periodicheskim elektricheskim polyami. Issleduyutsya razlichnye rezhimy tunnelirovaniya mezhdu dvumya tochkami sovmestno s dinamikoi spina v ramkakh elektricheskogo dipol'nogo spinovogo rezonansa. Obnaruzheny novye rezhimy evolyutsii, opisanie kotorykh vykhodit za ramki dvukhurovnevogo priblizheniya, v tom chisle dlya yavlenii interferentsii Landau-Zenera-Shtyukel'berga-Maiorany. V chastnosti, dlya sil'nogo tunnelirovaniya predskazana vozmozhnost' perevorota spina ne tol'ko na osnovnoi garmonike rezonansa, no i na subgarmonikakh, chto pozvolit osushchestvlyat' vrashcheniya spina na bolee nizkikh chastotakh po sravneniyu s zeemanovskim rasshchepleniem.

https://arxiv.org/abs/2208.14965

The use of dissipation for the controlled creation of nontrivial quantum many-body correlated states is of much fundamental and practical interest. What is the result of imposing number conservation, which, in closed system, gives rise to diffusive spreading? We investigate this question for a paradigmatic model of a two-band system, with dissipative dynamics aiming to empty one band and to populate the other, which had been introduced before for the dissipative stabilization of topological states. Going beyond the mean-field treatment of the dissipative dynamics, we demonstrate the emergence of a diffusive regime for the particle and hole density modes at intermediate length- and time-scales, which, interestingly, can only be excited in nonlinear response to external fields. We also identify processes that limit the diffusive behavior of this mode at the longest length- and time-scales. Strikingly, we find that these processes lead to a reaction-diffusion dynamics governed by the Fisher-Kolmogorov-Petrovsky-Piskunov equation, making the designed dark state unstable towards a state with a finite particle and hole density.
Results are published in P. A. Nosov, D. S. Shapiro, M. Goldstein, I. S. Burmistrov, "Reaction-diffusive dynamics of number-conserving dissipative quantum state preparation", Phys. Rev. B 107, 174312 (2023)

Driven-dissipative protocols are proposed to control and create nontrivial quantum many-body correlated states. Protocols conserving the number of particles stand apart. As well-known, in quantum systems with the unitary dynamics the particle number conservation and random scattering yield diffusive behavior of two-particle excitations (diffusons and cooperons). Existence of diffusive modes in the particle-number-conserving dissipative dynamics is not well studied yet. We explicitly demonstrate the existence of diffusons in a paradigmatic model of a two-band system, with dissipative dynamics aiming to empty one fermion band and to populate the other one. The studied model is generalization of the model introduced in F. Tonielli, J. C. Budich, A. Altland, and S. Diehl, Phys. Rev. Lett. 124, 240404 (2020). We find how the diffusion coefficient depends on details of a model and the rate of dissipation. We discuss how the existence of diffusive modes complicates engineering of macroscopic many-body correlated states.
Results are published in A.A. Lyublinskaya, I.S. Burmistrov, "Diffusive modes of two-band fermions under number-conserving dissipative dynamics", Pis'ma v ZhETF 118, 538 (2023)

The interplay of superconductivity and disorder generates a wealth of complex phenomena. In particular, the peculiar structure of diffusive electronic wave functions is predicted to increase the superconducting critical temperature in some range of disorder. In this work, we use an epitaxial monolayer of lead showing a simple band structure and homogeneous structural disorder as a model system of a two-dimensional superconductor in the weak-antilocalization regime. Then, we perform an extensive study of the emergent fluctuations of the local density of states (LDOS) and spectral energy gap in this material and compare them with both analytical results and the numerical solution of the attractive Hubbard model. We show that mesoscopic LDOS fluctuations allow us to probe locally both the elastic and inelastic scattering rates, which are notoriously difficult to measure in transport measurements.

A talk is based on M. Lizee, M. Stosiek, C. Brun, I.S. Burmistrov, T. Cren, Phys. Rev. B 107, 174508 (2023).

We study de Haas-van Alphen oscillations in a marginal Fermi liquid resulting from a three-dimensional metal tuned to a quantum-critical point (QCP). We show that the conventional approach based on extensions of the Lifshitz-Kosevich formula for the oscillation amplitudes becomes inapplicable when the correlation length exceeds the cyclotron radius. This breakdown is due to (i) non-analytic finite-temperature contributions to the fermion self-energy (ii) an enhancement of the oscillatory part of the self-energy by quantum fluctuations, and (iii) non-trivial dynamical scaling laws associated with the quantum critical point. We properly incorporate these effects within the Luttinger-Ward-Eliashberg framework for the thermodynamic potential by treating the fermionic and bosonic contributions on equal footing. As a result, we obtain the modified expressions for the oscillations of entropy and magnetization that remain valid in the non-Fermi liquid regime.

V etom doklade ya rasskazhu pro model' Andersona na ansamble sluchainykh regulyarnykh grafov (RRG) so stepen'yu vershin d pri nalichii besporyadka na dole uzlov β. Analiticheski budet pokazany granitsa podvizhnosti i obobshchenie zakona Kestena-MakKoya dlya spektral'noi plotnosti na sluchai chastichnogo besporyadka s ravnomernym raspredeleniem pri beskonechnoi amplitude. Budet rassmotrena dual'nost' mezhdu razryazhennym i ekstremal'no plotnym RRG. Takzhe korotko rasskazhu po lokalizovannye sostoyaniya v RRG s khimicheskim potentsialom 3-tsiklov i lokalizatsiyu na grafakh pri nalichii odnonapravlennykh reber, i kak chastichnyi besporyadok vliyaet na takie sistemy.

Generalized multifractality characterizes system size dependence of pure scaling local observables at Anderson transitions in all ten symmetry classes of disordered systems. Here we demonstrate that the concept of generalized multifractality can be extended to local observables situated neat boundaries of critical disordered noninteracting systems. We study the generalized boundary multifractality focusing on the spin quantum Hall symmetry class (class C). Employing the two-loop renormalization group analysis within Finkel'stein nonlinear sigma model we compute analytically the anomalous dimensions of the pure scaling operators located at the boundary of the system. We find that generalized boundary multifractal exponents are twice larger than their bulk counterparts. Also, in two dimensions we compute the corresponding boundary multifractal exponents numerically.
A talk is based on the following papers
1. S.S. Babkin, J.F. Karcher, I.S. Burmistrov, A.D. Mirlin, "Generalized surface multifractality in 2D disordered systems", Phys. Rev. B 108, 104205 (2023)
2. S.S. Babkin, I.S. Burmistrov, "Boundary multifractality in the spin quantum Hall symmetry class with interaction", arxiv:2308.16852

Issledovanie vliyaniya mnogochastichnykh protsessov na usloviya formirovaniya topologicheskikh faz yavlyaetsya aktual'noi problemoi teorii kondensirovannogo sostoyaniya. V nastoyashchei rabote my rassmotreli vopros ob indutsirovanykh zaryadovymi fluktuatsiyami topologicheskikh fazakh v ramkakh perturbativnogo podkhoda dlya rasshirennoi modeli tsepochki Kitaeva, prinadlezhashchei simmetriinomu klassu BDI. Naidennye popravki k kvazichastichnoi funktsii Grina na nulevoi chastote pozvolili yavnym obrazov vydelit' iz obshchego topologicheskogo invarianta sistemy (winding number) srednepolevoi i fluktuatsionnyi vklady. V rezul'tate, byli opisany topologicheskie perekhody, svyazannye isklyuchitel'no s zaryadovymi fluktuatsiyami. Pokazano, chto prichinoi realizatsii takikh perekhodov yavlyaetsya effektivnoe zapolnenie nodal'nykh mod sverkhprovodyashchego parametra poryadka, indutsirovannogo zaryadovymi fluktuatsiyami. V kontekste topologicheskikh fazovykh perekhodov takzhe issledovany osobennosti fluktuatsionnykh renormirovok spektral'nykh parametrov sistemy: smeshcheniya spektra, vremeni zhizni kvazichastits i effektivnoi massy.

Doklad po rabote M. S. Shustin, S. V. Aksenov, I. S. Burmistrov, "Topological phases induced by charge fluctuations in Majorana wires".

My izuchaem elektron-fononnuyu relaksatsiyu v modeli granulirovannoi metallicheskoi plenki, gde zerna obrazovany regulyarno raspolozhennymi potentsial'nymi bar'erami proizvol'noi prozrachnosti. Rasschitana skorost' relaksatsii akusticheskikh fononov v modeli Debaya s uchetom dvukh mekhanizmov elektron-fononnogo rasseyaniya: standartnogo vzaimodeistviya deformatsii reshetki s elektronnoi plotnost'yu i vzaimodeistviya za schet smeshcheniya granits zeren, vyzvannogo kolebaniyami reshetki. Pri samykh nizkikh temperaturakh moshchnost' elektronno-fononnogo okhlazhdeniya sootvetstvuet stepennoi zavisimosti po temperature, tipichnoi dlya chistykh sistem, no s koeffitsientom, rastushchim po mere umen'sheniya prozrachnosti granits zeren.
https://arxiv.org/abs/2306.15495

Otkrytie topologicheskikh fazovykh perekhodov polozhilo nachalo odnomu iz naibolee plodotvorno razvivayushchikhsya napravlenii sovremennoi fiziki tverdogo tela. Odnim iz naibolee izuchennykh klassov materialov s netrivial'noi topologiei elektronnykh sostoyanii yavlyayutsya topologicheskie izolyatory (TI), kotorye v ob'eme predstavlyayut soboi uzkozonnyi poluprovodnik s Eg ~ 0,05-0,4 eV, a na geterogranitse s trivial'nym dielektrikom imeyut besshchelevye elektronnye sostoyaniya. V poslednee vremya magnitnye topologicheskie izolyatory (MTI) stali ob'ektom znachitel'nogo nauchnogo interesa. Naibolee intensivno izuchennymi MTI yavlyayutsya MnBi₂Te₄ [1] (tak nazyvaemaya 124-faza) – sloistoe soedinenie, sostoyashchee iz semisloinykh paketov (SL) s idealizirovannoi posledovatel'nost'yu sloev Te-Bi-Te-Mn-Te-Bi-Te, a takzhe ego soedineniya - gomologi MnBi₄Te₇, MnBi₆Te₁₀ i t. d.
Potentsial'noe prakticheskoe primenenie MnBi₂Te₄ ogranicheno nalichiem tol'ko nebol'shikh kristallov iz-za preparativnykh problem, svyazannykh s ikh ogranichennoi termodinamicheskoi stabil'nost'yu [2]. Reshetku MnBi₂Te₄ mozhno stabilizirovat' putem zameshcheniya atomov margantsa na atomy 14 gruppy (Ge, Sn, Pb), chto v predel'nom sluchae zameshcheniya privodit k stabil'nym izostrukturnym soedineniyam, takim kak GeBi₂Te₄, SnBi₂Te₄, PbBi₂Te₄, kotorye, v svoyu ochered', takzhe predstavlyayut soboi TI [3–5].
V doklade predstavleny rezul'taty izucheniya elektronnoi i atomnoi struktury topologicheskikh izolyatorov na osnove MnBi₂Te₄ s primeneniem kompleksa eksperimental'nykh i teoreticheskikh metodov, takikh kak fotoelektronnaya spektroskopiya, skaniruyushchaya tunnel'naya mikroskopiya, teoriya funktsionala elektronnoi plotnosti i dr.
Rabota vypolnena pri podderzhke RNF 22-72-10074.

1. Otrokov M.M. et al. Nature. 2019. 576, 416–422.
2. Zeugner A. et al. Chem Mater. 2019. 31, 2795–2806.
3. Okamoto K. et al. Phys Rev B. 2012. 86, 195304.
4. Fragkos S. et al. Phys Rev Mater. 2021. 5, 014203.
5. Kuroda K. et al. Phys Rev Lett. 2011. 108, 206803.

Video

Chromosomes are exceedingly long topologically-constrained polymers compacted in a cell nucleus. We recently suggested that chromosomes are organized into loops by an active process of loop extrusion. Yet loops remain elusive to direct observations in living cells; detection and characterization of myriads of such loops is a major challenge. The lack of a tractable physical model of a polymer folded into loops limits our ability to interpret experimental data and detect loops. Here, we introduce a new physical model – a polymer folded into a sequence of loops, and solve it analytically. Our model shows how loops affect statistics of contacts in a polymer across different scales, explaining universally observed shapes of the contact probability. Moreover we analyze how folding into loops affects topological properties of crumpled polymers.

My izuchaem elektron-fononnuyu relaksatsiyu v modeli granulirovannoi metallicheskoi plenki, gde zerna obrazovany regulyarno raspolozhennymi potentsial'nymi bar'erami proizvol'noi prozrachnosti. Rasschitana skorost' relaksatsii akusticheskikh fononov v modeli Debaya s uchetom dvukh mekhanizmov elektron-fononnogo rasseyaniya: standartnogo vzaimodeistviya deformatsii reshetki s elektronnoi plotnost'yu i vzaimodeistviya za schet smeshcheniya granits zeren, vyzvannogo kolebaniyami reshetki. Pri samykh nizkikh temperaturakh moshchnost' elektronno-fononnogo okhlazhdeniya sootvetstvuet stepennoi zavisimosti po temperature, tipichnoi dlya chistykh sistem, no s koeffitsientom, rastushchim po mere umen'sheniya prozrachnosti granits zeren.

https://arxiv.org/abs/2306.15495

Ispol'zuya teoriyu sluchainykh matrits, my daem statisticheskoe opisanie statsionarnoi intensivnosti polya vnutri khaoticheskoi polosti, pitaemoi padayushchimi volnami cherez konechnoe chislo otkrytykh kanalov, predpolagaya, chto invariantnost' otnositel'no obrashcheniya vremeni vnutri polosti polnost'yu narushena. V chastnosti, pokazano, chto pri otsutstvii vnutrennikh poter' plotnost' veroyatnosti dlya odnotochechnoi intensivnosti zatukhaet po stepennomu zakonu dlya bol'shikh intensivnostei. Takoe povedenie rezko otlichaetsya ot zakona Releya (eksponentsial'noe zatukhanie), kotoryi okazyvaetsya spravedlivym tol'ko v predele beskonechnogo chisla kanalov. Takzhe byla naidena sovmestnaya plotnost' veroyatnosti intensivnostei v L > 1 tochkakh nablyudeniya, a zatem izvlechena sootvetstvuyushchaya statistika dlya minimal'noi i maksimal'noi intensivnosti po ansamblyu vybrannykh tochek. Pri L → ∞ rezul'tiruyushchaya statistika predel'nykh ekstremal'nykh znachenii okazyvaetsya sil'no otlichayushcheisya ot klassicheskikh raspredelenii ekstremal'nykh znachenii.

We develop an analytical approach to the study of one-dimensional free fermions subject to random projective measurements of local site occupation numbers, based on the Keldysh path-integral formalism and replica trick. In the limit of rare measurements, \gamma / J << 1 (where \gamma is measurement rate per site and J is hopping constant in the tight-binding model), we derive a non-linear sigma model (NLSM) as an effective field theory of the problem. Its replica-symmetric sector is described by a U(2) / U(1) x U(1) ~ S2 sigma model with diffusive behavior, and the replica-asymmetric sector is a two-dimensional NLSM defined on SU(R) manifold with the replica limit R -> 1. On the Gaussian level, valid in the limit \gamma / J -> 0, this model predicts a logarithmic behavior for the second cumulant of number of particles in a subsystem and for the entanglement entropy. However, the one-loop renormalization group analysis allows us to demonstrate that this logarithmic growth saturates at a finite value ~(J / \gamma)^2 even for rare measurements, which corresponds to the area-law phase. This implies the absence of a measurement-induced entanglement phase transition for free fermions. The crossover between logarithmic growth and saturation, however, happens at exponentially large scale, ln(l_corr) ~ J / \gamma. This makes this crossover very sharp as a function of the measurement frequency \gamma/J, which can be easily confused with a transition from the logarithmic to area law in finite-size numerical calculations. We have performed a careful numerical analysis, which supports our analytical predictions.

https://arxiv.org/abs/2304.03138

After a decade of many claims to the opposite, there now is a growing consensus that generic disordered quantum wires, e.g. the XXZ-Heisenberg chain, do not exhibit many-body localization (MBL) - at least not in a strict sense within a reasonable window of disorder values W. Specifically, computational studies of short wires exhibit an extremely slow but unmistakable flow of physical observables with increasing time and system size ("creep") that is consistently directed away from (strict) localization. Our work sheds fresh light on delocalization physics: Strong sample-to-sample fluctuations indicate the absence of a generic time scale, i.e. of a naive "clock rate"; however, the concept of an "internal clock" survives, at least in an ensemble sense. Specifically, we investigate the relaxation of the imbalance I(t) and its temporal fluctuations F(t), the entanglement and Renyi entropies, Se(t) and S2(t), in a 1D system of interacting disordered fermions. We observe that adopting Se(t), S2(t) as a measure for the internal time per sample reduces the sample-to-sample fluctuations but does not eliminate them. However, a (nearly) perfect collapse of the average and for different W is obtained when plotted against or , indicating that the average entropy appropriately models the ensemble-averaged internal clock. We take the tendency for faster-than-logarithmic growth of together with smooth dependency on W of all our observables within the entire simulation window as support for the cross-over scenario, discouraging an MBL transition within the traditional parametric window of computational studies.

https://arxiv.org/abs/2302.11384

Teoreticheski izucheny ostsillyatsii de Gaaza-van Al'fena v izolyatorakh. Izolyatory v nashei rabote opisyvayutsya model'yu, v kotoroi energeticheskaya shchel' obrazuetsya v rezul'tate gibridizatsii energeticheskikh urovnei v tochke ikh peresecheniya za schet vzaimodeistviya mezhdu fermionami. Izuchen mekhanizm, pri kotorom energeticheskaya shchel', vychislennaya samosoglasovannym obrazom, stanovitsya periodicheskoi funktsiei obratnogo magnitnogo polya. Eto i privodit k ostsillyatsiyam de Gaaza-van Al'fena v nashem sluchae. Amplituda eksponentsial'no podavlena v meru energeticheskoi shcheli i magnitnogo polya. Takzhe pokazano, chto amplituda takikh ostsillyatsii sama est' periodicheskaya funktsiya obratnoi temperatury s periodom, opredelyaemym kombinatsiei iz energeticheskoi shcheli i magnitnogo polya.
arXiv:2302.13923

Nelineinyi transport i opticheskie yavleniya v dvumernykh elektronnykh sistemakh nakhodyatsya v tsentre vnimaniya sovremennykh issledovanii v oblasti fiziki kondensirovannogo sostoyaniya. Osobennyi interes vyzyvayut effekty vtorogo poryadka, takie kak, generatsiya postoyannogo elektricheskogo toka i toka na udvoennoi chastote peremennym elektricheskim polem padayushchego na obrazets izlucheniya. Takie effekty voznikayut pri otsutstvii prostranstvennoi inversii v obraztse, kotoroe mozhet byt' svyazano s kristallicheskoi reshetkoi, volnovym vektorom padayushchego fotona, nalichiem p-n perekhoda ili asimmetrichnogo elektrostaticheskogo potentsiala. Spektroskopiya nelineinykh tokov, takim obrazom, chuvstvitel'na k strukturnym neodnorodnostyam, simmetrii kristallicheskoi reshetki, upakovke i «zakruchennosti» dvumernykh kristallicheskikh sloev. V obraztsakh malogo razmera prostranstvennaya simmetriya estestvennym obrazom narushaetsya na krayakh, chto privodit k dopolnitel'nym, kraevym, vkladam v nelineinye effekty. Sootvetstvuyushchie fotogal'vanicheskie toki tekut vdol' kraev obraztsa, pri etom ikh velichina i napravlenie kontroliruyutsya polyarizatsiei elektromagnitnogo polya.

V doklade budut predstavleny rezul'taty teoreticheskikh i eksperimental'nykh issledovanii kraevykh fototokov, voznikayushchikh pri osveshchenii kraya dvumernoi sistemy peremennym elektricheskim polem. Budut rassmotreny razlichnye mekhanizmy generatsii kraevykh tokov. V chastnosti, v provodyashchikh dvumernykh sistemakh (naprimer, legirovannom grafene) kraevoi tok voznikaet za schet vypryamleniya «ob'emnogo» peremennogo toka kraem. S uvelicheniem chastoty vklyuchayutsya mezhzonnye opticheskie perekhody, kotorye privodyat k generatsii neravnovesnykh elektronov i dyrok – v svoyu ochered', neravnovesnye nositeli, rasseivayas' na krayu, sozdayut postoyannyi tok. Budet prodemonstrirovan mikroskopicheskii metod rascheta kraevykh tokov, osnovannyi na reshenii kineticheskogo uravneniya. Pomimo postoyannogo toka peremennoe pole volny sozdaet kraevoi tok na udvoennoi chastote – proiskhodit generatsiya vtoroi garmoniki na krayu dvumernoi sistemy. Kraevoi tok na udvoennoi chastote napravlen v obshchem sluchae pod uglom k krayu, i ego napravlenie opredelyaetsya polyarizatsiei padayushchego izlucheniya. V doklade budet predstavlena teoriya kraevogo effekta generatsii vtoroi garmoniki, kotoraya predskazyvaet, naprimer, prostranstvennye ostsillyatsii toka, svyazannye s vozbuzhdeniem kraevykh plazmonov.

Teoreticheski izucheny ostsillyatsii de Gaaza-van Al'fena v izolyatorakh. Izolyatory v nashei rabote opisyvayutsya model'yu, v kotoroi energeticheskaya shchel' obrazuetsya v rezul'tate gibridizatsii energeticheskikh urovnei v tochke ikh peresecheniya za schet vzaimodeistviya mezhdu fermionami. Izuchen mekhanizm, pri kotorom energeticheskaya shchel', vychislennaya samosoglasovannym obrazom, stanovitsya periodicheskoi funktsiei obratnogo magnitnogo polya. Eto i privodit k ostsillyatsiyam de Gaaza-van Al'fena v nashem sluchae. Amplituda eksponentsial'no podavlena v meru energeticheskoi shcheli i magnitnogo polya. Takzhe pokazano, chto amplituda takikh ostsillyatsii sama est' periodicheskaya funktsiya obratnoi temperatury s periodom, opredelyaemym kombinatsiei iz energeticheskoi shcheli i magnitnogo polya.

Pokazano, chto v energii ferromagnitnoi (FM) plenki, nakhodyashcheisya na paramagnitnoi (PM) (FM vyshe temperatury Kyuri) ili sverkhprovodyashchei (SP) (londonskii predel) podlozhke, poyavlyaetsya chlen, imeyushchii vid poverkhnostnoi energii Dzyaloshinskogo-Morii (DM). Etot chlen imeet magnitostaticheskoe proiskhozhdenie: neodnorodnoe raspredelenie namagnichennosti v FM plenke indutsiruet namagnichennost' ili sverkhprovodyashchii tok v PM i SP podlozhke, sootvetstvenno, kotorye vliyayut na namagnichennost' plenki posredstvom sobstvennykh polei rasseyaniya. Pokazano, chto effektivnoe vzaimodeistvie DM privodit k (1) stabilizatsii kiral'nykh magnitnykh tekstur, takikh kak magnitnyi skirmion, v sisteme FM/PM; (2) nevzaimnomu rasprostraneniyu spinovykh voln v FM/PM i FM/SP. Sil'naya temperaturnaya chuvstvitel'nost' effektivnoi postoyannoi DM vblizi kriticheskoi temperatury PM ili SP pozvolyaet nastraivat' velichinu vzaimodeistviya mezhdu plenkoi i podlozhkoi.

M. A. Kuznetsov, K. R. Mukhamatchin, and A. A. Fraerman, Effective interfacial Dzyaloshinskii-Moriya interaction and skyrmion stabilization in ferromagnet/paramagnet and ferromagnet/superconductor hybrid systems, arXiv:2212.07315 (2022).

Issledovana parametricheskaya statistika v modeli Rozentsveiga-Portera, gamil'tonian kotoroi yavlyaetsya summoi gaussovoi i diagonal'noi sluchainykh matrits. S pomoshch'yu nelineinoi supersimmetrichnoi sigma modeli polucheno analiticheskoe vyrazhenie dlya parnykh korrelyatsionnykh funktsii global'noi i lokal'noi plotnosti sostoyanii vo fraktal'noi faze v sluchae diagonal'nogo izmeneniya gamil'toniana dlya unitarnogo ansamblya (klass simmetrii A). Sluchai nediagonal'nogo vozmushcheniya gamil'toniana i ortogonal'noi simmetrii (klass AI) izucheny putem chislennoi diagonalizatsii. Osoboe vnimanie udeleno issledovaniyu povedeniya vospriimchivosti fidelity sobstvennykh funktsii k parametru vozmushcheniya v razlichnykh fazakh (ergodicheskoi, fraktal'noi, lokalizovannoi).

Doklad po rabote E. Burovski, N. Prokof'ev, B. Svistunov, M. Troyer, "The Fermi-Hubbard model at unitarity"

https://arxiv.org/abs/cond-mat/0605350

Problema temperaturnoi zavisimosti sverkhtekuchei zhestkosti \Theta v sil'no neuporyadochennykh sverkhprovodnikakh s psevdoshchel'yu aktual'na dlya poiska sverkhprovodyashchikh superindektivnostei – ustroistv, vostrebovannykh v ryade oblastei sovremennoi kvantovoi tekhniki. Teoreticheskoe opisanie etoi zadachi soderzhit dve slozhnosti: 1) neobkhodimo posledovatel'no opisat' sushchestvenno neodnorodnoe sverkhprovodyashchee sostoyanie, kotoroe, kak izvestno, sushchestvuet v takikh sverkhprovodnikakh [1,2] dazhe na umerennom udalenii ot perekhoda sverkhprovodnik-izolyator, i 2) posle etogo neobkhodimo vychislit' makroskopicheskii elektromagnitnyi otklik poluchayushcheisya neuporyadochennoi sredy, chto samo po sebe yavlyaetsya slozhnoi zadachei. V etom doklade my rassmotrim obe eti problemy i vyvedem analiticheskoe uravnenie, opisyvayushchee temperaturnoe izmenenie sverkhtekuchei zhestkosti. Pri nizkikh temperaturakh eto izmenenie napominaet stepennoi zakon \Theta(T = 0) - \Theta(T) \propto T^{b}, gde pokazatel' stepeni b ~ 2-3 zavisit ot besporyadka. Etot rezul'tat nakhoditsya v kachestvennom soglasii s eksperimental'nymi rezul'tatami, nedavno poluchennymi Thibault Charpentier iz Instituta Neelya.
[1] B. Sacépé, T. Dubouchet, C. Chapelier, M. Sanquer, M. Ovadia, D. Shahar, M.V. Feigel'man and L.B. Ioffe, "Localization of preformed Cooper pairs in disordered superconductors", Nature Physics 7, 3 (2011), pp. 239–244.
[2] A.V. Khvalyuk and M.V. Feigel'man, "Distribution of the order parameter in strongly disordered superconductors: An analytic theory", Phys. Rev. B 104 (2021), pp. 224505.

In a recent paper [Phys. Rev. B 103, 174519 (2021)] it has been theoretically shown that a Néel magnetic skyrmion and a superconducting Pearl vortex can form bound pairs in bilayers of the superconductor and ferromagnetic thin films due to the stray fields. Depending on the parameters of the system, the centers of the skyrmion and the vortex can be located either strictly above each other or at a finite distance of the order of the skyrmion radius. However, the analysis in that paper was limited to the main order of the perturbation theory in the magnetic field of the vortex. The report will present a more detailed study of such bound pairs in systems in which stabilization of the skyrmion is determined by the Dzyaloshinskii–Moriya interaction. Firstly, it will be shown that with an increase in the effective strength of the vortex, a counterintuitive phenomenon occurs: the repulsion between the skyrmion and the vortex is suppressed, and the distance between their centers decreases [JETP Letters, 116(11), 801-807 (2022) / arXiv:2210.08790]. Secondly, for the coaxial skyrmion and vortex, a significant change of the skyrmion is predicted: the chirality can change and/or the radius can increase significantly. In addition, with the same heterostructure parameters, but depending on the initial magnetization distribution in a ferromagnet, up to three different bound pairs of "skyrmion – vortex" can arise, where one skyrmion has negative chirality, and the other two have different radii and positive chirality [arXiv:2212.08351 / submitted to PRL].

Comment on recent paper by I. Horváth and P. Markoš, "Super-universality in Anderson localization", Phys. Rev. Lett. 129, 106601 (2022) [arXiv:2110.11266]
Details can be found in arXiv:2210.10539

Kharakteristiki sverkhprovodyashchikh detektorov odinochnykh fotonov v znachitel'noi stepeni opredelyayutsya skorost'yu obmena energii mezhdu elektronnoi podsistemoi i fononami v dielektricheskoi podlozhke. V rabote provedeno sistematicheskoe eksperimental'noe issledovanie teplovogo kondaktansa granitsy mezhdu sverkhprovodyashchim provodom iz NbN i shest'yu tipami dielektricheskikh podlozhkek. Teplovye svoistva granitsy opredeleny putem analiza temperaturnoi zavisimosti toka zakhvata v ramkakh prostoi modeli rezistivnogo sostoyaniya. Izmerennye velichiny teplovogo kondaktansa granitsy v tselom khorosho opisyvayutsya model'yu teploperenosa mezhdu dvumya chernymi telami s raznymi temperaturami: v provode i v podlozhke.

We study the superconducting instability of a two-dimensional disordered Fermi liquid weakly coupled to the soft fluctuations associated with proximity to an Ising-ferromagnetic quantum critical point. We derive interaction-induced corrections to the Usadel equation governing the superconducting gap function, and show that diffusion and localization effects drastically modify the interplay between fermionic incoherence and strong pairing interactions. In particular, we obtain the phase diagram, and demonstrate that: (i) there is an intermediate range of disorder strength where superconductivity is enhanced, eventually followed by a tendency towards the superconductor-insulator transition at stronger disorder; and (ii) diffusive particle-particle modes (so-called `Cooperons') acquire anomalous dynamical scaling z=4, indicating strong non-Fermi liquid behaviour.

We report on experimental study of the effect of disorder on electronic parameters and inelastic scattering mechanisms in ultrathin superconducting NbN films, which are commonly used in single-photon detectors. An increase in disorder in the studied 2.5 nm thick NbN films characterized by Ioffe-Regel parameter from 6.3 to 1.6 is accompanied by a decrease in the critical temperature Tc from 11.5 K to 3.4 K. By measuring magnetoconductance in the range from Tc to ~3Tc, we extract the inelastic scattering rates of electrons, including electron-phonon (e-ph) scattering rates tau_{e-ph}^{-1}. We observe that au_{e-ph}^{-1} and their temperature dependencies are insensitive to disorder that is not described by the existing models of the e-ph scattering in disordered metals and can be due to the presence of weakly disordered metal grains. As the temperature decreases the temperature dependence au_{e-ph}^{-1} changes from T^3 to T^2, which can be result of a decrease in the dimension of the phonons involved in the e-ph scattering. The obtained values of material parameters of ultrathin NbN films can be useful for optimization of performance of NbN-based electronic devices.

Chaos is synonymous to unpredictability. In the case of classical systems this unpredictability is expressed through exponential sensitivity of trajectories to tiny fluctuations of the Hamiltonian or to the initial conditions. It is well known that chaos is closely related to ergodicity or emergence of statistical mechanics at long times, but the precise relations between them are still debated. In quantum systems the situation is even more controversial with trajectories being ill-defined. A standard approach to defining quantum chaos is through emergence of the random matrix theory. However, as I will argue, this approach is rather related to the eigenstate thermalization hypothesis and ergodicity than to chaps. In this talk I will suggest that one can use fidelity susceptibility of equivalently geometric tensor and quantum Fisher information as a definition of chaos, which applies both to quantum and classical systems and which is related to long time tails of the auto-correlation functions of local perturbations. Through this approach we can establish of existence of the intermediate chaotic but non-ergodic regime separating integrable and ergodic phases, which have maximally sensitive eigenstates. I will discuss how this measure is also closely related to recently proposed definition of chaos through the Krylov complexity or the operator growth and that there is very interesting and still unexplained duality between short and long time behavior of chaotic and integrable systems As a specific example of this approach I will apply these ideas to interacting disordered systems and show that (many-body) localization is unstable in thermodynamic limit irrespective of the disorder strength.

My stroim teoriyu dlya velichiny sverkhtekuchei plotnosti v sil'no neuporyadochennykh sverkhprovodnikakh vsled za nedavnimi eksperimentami grupp B. Sasepe i N. Roka iz Instituta Neelya. Osnovnoi rezul'tat sostoit v tom, v sil'no neuporyadochennykh plenkakh s sil'nymi prostranstvennymi fluktuatsiyami parametra poryadka temperaturnaya zavisimost' sverkhtekuchei plotnosti mozhet byt' opisana zavisimost'yu, blizkoi k stepennoi, t.e. \rho_S(T) = \rho_S(0) - a T^b, na umerenno nizkikh temperaturakh T_min < T < T_max. Pri etom, b~2 — zavisyashchii ot sily besporyadka pokazatel' stepeni, a temperaturnye masshtaby opredeleny kak T_min ~ \lambda \Delta, T_max ~ 2 \Delta gde \Delta — tipichnyi parametr poryadka pri T=0, a \lambda — bezrazmernaya postoyannaya kuperovskogo prityazheniya. Pri malykh besporyadkakh temperaturnaya zavisimost' vsekh fizicheskikh velichin imeet BKSh-podobnoe eksponentsial'noe povedenie, kak i dolzhno byt'.

The interplay of Anderson localization and electron-electron interactions is known to lead to enhancement of superconductivity due to multifractality of electron wave functions. We develop the theory of multifractally-enhanced superconducting states in two-dimensional systems in the presence of spin-orbit coupling. Using the Finkel'stein nonlinear sigma model, we derive the modified Usadel and gap equations that take into account renormalizations caused by the interplay of disorder and interactions. Multifractal correlations induce energy dependence of the superconducting spectral gap. We determine the superconducting transition temperature and the superconducting spectral gap in the case of Ising and strong spin orbit couplings. In the latter case the energy dependence of superconducting spectral gap is convex whereas in the former case (as well as in the absence of spin-orbit coupling) it is concave. Multifractality enhances not only the transition temperature but, in the same way, the spectral gap at zero temperature. Also we study mesoscopic fluctuations of the local density of states in the superconducting state. Similarly to the case of normal metal, spin-orbit coupling reduce the amplitude of fluctuations.
Results are reported in E.S. Andriyakhina, I.S. Burmistrov, ZhETF 162, 522 (2022).

My obobshchili klassicheskoe reshenie dlya elektronnoi plotnosti sostoyanii vnutri kora vikhrya v gryaznom predele [1] na sluchai granulirovannogo sverkhprovodnika. Byl vyveden i reshen chislenno diskretnyi analog uravneniya Uzadelya dlya sluchaya s odinochnym vikhrem. Obnaruzhena shchel' v spektre odnoelektronnykh sostoyanii razmerom dokhodyashchaya do poloviny sverkhprovodyashchei shcheli v ob'emnom sverkhprovodnike. Otsutstvie odnochastichnykh sostoyanii na malen'kikh energiyakh ob'yasnyaet sil'noe podavlenie mikrovolnovoi dissipatsii v granulirovannom alyuminii [2].

[1] R. J. Watts-Tobin and G. M. Waterworth, Z. Physik 261, 249 (1973)
[2] B. Plourde, invited talk at the International Workshop ”Localization, Interactions and Superconductivity”, Chernogolovka, Russia, June 30 - July 4, 2018

V doklade poidet rech' ob effektakh, obnaruzhennykh v poslednie gody v dielektricheskikh (!) soedineniyakh perekhodnykh metallov i vyzvannykh nalichiem sushchestvennogo spin-orbital'nogo vzaimodeistviya. Budet obsuzhdat'sya vliyanie dannogo vzaimodeistviya na mott-khabbardovskii perekhod, effekt Yana-Tellera i anizotropiyu obmennogo vzaimodeistviya (no nikakoi topologii i kvantovogo effekta Kholla).

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We develop a theory of anomalous elasticity in disordered two-dimensional flexible materials with orthorhombic crystal symmetry. Similar to the clean case, we predict existence of infinitely many flat phases with anisotropic bending rigidity and Young's modulus showing power-law scaling with momentum controlled by a single universal exponent the very same as in the clean isotropic case. With increase of temperature or disorder these flat phases undergo crumpling transition. Remarkably, in contrast to the isotropic materials where crumpling occurs in all spatial directions simultaneously, the anisotropic materials crumple into tubular phase. In distinction to clean case in which crumpling transition happens at unphysically high temperatures, a disorder-induced tubular crumpled phase can exist even at room-temperature conditions. Our results are applied to anisotropic atomic single layers doped by adatoms or disordered by heavy ions bombarding.

Analiticheski issleduyutsya plazmennye uedinennye volny (solitony) v beskonechnoi dvumernoi elektronnoi sisteme pomeshchennoi mezhdu dvumya ideal'no provodyashchimi elektrodami (zatvorami), parallel'nymi ploskosti 2D elektronnoi sistemy. Dlya opisaniya plazmennykh solitonov reshayutsya uravnenie nepreryvnosti, uravnenie Eilera i uravnenie Puassona, svyazyvayushchie samosoglasovannye plotnost' zaryada, srednyuyu skorost' elektronov i potentsial plazmennoi volny. Ranee plazmennye solitony v takoi sisteme rassmatrivalis' tol'ko v rezhime slaboi nelineinosti, kogda prostranstvennaya neodnorodnost' solitona velika po sravneniyu s rasstoyaniem mezhdu 2D sistemoi i zatvorami, a vozmushchenie kontsentratsii malo po sravneniyu s ravnovesnoi kontsentratsiei elektronov v sisteme. V doklade solitony proanalizirovany s ispol'zovaniem model'nogo podkhoda, v ramkakh kotorogo uravnenie Puassona zamenyaetsya na priblizhennoe uravnenie. Dannyi podkhod pozvolyaet rassmotret' solitony s vozmushcheniem kontsentratsii poryadka ravnovesnoi. Polucheno, chto solitony sushchestvuyut tol'ko esli ikh skorost' lezhit v diapazone ot vp do 2vp, gde vp — skorost' lineinykh plazmonov v dlinnovolnovom predele. Takzhe proanalizirovany ostal'nye parametry solitona — amplituda i velichina prostranstvennoi neodnorodnosti — v zavisimosti ot skorosti. Rezul'taty opublikovany v [PRB 105, L201403 (2022)].

V rabote razvita teoriya anomal'noi uprugosti dlya dvumernykh gibkikh materialov s ortorombicheskoi kristallicheskoi strukturoi i vmorozhennym besporyadkom. Analogichno chistomu sluchayu, my predskazyvaem nalichie beskonechnogo chisla ploskikh faz s anizotropnymi izgibnoi zhestkost'yu i modulem Yunga, kotorye pokazyvayut stepennoi skeiling pri uvelichenii razmerov sistemy, kotoryi kontroliruetsya toi zhe kriticheskoi eksponentoi, chto i v chistom izotropnom sluchae. Pod vozdeistviem temperatury ili besporyadka ploskie fazy razrushayutsya posredstvom perekhoda skomkovaniya (crumpling transition). Primechatel'no, chto v otlichie ot izotropnogo sluchaya, anizotropnye materialy perekhodyat v trubchatuyu fazu, vmesto skomkannoi fazy. Analogichnyi perekhod dlya chistykh materialov proiskhodit pri anomal'no vysokikh temperaturakh, togda kak trubchataya faza, perekhod v kotoruyu vyzvan besporyadkom, mozhet sushchestvovat' v usloviyakh komnatnykh temperatur. Rezul'taty dannoi raboty primenimy k anizotropnym monosloyam, dopirovannym adatomami ili podvergnutym bombardirovkoi tyazhelymi atomami.

Dzhozefsonovskii kontakt s otritsatel'nym kriticheskim tokom Ic<0 (eshche nazyvaemyi pi-kontaktom) – eto khorosho izvestnyi fizicheskii ob'ekt s dolgoi istoriei issledovanii. V doklade budet opisana evolyutsiya idei v etoi oblasti, a takzhe predstavlen novyi mekhanizm vozniknoveniya pi-kontakta v odnomernykh provodyashchikh sistemakh [https://arxiv.org/abs/2202.08039 i Phys. Rev. B 105, L201401 (2022)].

Svoim raznoobraziem mikromagnitnye struktury obyazany konkurentsii nebol'shogo kolichestva faktorov, kak pravilo, trekh: obmennogo vzaimodeistviya, magnitostatiki i magnitnoi anizotropii. S rasshireniem za schet magnitoelektrikov i mul'tiferroikov kruga materialov, v kotorykh rassmatrivayutsya zadachi mikromagnetizma, pomimo klassicheskikh trekh sil poyavlyaetsya novyi faktor - perestraivaemoe elektricheskim polem vzaimodeistvie Dzyaloshinskogo-Morii. Eto vzaimodeistvie lineino po prostranstvennym proizvodnym ot namagnichennosti i obuslavlivaet vozniknovenie kiral'nykh magnitnykh struktur. Magnitoelektricheskie yavleniya v mikromagnetizme budut rassmotreny na primere takikh yavlenii kak dvizhenie domennykh granits pod deistviem elektricheskogo polya, elektroindutsirovannoe zarozhdenie tsilindricheskikh magnitnykh domenov s 180-gradusnymi i 90-gradusnymi stenkami, magnitnykh neodnorodnostei tipa «0-gradusnaya domennaya granitsa», magnitnykh vikhrei i skirmionov.

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Ya kratko rasskazhu o prostoi zadache, kasayushcheisya gibridnykh struktur dvumernogo elektronnogo gaza i sverkhprovodnika v rezhime kvantovogo effekta Kholla. Rech' poidet o sochetanii Andreevskogo otrazheniya i kiral'nogo nelokal'nogo transporta po kraevym kanalam pri faktore zapolneniya 2 (v prenebrezhenii spinovym rasshchepleniem). V takoi strukture mozhno organizovat' interferometr tipa Fabri-Pero s nanoskopicheskim sverkhprovodyashchim kontaktom vnutri. Okazyvaetsya, chto v takoi model'noi zadache potok magnitnogo polya privodit k otnositel'nym ostsillyatsiyam veroyatnostei kross-Andreevskogo i pryamogo prokhozhdeniya kvazichastits. Po suti, mozhno govorit' o tonkoi nastroike razdeleniya zaryada i tepla v nelokal'nom otklike pri pomoshchi effekta Aaronova-Boma.

Za poslednee desyatiletie mnogie eksperimenty pokazali, chto v dopirovannom topologicheskom izolyatore Bi2Se3 pri temperature ~ 3K voznikaet sverkhprovodyashchee sostoyanie. Sverkhprovodyashchaya faza imeet S2 vrashchatel'nuyu simmetriyu, v to vremya kak normal'naya faza imeet vrashchatel'nuyu simmetriyu S3. Dannaya sverkhprovodimost' nazyvaetsya nematicheskoi. V doklade budut rasskazany osnovnye eksperimental'nye nablyudeniya po dannoi teme. Dokladchik izlozhit svoi osnovnye rezul'taty. Pokazano, chto geksagonal'nye iskazheniya poverkhnosti Fermi mogut sdelat' nematicheskii sverkhprovodyashchii parametr poryadka osnovnym sostoyaniem. Izuchen otklik nematicheskogo sverkhprovodnika na zeemanovskoe pole. Pokazano, chto kuperovskie pary dayut nebol'shoi paramagnitnyi vklad v otklik sistemy. Vychislen vklad poverkhnostnykh i ob'emnykh sostoyanii v kvazichastichnuyu interferentsiyu na poverkhnosti nematicheskogo sverkhprovodnika. Tak zhe budet rasskazano o vozmozhnosti upravlyat' napravleniem nematichnosti s pomoshch'yu zeemanovskogo polya.

Scaling of various local observables with a system size at Anderson transition criticality is characterized by a generalized multifractality. We study the generalized multifractality in the spin quantum Hall symmetry class (class C) in the presence of interaction. We employ Finkel'stein nonlinear sigma model and construct the pure scaling derivativeless operators for class C. Within two-loop renormalization group analysis we compute the anomalous dimensions of these pure scaling operators and demonstrate that they are affected by the interaction. We find that the interaction breaks exact symmetry relations between generalized multifractal exponents known for a noninteracting problem.

Rassmotren protsess vozbuzhdeniya sil'nogo kvazistaticheskogo magnitnogo polya pri vzaimodeistvii tsirkulyarno polyarizovannoi volny vysokoi intensivnosti (10^23 Vt/sm^2 i vyshe) s plazmennym sloem. Pokazano, chto v besstolknovitel'nom rezhime vzaimodeistviya prodol'noe magnitnoe pole voznikaet za schet sily radiatsionnogo treniya. Eta spetsificheskaya realizatsiya obratnogo effekta Faradeya mozhet byt' ispol'zovana dlya poiska makroskopicheskikh proyavlenii radiatsionnogo treniya v eksperimentakh, provedenie kotorykh planiruetsya na sverkhmoshchnykh lazernykh ustanovkakh.

In the late 19th century, Louis Pasteur discovered that biology shows a preference for molecules with a specific handedness. Ever since, researchers have been trying to understand the origin of life’s homochirality and its implications. For example, electron transport in organisms, an essential part of basic biological processes such as respiration and photosynthesis, is realized via insulating helical molecules. Recent studies further found that the transmission probability of electrons through such molecules is strongly spin-dependent, with the preferred spin direction set by the chirality. This direct connection between spin and chirality raises numerous fundamental questions. It thus opens a new arena of research at the interface between biology and quantum physics. In my talk, I will review the most important experimental findings and describe a theoretical model that explains the origin of spin-dependent transport: The helical geometry induces robust spin filtering accompanied by, and intimately related to, strongly enhanced overall transmission through chiral molecules. In particular, I will focus on spin-selectivity in the chiral system with strong electron-phonon interactions. Finally, I will present some ideas for integrating organic molecules into solid-state devices for various applications.

Video

Frustratsiya v magnitnykh sistemakh - eto situatsiya, kogda ne vse magnitnye vzaimodeistviya mogut byt' minimizirovany klassicheski odnovremenno, i iz-za etogo razlichnye sostoyaniya mogut byt' polnost'yu vyrozhdeny. Takoe vyrozhdenie usilivaet kvantovye popravki i magnon-magnonnoe vzaimodeistvie, kotorye mogut polnost'yu razrushit' uporyadochennoe sostoyanie. Frustratsiya v dannykh sistemakh mozhet byt' vyzvana kak geometriei reshetki, tak i anizotropnymi vzaimodeistviyami. My pokazhem svoistva takikh sistem detal'no na primere predlozhennoi Alekseem Kitaevym modeli anizotropnykh vzaimodeistvii na geksagonal'noi reshetke, kotoraya otkryla put' k tochno reshaemym spinovozhidostnym fazam.

We study the density of states (DoS) ν(E) in a normal-metallic (N) film contacted by a bulk superconductor (S). We assume that the system is diffusive and the SN interface is transparent. In the limit of thin N layer (compared to the coherence length), we analytically find three different types of the DoS peculiarity at energy equal to the bulk superconducting order parameter Δ₀. (i) In the absence of the inverse proximity effect, the peculiarity has the check-mark form with ν(Δ₀)=0 as long as the thickness of the N layer is smaller than a critical value. (ii) When the inverse proximity effect comes into play, the check-mark is immediately elevated so that ν(Δ₀)>0. (iii) Upon further increasing of the inverse proximity effect, ν(E) gradually evolves to the vertical peculiarity (with an infinite-derivative inflection point at E=Δ₀). This crossover is controlled by a materials-matching parameter which depends on the relative degree of disorder in the S and N materials.
arXiv:2205.06171

Weyl semimetal is a solid material with isolated touching points between conduction and valence bands in its Brillouin zone---Weyl points. Low energy excitations near these points exhibit a linear dispersion and act as relativistic massless particles. Weyl points are stable topological objects robust with respect to most perturbations. We study effects of weak disorder on the spectral and transport properties of Weyl semimetals in the limit of low energies. We use a model of Gaussian white-noise potential and apply dimensional regularization scheme near three dimensions to treat divergent terms in the perturbation theory. In the framework of self-consistent Born approximation, we find closed expressions for the average density of states and conductivity. Both quantities are analytic functions in the limit of zero energy. We also include interference terms beyond the self-consistent Born approximation up to the third order in disorder strength. These interference corrections are stronger than the mean-field result and non-analytic as functions of energy. Our main result is the dependence of conductivity on the electron concentration $\sigma = \sigma_0 + A n^{1/3} + (B/\sigma_0) n^{2/3} \ln|n|$ with $A \approx -0.142$ and $B \approx 0.019$.

Skirmiony predstavlyayut soboi topologicheski zashchishchennye spinovye tekstury, kotorye mogut sluzhit' budushchimi elementami spintronnoi pamyati i ustroistv logiki. Poetomu zarozhdenie skirmionov v topologicheskikh sistemakh, takikh kak topologicheskii izolyator/ferromagnetik, yavlyaetsya interesnym voprosom, osobenno tak kak v etikh sistemakh pokazano chto skirmiony dvigayutsya bystree. Ya opishu zarozhdenie skirmionov, vyzvannoe spin-perenosnymi uglovymi momentami, kharakternymi dlya granitsy topologicheskogo izolyatora s ferromagnitnym izolyatorom. Ispol'zuya mikromagnitnoe modelirovanie i energetiku, my opisyvaem svoistva nukleatsii skirmionov na poverkhnosti topologicheskikh izolyatorov, takie kak vremya zarozhdeniya, kriticheskoe elektricheskoe pole i chisla skirmionov [1]. Ya pokazhu chto vremya zarozhdeniya obratno proportsional'no prilozhennomu elektricheskomu polyu, i takzhe opishu zavisimosti kriticheskogo polya nukleatsii ot zatukhaniya Gil'berta i temperatury. Krome togo, ya obsuzhu vliyanie vzaimodeistviya Dzyaloshinskogo-Morii i prodemonstriruyu chto temperaturnaya zavisimost' mozhet byt' ob'yasnena umen'sheniem shcheli magnonnogo vozbuzhdeniya. Vo vtoroi chasti ya opishu topologicheskie solitony v sistemakh s vnutriploskostnoi magnitnoi anizotropiei. Eti solitony nazyvayutsya bimeronami i yavlyayutsya analogami skirmionov (imeyut tot zhe topologicheskii zaryad). Snachala ya opishu ikh stabil'nost', staticheskie i dinamicheskie svoistva v ferromagnetikakh [2]. Zatem ya pereidu k antiferromagnetikam, gde ya pokazhu, chto po analogii so skirmionami eti topologicheskie solitony ne obladayut skirmionnym effektom Kholla, i sredi prochikh interesnykh svoistv demonstriruyut khaotichnoe povedenie pri vozbuzhdenii peremennymi tokami v sistemakh s nizkim zatukhaniem
1. D. Kurebayashi, O.A. Tretiakov, arXiv:2112.12967 (2021).
2. B. Gobel, I. Mertig, O.A. Tretiakov, Phys. Rep. 895, 1 (2021).

Twist-angle engineering of 2D materials has led to the recent discoveries of novel many-body ground states in moiré systems such as correlated insulators, unconventional superconductivity, strange metals, orbital magnetism and topologically nontrivial phases. These systems are clean and tuneable, where all phases can coexist in a single device, which opens up enormous possibilities to address key questions about the nature of correlation induced superconductivity and topology, and allows to create entirely novel quantum phases with enhanced interactions. In this talk we will introduce some of the main concepts underlying these systems, concentrating on magic angle twisted bilayer graphene (MATBG) and show how symmetry-broken states emerge at all integer electron fillings [1]. We further will discuss recent experiments including screened interactions [2], Chern insulators [4], magnetic Josephson junctions [4], quantum criticality [5], re-entrant correlated insulators at high magnetic fields [6] and discuss some of the avenues for novel quantum sensing applications [7].

[1] Nature, 574, 653 (2019).
[2] Nature, 583, 375–378 (2020).
[3] Nature Physics, 17, 710 (2021).
[4] arXiv:2110.01067 (2021).
[5] arXiv:2108.07753 (2021).
[6] arXiv:2201.09260 (2021).
[7] arXiv:2111.08735 (2021).

Generation and detection of spinfull Cooper pairs in conventional superconductors has been intensely pursued by designing increasingly complex magnet-superconductor hybrids. We demonstrate theoretically that magnons with nonzero wavenumbers universally induce a cloud of spinfull triplet Cooper pairs around them in an adjacent conventional superconductor. The resulting composite quasiparticle, termed magnon-cooparon, consists of a spin flip in the magnet screened by a cloud of the spinfull superfluid condensate. Thus, it inherits a large effective mass, which can be measured experimentally. Furthermore, we demonstrate that two magnetic wires deposited on a superconductor serve as a controllable magnonic directional coupler mediated by the nonlocal and composite nature of magnon-cooparons. Our analysis predicts a quasiparticle that enables generation, control, and use of spinfull triplet Cooper pairs in the simplest magnet-superconductor heterostructures.

Vikhri, kotorye poyavlyayutsya v potokakh elektronov, vyzyvayut interes, tak kak yavlyayutsya neoproverzhimym effektom elektronnoi gidrodinamiki. Odnako do sikh po otsutstvovala obshchaya skhema, pozvolyayushchaya svyazat' zavikhrennost', nablyudaemuyu na makrourovne, s mikroskopicheskimi mekhanizmami vzaimodeistviya i rasseyaniya. V nashei rabote my pokazyvaem, chto zavikhrennost' ustoichivym obrazom voznikaet iz-za nelokal'nosti provodimosti \sigma(k), i eto delaet zavikhrennost' svoistvom, kotoroe prisutstvuet v razlichnymi rezhimakh dvizheniya. Pri etom ballisticheskii i gidrodinamicheskii techeniya v realistichnoi geometrii dayut zavikhrennosti, blizkie po absolyutnomu znacheniyu v obeikh rezhimakh. Tem ne menee, ballisticheskie vikhri na neskol'ko poryadkov bolee ustoichivy k prisutstvii protsessov, relaksiruyushchikh impul's, chem gidrodinamicheskie vikhri. Poetomu to, kak legko vikhri gasyatsya besporyadkom i rasseyaniem fononov, mozhet sluzhit' diagnostikoi mikroskopicheskogo proiskhozhdeniya zavikhrennosti v potokakh elektronov.

Ya rasskazhu o trekh nedavnikh rabotakh (arXiv:2112.11250, arXiv:2112.13446 i arXiv:2202.03815), v kotorykh issledovalis' raznye modeli sluchainykh landshaftov v prostranstve vysokoi razmernosti s tsel'yu proyasneniya universal'nykh aspektov yavleniya topologicheskoi trivializatsii.

Poyavivshiisya v poslednyuyu dekadu novyi tip geterostruktur na osnove ZnO/MgZnO pozvolyaet zaglyanut' v fiziku dvumernykh elektronnykh sistem (DES) sushchestvenno dal'she, chem eto bylo vozmozhno v traditsionnykh poluprovodnikakh – kremnii i arsenide galliya. Prichinoi tomu yavlyayutsya sil'nye mezhchastichnye korrelyatsii v sochetanii s malym neodnorodnym ushireniem energeticheskikh urovnei. V etikh dvumernykh sistemakh sravnitel'no legko dostigaetsya parametr Vignera-Zeitsa r_s~5–12. Pri takom nevedomom ranee sochetanii parametrov «ne rabotayut» prezhnie teoreticheskie modeli, desyatiletiyami obkatannye na dvumernom elektronnom gaze. Kachestvennuyu transformatsiyu preterpevayut dazhe «khorosho izuchennye» odnochastichnye yavleniya, takie kak tselochislennyi kvantovyi effekt Kholla (KEKh) – potomu kak vsledstvie kulonovskogo vzaimodeistviya apriori zaputannoi stanovitsya sama sistema urovnei Landau. V prezhnikh magnitotransportnykh issledovaniyakh pokazano, chto samo yavlenie KEKh v geterostrukturakh ZnO ostaetsya, odnako osnovnoe sostoyanie sistemy sil'no modifitsirovano.

V dannoi rabote obnaruzhen ferromagnitnyi perekhod v rezhime tselochislennogo KEKh s chetnymi faktorami zapolneniya v sistemakh na osnove ZnO. Metodami fotolyuminestsentsii i neuprugogo rasseyaniya sveta udalos' okharakterizovat' fazovyi sostav DES, nablyudat' diapazony parametrov sistemy, otvechayushchie ferro- i paramagnitnomu uporyadocheniyu [1]. Postroena fazovaya diagramma dlya sostoyaniya KEKh \nu=2 pri izmenenii parametrov elektronnoi kontsentratsii i ugla naklona magnitnogo polya. Iz fazovoi diagrammy izvlecheny perenormirovannye fermi-zhidkostnye parametry dlya effektivnoi massy i spinovoi vospriimchivosti DES. Pokazano, chto imenno vozrastayushchaya rol' kulonovskikh korrelyatsii pri umen'shenii kontsentratsii DES yavlyaetsya pervoprichinoi dannogo fazovogo prevrashcheniya.

Pomimo fenomenologii ferromagnitnogo perekhoda v nastoyashchei rabote proveden analiz mikroskopicheskogo mekhanizma etogo yavleniya. Metodom neuprugogo rasseyaniya sveta proslezheno povedenie nizkoenergeticheskikh kollektivnykh vozbuzhdenii pri izmenenii kontsentratsii DES i pokazano, chto ferromagnitnyi perekhod nastupaet vsledstvie smyagcheniya tsiklotronnogo spin-flip vozbuzhdeniya (CSFE), i posleduyushchego lavinoobraznogo perekhoda elektronov mezhdu sosednimi urovnyami Landau s protivopolozhnymi spinovymi proektsiyami [2]. Analogichno, v terminakh kollektivnykh spinovykh vozbuzhdenii ob'yasnyaetsya i obratnyi perekhod ferromagnetik-paramagnetik [3]. V oboikh sluchayakh pokazana klyuchevaya rol' nalichiya magnitorotonnogo minimuma v dispersii spinovykh vozbuzhdenii.

Eksperimental'nye dannye po energii vovlechennykh kollektivnykh vozbuzhdenii khorosho soglasuyutsya s raschetom, provedennym metodami tochnoi diagonalizatsii i ekranirovannogo priblizheniya Khartri-Foka [2,3].

[1] A.B.Vankov, B.D.Kaysin, I.V.Kukushkin, Phys.Rev.B 96, 235401 (2017).
[2] A.B.Vankov, B.D.Kaysin, I.V.Kukushkin, Phys.Rev.B 98 121412(R) (2018).
[3] A.B.Vankov, I.V.Kukushkin, Phys.Rev.B 104, 165144 (2021).

V rabote predlozhen sposob vychisleniya anomal'no uporyadochennogo vo vremeni korrelyatora v obobshchenii modeli Sachdeva-Ie-Kitaeva (SYK) s nenulevoi prostranstvennoi razmernost'yu. Nash rezul'tat primenim ne tol'ko na malykh vremenakh, kogda khaotichnye svoistva sistemy razvity slabo, no i na bol'shikh – poryadka vremeni Erenfesta. My pokazali, chto informatsiya o prilozhennom vozmushchenii, kotoruyu opisyvaet dannyi korrelyator, rasprostranyaetsya ballisticheski v vide fronta. Nami vpervye byla vychislena skorost' fronta dlya modelei dannogo tipa.

V ochen' chistykh obraztsakh normal'nykh provodnikov elektrony provodimosti pri nizkikh temperaturakh mogut formirovat' vyazkuyu elektronnuyu zhidkost'. V rabote izuchayutsya vysokochastotnye techeniya takoi zhidkosti v magnitnom pole. Pokazano, chto ee koeffitsienty sdvigovoi vyazkosti imeyut rezonans pri chastote techeniya, blizkoi k udvoennoi tsiklotronnoi chastote elektronov. Takoi rezonans obuslovlen sobstvennoi dinamikoi tenzora vyazkikh napryazhenii elektricheski zaryazhennoi zhidkosti v magnitnom pole i, pri otsutstvii rezonansov na drugikh garmonikakh tsiklotronnoi chastoty, yavlyaetsya priznakom realizatsii gidrodinamicheskogo vysokochastotnogo transporta. Pokazano, chto v ochen' chistykh i dostatochno shirokikh obraztsakh predskazannyi vyazkouprugii rezonans proyavlyaetsya v koeffitsiente zatukhaniya magnitoplazmonov. Izucheny takzhe poperechnye sdvigovye magnitozvukovye volny, kotorye mogut vozbuzhdat'sya v elektronnoi zhidkosti pri dostatochno bol'shoi sile mezhchastichnogo vzaimodeistviya. V ramkakh gidrodinamicheskogo priblizheniya rasschitan ikh zakon dispersii i ikh vklad v lineinyi otklik zhidkosti na radiochastotnoe elektricheskoe pole. Chastota poperechnykh voln v predele malykh volnovykh vektorov ravna udvoennoi tsiklotronnoi chastote. Eto privodit, dlya techenii v dostatochno uzkikh obraztsakh, k proyavleniyu vyazkouprugogo rezonansa za schet komponenty techeniya, sformirovannoi magnitozvukovymi volnami. Dlya mikroskopicheskogo obosnovaniya ispol'zovannogo gidrodinamicheskogo opisaniya bylo pokazano, chto kineticheskoe uravnenie dlya vysokochastotnoi dinamiki kvazichastits elektronnoi fermi-zhidkosti v predele bol'shoi velichiny mezhchastichnogo vzaimodeistviya svoditsya k gidrodinamicheskim uravneniyam Nav'e-Stoksa s perenormirovannymi koeffitsientami. Tsiklotronnaya chastota, vkhodyashchaya v vysokochastotnuyu vyazkost' v etikh uravneniyakh, perenormiruetsya mezhchastichnym vzaimodeistviem i stanovitsya otlichnoi ot neperenormiruemoi "obychnoi" tsiklotronnoi chastoty, opredelyayushchei tsiklotronnyi rezonans. Dany argumenty v pol'zu togo, chto vozbuzhdenie izuchennykh poperechnykh magnitozvukovykh voln ob'yasnyaet anomal'nyi pik v fotosoprotivlenii naibolee kachestvennykh vysokopodvizhnykh kvantovykh yam GaAs, v kotorykh, po-vidimomu, realizuetsya gidrodinamicheskii rezhim elektronnogo transporta.

An open quantum system is continuously "monitored" by its environment, so its dynamics consists of two competing processes: unitary evolution, which generates entanglement and generically leads to chaotic dynamics, and non-unitary operations resulting from measurements and noisy couplings to the environment, that tend to irreversibly destroy quantum information by revealing it. A minimal model that captures these competing processes consists of a quantum circuit made up of random unitary gates interlaced with local projective measurements. Remarkably, this minimal model undergoes a dynamical phase transition as the rate of measurements is increased. In this talk, I will introduce an exact replica statistical mechanics approach to this problem, and show that the transition is described by a CFT with central charge c=0. I will also present numerical results on the spectrum of this theory using a transfer matrix approach that indicate multifractal scaling of correlation functions at the critical point, reflected in a continuous spectrum of scaling dimensions.

We study an array of strongly correlated quantum dots of complex SYK type and account for the effects of quadratic terms added to the SYK Hamiltonian; both local terms and inter-dot tunneling are considered in the non-Fermi-liquid temperature range T≫TFL. Electric σ(ω,p) and thermal κ(ω,p) conductivities are calculated as functions of frequency and momentum, for arbitrary values of the particle-hole asymmetry parameter E. At low-frequencies ω≪T we find the Lorentz ratio L=κ(0,0)/σ(0,0) to be non-universal and temperature-dependent. At ω≫T the conductivity σ(ω,p) contains a pole with nearly linear dispersion ω≈splnωT reminiscent of the "zero-sound", known for Fermi-liquids.

Dvumernye elektronnye sistemy v kvantuyushchem magnitnom pole predstavlyayut isklyuchitel'nyi interes s tochki zreniya vovlecheniya kvazichastits s ne bozevskoi i ne fermievskoi statistikoi (enionnoi), v oblast' prikladnykh fizicheskikh zadach. Drobnye sostoyaniya DKEKh yavlyayutsya edinstvennymi na segodnyashnii den' eksperimental'no realizovannymi kandidatami na rol' sistemy kvazichastits s enionnoi statistikoi. Dlya vyyavleniya statisticheskikh i termodinamicheskikh svoistv enionnykh sistem eksperimental'no sformirovan makroskopicheskii ansambl' neitral'nykh vozbuzhdenii v DKEKh 1/3. Okazalos', chto vozbuzhdeniya imeyut sverkhdlinnye vremena zhizni i proyavlyayut bozevskie svoistva.

(Neobychnoe vremya: 16.00!)

Odnim iz glavnykh kandidatov na rol' vzaimodeistviya, privodyashchego k sverkhprovodimosti v pniktidakh i khal'kogenidakh zheleza vystupayut spinovye fluktuatsii. Oni privodyat k vozniknoveniyu sverkhprovodyashchego parametra poryadka s±-tipa. Dannoe neobychnoe sverkhprovodyashchee sostoyanie obladaet odnim zamechatel'nym svoistvom: ono mozhet pereiti v s++-sostoyanie pri uvelichenii nemagnitnogo besporyadka. Obnaruzhenie takogo perekhoda podtverdit sushchestvovanie s±-sostoyaniya v chistykh sverkhprovodnikakh na osnove zheleza i, sootvetstvenno, podtverdit spin-fluktuatsionnyi mekhanizm sverkhprovodimosti. V dannoi rabote issledovana temperaturnaya zavisimost' londonovskoi glubiny proniknoveniya v ramkakh podkhoda Eliashberga dlya dvukhzonnoi modeli s++- i s±-sverkhprovodnikov s nemagnitnymi primesyami i opredelen nabor kharakternykh osobennostei, ukazyvayushchikh na nalichie perekhoda s±→s++, a takzhe provedeno kriticheskoe sravnenie s imeyushchimisya eksperimental'nymi dannymi.

We study an array of strongly correlated quantum dots of complex SYK type and account for the effects of quadratic terms added to the SYK Hamiltonian; both local terms and inter-dot tunneling are considered in the non-Fermi-liquid temperature range T >> T_FL Electric σ(ω, p) and thermal κ(ω, p) conductivities are calculated as functions of frequency and momentum, for arbitrary values of the particle-hole asymmetry parameter. At low frequencies ω << T we find the Lorentz ratio L = κ(0, 0)/σ(0, 0) to be non-universal and temperature-dependent. At ω >> T the conductivity σ(ω, p) contains a pole with nearly linear dispersion ω ≈ sp ln (ω/T) reminiscent of the "zero-sound", known for Fermi-liquids.

We propose a superconducting quantum circuit based on a general symmetry principle—combinatorial gauge symmetry—designed to emulate topologically ordered quantum liquids and serve as a foundation for the construction of topological qubits. The proposed circuit exhibits rich features: in the classical limit of large capacitances its ground state consists of two superimposed loop structures; one is a crystal of small loops containing disordered U(1) degrees of freedom, and the other is a gas of loops of all sizes associated with Z2 topological order. We show that these classical results carry over to the quantum case, where phase fluctuations arise from the presence of finite capacitances, yielding Z2 quantum topological order. A key feature of the exact gauge symmetry is that amplitudes connecting different Z2 loop states arise from paths having zero classical energy cost. As a result, these amplitudes are controlled by dimensional confinement rather than tunneling through energy barriers. We argue that this effect may lead to larger energy gaps than previous proposals that are limited by such barriers, potentially making it more likely for a topological phase to be experimentally observable. Finally, we discuss how our superconducting circuit realization of combinatorial gauge symmetry can be implemented in practice.

PRX QUANTUM 2, 030341 (2021)

(Neobychnoe vremya: 16.00! Translyatsiya: Zoom)

Majorana zero modes are a much sought-after consequence of one-dimensional topological superconductivity. Here we show that, in turn, zero modes accompanying dynamical instanton events strongly enhance - in some cases even enable - superconductivity. We find that the dynamics of a one-dimensional topological triplet superconductor is governed by a theta-term in the action. For isotropic triplets, this term enables algebraic charge-2e superconductivity, which is destroyed by fluctuations in non-topological superconductors. For anisotropic triplets, zero modes suppress quantum phase slips and stabilize superconductivity over a large region of the phase diagram. We present predictions of correlation functions and thermodynamics for states of topologically enhanced superconductivity.

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Vychislen srednii dzhozefsonovskii tok I_c*\sin\phi cherez izolyator Andersona bol'shoi tolshchiny (mnogo bol'she dliny lokalizatsii \xi). Pokazano, chto amplituda toka ubyvaet priblizitel'no eksponentsial'no s tolshchinoi bar'era, odnako effektivnaya dlina ubyvaniya vo mnogo raz prevyshaet dlinu lokalizatsii elektronnykh sostoyanii v izolyatore. Tem samym, ob'yasnen davno izvestnyi eksperimental'nyi rezul'tat, izvestnyi pod nazvaniem "long range Josephson effect". Razvitaya teoriya pokazyvaet chto kachestvenno etot effekt svyazan s a) sil'nymi fluktuatsiyami volnovykh funktsii lokalizovannykh sostoyanii, i b) mottovskimi rezonansami na parakh lokalizovannykh sostoyanii. Pokazano, chto pri tolshchine izolyatora L bol'she "mottovskoi dliny" L_M = \xi \ln(\delta_\xi/\Delta) izmenyaetsya znak amplitudy toka I_c, to est' realizuetsya sverkhprovodyashchii "pi-kontakt".

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I will start this talk with an overview of recent work on quantum dynamics in many body systems far from equilibrium. This work has led to an understanding from the perspective of quantum information, of how a such systems may approach an equilibrium state at long times, in which initial conditions are effectively forgotten. It has also led to an appreciation that there are classes of system in which an equilibrium state is not reached at long times. One of these classes is made up of many-body localised systems, in which randomness in the Hamiltonian is responsible for a long-lived memory of the initial state of a system. By varying the strength of randomness, a transition can be induced between localised and ergodic phases, which seems very different from conventional symmetry-breaking phase transitions.
In the second part of the talk I will discuss minimal models for quantum chaos and many-body localisation. The models are Floquet quantum circuits for lattice spin systems, in which time evolution is generated by unitary gates that couple neighbouring sites. In particular, I will examine the circumstances in which a version of the so-called diagonal approximation (originally developed for the semiclassical limit in low-dimensional chaotic systems) can be applied to these systems. Within this framework I will show that the many-body delocalisation transition can be seen as a form of symmetry breaking transition, having many of the features generally associated with conventional phase transitions in classical statistical mechanical models.

Joint work with Sam Garratt: Phys. Rev. X 11, 021051 (2021) and Phys. Rev. Lett. 127, 026802 (2021)

(Neobychnoe vremya: 11.00! Translyatsiya: Zoom)

A limit shape phenomenon in statistical mechanics is the appearance of a most probable macroscopic state. This state is usually characterized by a well-defined boundary separating frozen and liquid spatial regions. The earliest studies related to this phenomenon in the context of crystal shapes are in works by Pokrovsky and Talapov [1]. We will review a few examples of the models leading to the appearance of limit shapes. Then we consider a class of topological phase transitions in the limit shape problem of statistical mechanics. The problem considered is generally known as the Arctic circle problem. The considered transition can be visualized as the merging of two melted regions (Arctic circles). We establish the mapping, which identifies the transition as the transition known in lattice QCD and random matrix problems [2,3]. The transition is a continuous phase transition of the third order. We identify universal features of the limiting shape close to the transition using the hydrodynamic description.
[1] V. L. Pokrovsky and A. L. Talapov, Phys. Rev. Lett. 42, 65 (1979). "Ground State, Spectrum, and Phase Diagram of Two-Dimensional Incommensurate Crystals."
[2] D. J. Gross and E. Witten, Phys. Rev. D, 21 (2): 446, (1980). "Possible third-order phase transition in the large-n lattice gauge theory"; S. R. Wadia, Phys. Lett. B 93, 403 (1980). "$N=\infty$ phase transition in a class of exactly soluble model lattice gauge theories."
[3] M. R. Douglas and V. A. Kazakov. Phys. Lett. B, 319 (1-3): 219–230, 1993. "Large n phase transition in continuum QCD2."

Video

(Neobychnoe vremya: 11.30! Translyatsiya: Zoom)

In the first part, I will briefly summarize our current understanding of the relation between Anderson localization on random regular graphs and many-body localization (MBL) [1]. In the second part, I will review several recent preprints, which question observability of genuine MBL transition in state-of-the-art numerical simulations [2,3,4].

[1] Tikhonov, Mirlin; Annals of Physics, 168525
[2] Morningstar, Colmenarez, Khemani, Luitz, Huse; arXiv:2107.05642
[3] Sels; arXiv:2108.10796
[4] Sierant, Zakrzewski; arXiv:2109.13608

(Ceminar v normal'nom rezhime, s translyatsiei: Zoom)

V samoe poslednee vremya nablyudaetsya interes k nelokal'nomu kvazichastichnomu otkliku v strukturakh s maioranovskimi nanoprovolokami [1]. Predpolagaetsya, chto issledovanie nelokal'noi provodimosti pomozhet prolit' svet na proiskhozhdenie podshchelevogo transporta i nadezhno ustanovit' tochku topologicheskogo fazovogo perekhoda. Ya rasskazhu ob eksperimente [2], postavlennom v trivial'noi faze i demonstriruyushchem vtorichnost' nelokal'noi provodimosti po sravneniyu s nelokal'nym teplovym otklikom. V osnove eksperimenta lezhit sochetanie nelokal'nogo transporta s nelokal'nym shumovym otklikom, pozvolivshee prodemonstrirovat' effektivnoe razdelenie tepla i zaryada na sverkhprovodyashchem kontakte. V rezul'tate takogo razdeleniya srednii zaryad proshedshei kvazichastitsy okazyvaetsya blizok k nulyu, tak chto nelokal'nyi kvazichastichnyi transport yavlyaetsya zaryadovo-neitral'nym. Krome togo, nablyudenie predskazannogo nedavno Andreevskogo vypryamleniya [3] demonstriruet, chto etot effekt ne yavlyaetsya unikal'nym svoistvom topolicheskogo fazovogo perekhoda.

[1] D. Puglia et al., Phys. Rev. B 103, 235201 (2021) https://journals.aps.org/prb/abstract/10.1103/PhysRevB.103.235201

[2] A.O. Denisov et al., Semicond. Sci. Tech., 36, 09LT04 (2021) https://iopscience.iop.org/article/10.1088/1361-6641/ac187b/meta

[3] T.Ö. Rosdahl et al., Phys. Rev. B 97, 045421 (2018) https://journals.aps.org/prb/abstract/10.1103/PhysRevB.97.045421

A mechanism of electron-mediated pumping of heat in the absence of net charge transfer is proposed. It may be realized in charge-neutral electron systems, such as graphene, coupled to an external electric potential. The flow of heat in this pumping cycle is not accompanied by a buildup of voltage along the system, which offers advantages over traditional thermoelectric cooling setups. Efficiency of heat pumping and magnitude of heat flux are studied in the hydrodynamic regime for weak disorder. In a pristine system, even for an infinitesimal pumping potential the heat flux remains finite. In particular, for a potential in the form of a traveling wave moving with velocity c the pumping is perfect; the entire heat content of the electron liquid is advected with velocity c. For a general pumping cycle the heat flux is determined by the cycle geometry and disorder strength.

The Riemann Hypothesis concerns the positions of the zeros of the Riemann zeta-function. It has been one of the central unsolved problems in mathematics for over 150 years. Surprisingly, there appear to be deep connections between the theory of the Riemann zeta-function and quantum physics, and these have stimulated close collaborations between the two areas. In particular, analogies with quantum chaos and random matrix theory have been the focus of considerable attention. In this colloquium I will review some of these ideas and their implications.

Video

We develop the theory of anomalous elasticity in two-dimensional flexible materials with orthorhombic crystal symmetry. We show that in the universal region, where characteristic length scales are larger than the rather small Ginzburg scale ~10 nm, these materials possess flat phases with anisotropic bending rigidity and Young's modulus. Remarkably, the problem has continuous hidden symmetry, which leads to formation of the line of fixed points. We demonstrate that due to this symmetry the power law scaling with momentum is controlled by the single universal exponent (the same along the whole line). We demonstrate that these anisotropic flat phases are uniquely labeled by the ratio of absolute Poisson's ratios. We apply our theory to monolayer black phosphorus (phosphorene).

We consider a planar SIS-type Josephson junction between diffusive superconductors (S) through an insulating tunnel interface (I). We construct fully self-consistent perturbation theory with respect to the interface conductance. As a result, we find correction to the first Josephson harmonic and calculate the second Josephson harmonic. At arbitrary temperatures, we correct previous results for the nonsinusoidal current-phase relation in Josephson tunnel junctions, which were obtained with the help of conjectured form of solution. Our perturbation theory also describes the difference between the phases of the order parameter and of the anomalous Green functions. The talk is based on the paper [1].

[1] A.S. Osin and Ya.V. Fominov, arXiv:2105.05786

Video

The multifractality provides a way of ergodicity breaking in term of chaotization and equipartitioning over degrees of freedom. On the other hand, in quantum information theory it is the entanglement entropy which represents the main measure of ergodicity and thermalization. In this talk I will represent an exact relation between the above measures, showing that the fractal dimension of the non-ergodic wave function puts an upper bound on its entanglement entropy [A]. I will also provide a couple of explicit examples demonstrating that the entanglement entropy may reach its ergodic (Page) value when the wave function is still highly non-ergodic and occupies a zero fraction of the total Hilbert space. If time permits I will briefly discuss some other possible deviations from ergodicity relevant for the chaotic many-body systems [B-E].

[A] G. De Tomasi, I. M. K., “Multifractality meets entanglement: relation for non-ergodic extended states”, Phys. Rev. Lett. 124, 200602 (2020) [arXiv:2001.03173]
[B] I. M. K., M. Haque, and P. McClarty, “Eigenstate Thermalization, Random Matrix Theory and Behemoths”, Phys. Rev. Lett. 122, 070601 (2019) [arXiv:1806.09631].
[C] M. Haque, P. A. McClarty, I. M. K. , “Entanglement of mid-spectrum eigenstates of chaotic many-body systems—deviation from random ensembles.” [arXiv:2008.12782].
[D] A. Bäcker, I. M. K., M. Haque,, “Multifractal dimensions for chaotic quantum maps and many-body systems”, Phys. Rev. E 100, 032117 (2019) [arxiv:1905.03099].
[E] G. De Tomasi, I. M. K. , "Ergodic Entanglement of many-body multifractal states in quadratic Hamiltonians", in preparation

Video

Superconductor-ferromagnet heterostructures hosting vortices and skyrmions are new area of an interplay between superconductivity and magnetism. We study [1] an interaction of a Neel-type skyrmion and a Pearl vortex in thin heterostructures due to stray fields. Surprisingly, we find that it can be energetically favorable for the Pearl vortex to be situated at some nonzero distance from the center of the Neel-type skyrmion. The presence of a vortex-antivortex pair is found to result in increase of the skyrmion radius. Our theory predicts that a spontaneous generation of a vortex-anti-vortex pair is possible under some conditions in the presence of a Neel-type skyrmion that is in agreement with recent experiment [2].
[1] E.S. Andriyakhina. and I.S. Burmistrov “Interaction of a Néel–type skyrmion and a superconducting vortex” // arXiv: https://arxiv.org/abs/2102.05434.
[2] A.P. Petrović et al. “Skyrmion-(Anti)vortex coupling in a chiral magnet-superconductor heterostructure” // Phys.Rev. Lett.126, 117205 (2021).

Video

We investigate the structure of the quasiparticle states localized in a superconducting vortex core in the vicinity of a planar defect. It is shown that even a highly transparent defect leads to a significant modification of the excitation spectrum, with the opening of a minigap at the Fermi energy. The magnitude of the minigap exceeds the mean level spacing for a clean vortex already for small values of the reflection coefficient off the defect. It is maximal for the vortex sitting right at the defect, decreases with increasing the distance from the defect and closes at some point. We then generalize the problem for various configurations of several linear defects (periodic structures, two crossing lines, stars). Though the minigap remains, a strong commensurability effect is observed. For two crossing linear defects, the magnitude of the minigap strongly depends on how close the intersection angle is to a rational number.

Video

(Ceminar v normal'nom rezhime, s translyatsiei: Zoom)

We consider a planar SIS-type Josephson junction between diffusive superconductors (S) through an insulating tunnel interface (I). We construct fully self-consistent perturbation theory with respect to the interface conductance. As a result, we find correction to the first Josephson harmonic and calculate the second Josephson harmonic. At arbitrary temperatures, we correct previous results for the nonsinusoidal current-phase relation in Josephson tunnel junctions, which were obtained with the help of conjectured form of solution. Our perturbation theory also describes the difference between the phases of the order parameter and of the anomalous Green functions.

[1] A.S. Osin and Ya.V. Fominov, arXiv:2105.05786

Recently, the standard picture of ALT in long-range systems [1, 2] has been argued from the following perspective. There have been reported [3-6] several counterintuitive examples of single-particle systems with long-range hopping, where almost all states are (at least power-law) localized even in a nominally ergodic regime, where the standard locator expansion breaks down [1, 2]. Some of these "new" models demonstrate critical behavior [3, 4] for disorder strengths below the ones at the ALT [1, 2]. In the other ones [6, 7] wave-function spatial decay rates obey a "mysterious" duality [6] mapping different powers of power-law bending [2]. The seminal paper on second-type models [7] has been unnoticed until recently.
What is the striking difference between the standard long-range models [1-2] and the new ones [3-8]? The systems [3-8] belong to a new universality class where correlations of hopping terms play a significant role in the localization properties. In my talk I address this intriguing question. I present a general approach applicable to all such models and uncover the role of correlations and the origin of the duality [A]. This method is based on the localization-delocalization principles both in the coordinate and in the momentum space. I will show that the so-called Mott's criterion (which is shown to be the sufficient criterion of ergodic delocalization) and the Anderson criterion (which is shown to be the sufficient criterion of localization) are not complimentary. There is a gap between their regions of validity where the non-ergodic extended phases and the novel correlation-induced localization may occur. To illustrate the above mentioned principles I will consider the models either with infinitely-long range hopping [3-5] or with power-law decaying ones [1-2, 6-8, A-F] and focus mostly on the latter class. The well-known example of the latter class is the power-law random banding matrices (PLRBM).
Furthermore, we extend the above mentioned models by a new class that bridge between the models with uncorrelated hopping and those with fully correlated ones. These are the models with translation-invariant (TI) long-range hopping terms which allow one to apply the above mentioned principles both in the coordinate and momentum spaces completing their phase diagrams. A remarkable feature of these random TI models is the presence of the Poisson spectral statistics within the delocalized phase. This goes against the common wisdom that the Poisson statistics signals of localization. The reason for such a behavior is that the Poisson spectral statistics emerges in the parameter region where the states in the coordinate space are, indeed, extended and weakly ergodic but those in the momentum space are localized. The common wisdom assumes by default that the states in momentum space are always chaotically extended. The TI models introduced in this paper constitute a class of models where this assumption fails. If time permits, I will mention some of the recent results on the topic for higher-dimensions, anisotropic models, and the effects of partial correlations in TI models.

Literature:
[1] L. S. Levitov, Europhy. Lett. 9, 83 (1989); Phys. Rev. Lett. 64, 547 (1990).
[2] A. D. Mirlin, Y. V. Fyodorov, F.-M. Dittes, J. Quezada, and T. H. Seligman, Phys. Rev. E 54, 3221 (1996).
[3] H. K. Owusu, K. Wagh, and E. A. Yuzbashyan, J. Phys. A: Math. Theor. 42, 035206 (2009).
[4] A. Ossipov, J. Phys. A 46, 105001 (2013).
[5] G. L. Celardo, R. Kaiser, and F. Borgonovi, Phys. Rev. B 94, 144206 (2016).
[6] X. Deng, V. E. Kravtsov, G. V. Shlyapnikov and L. Santos, Phys. Rev. Lett. 120, 110602 (2018).
[7] A. L. Burin and L. A. Maksimov, JETP Lett. 50, 338 (1989).
[8] J. T. Cantin, T. Xu, and R. V. Krems, Phys. Rev. B 98, 014204 (2018).
[A] P. Nosov, I. M. K., V. E. Kravtsov, “Correlation-induced localization” Phys. Rev. B 99, 104203 (2019) [arXiv:1810.01492]
[B] P. A. Nosov, I. M. K., “Robustness of delocalization to the inclusion of soft constraints in long-range random models”, Phys. Rev. B 99, 224208 (2019) [arXiv:1904.11509].
[C] A. Kutlin, I. M. K., “Renormalization to localization without a small parameter”, SciPost Phys. 8, 049 (2020) [arXiv:2001.06493]
[D] X. Deng, A. L. Burin, I. M. K., “Anisotropy-driven localization transition in quantum dipoles” [arXiv:2002.00013]
[E] A. G. Kutlin, I. M. K., "Multifractality emergence in energy stratified random models", in preparation
[F] W. C. Tang, I. M. K., “Non-ergodic delocalized phase with Poisson level statistics”, in preparation

We consider a Rosenzweig-Porter (RP) random matrix model with broad distribution of off-diagonal matrix elements which emerge as a model equivalent to the Anderson model on random regular graph. In this work we study the survival probability of a quantum particle with wave function initially localized on one site described by such type of model and show that the strongly non-Gaussian, broad distribution of hopping leads to the stretch-exponential decay of survival probability with time. We show that the ergodic phase with the stretch-exponential behavior of survival probability emerges in this model exactly where on a finite Bethe lattice there is a multifractal phase and relate the stretch exponent $\kappa$ with the kernel \epsilon_{\beta} of the transfer-matrix equation on a Bethe lattice.
We also consider the extension of this RP model relaxing the symmetry inherited from the Bethe lattice and find lines of phase transitions from the exponential to the stretch exponential behavior of survival probability.

(Seminar v normal'nom rezhime, s translyatsiei: Zoom)

We consider a non-equilibrium generalization of the mixed SYK4 +SYK2 model and calculate the energy dissipation rate W(ω) that results due to periodic modulation of random quadratic matrix elements with a frequency ω. We find that W(ω) possesses a peak at ω close to the polaron energy spliting E1 found recently in [1], demonstrating physical significance of the energy E1. Next, we study the effect of energy pumping with a finite amplitude A1 at the resonance frequency ω = E1 and calculate, in presence of pumping, non-equilibrium boson distribution function and dissipation rate due to low-frequency parametric modulation. At sufficiently strong pumping, low-frequency dissipation rate recovers its large value, pertinent to the pure SYK4 limit.

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Doklad po rabote arXiv:2101.08535

Seminar budet v Zume. Dostup - tol'ko po predvaritel'noi registratsii. Chtoby poluchit' dostup, napishite zaranee sekretaryu seminara Aleksandru Kopasovu kopasov@ipmras.ru.

(Ceminar v normal'nom rezhime, s translyatsiei: Zoom)

V rabote byla teoreticheski issledovana nakachka magnonnykh par v Dirakovskie tochki spektra magnonov ferromagnetika na reshetke tipa pchelinye soty. V chastnosti byl rassmotren tak nazyvaemyi protsess Sula vtorogo roda, v kotorom, blagodarya vzaimodeistviyu mezhdu magnonami, dva kvanta elektromagnitnogo polya nakachki pogloshchayutsya sistemoi, v rezul'tate chego sozdaetsya para magnonov. Byl izuchen bozonnyi analog kuperovskoi lestnitsy protsessov pererasseyaniya takoi pary magnonov, i bylo pokazano, chto pri opredelennykh usloviyakh pary dirakovskikh magnonov yavlyayutsya naibolee neustoichivymi v sisteme, a chastota polya nakachki, sootvetstvuyushchaya energii dirakovskikh tochek, - rezonansnoi. Nami vydvinuto predpolozhenie, chto v rezul'tate takoi neustoichivosti ferromagnetik perekhodit v novoe sostoyanie s nulevoi namagnichennost'yu.

V.A Zyuzin, "Pumped Dirac magnons paired state”, arXiv:2012.12051

We show theoretically that in the superconducting nanostructures the gapped states of different topology are not always protected by separating gapless states. Depending on the structure design parameters, they can be either protected or not, with a protection–unprotection transition separating these two distinct situations. We build up a general theoretical description of the transition vicinity in the spirit of Landau theory. We speculate that similar protection–unprotection transitions may also occur for other realizations of topological protection in condensed matter systems.

Video

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Rassmatrivaetsya zadacha o strukture sostoyanii, lokalizovannykh v kore vikhrya, raspolozhennogo vblizi granitsy mezhdu dvumya chistymi sverkhprovodnikami. Granitsa predpolagaetsya dostatochno prozrachnoi, s koeffitsientom otrazheniya R<<1, chto predstavlyaet soboi predel obratnyi standartnomu priblizheniyu tunnel'nogo gamil'toniana, primenimomu dlya plokho prozrachnykh granits. Pokazano, chto nalichie granitsy privodit k obrazovaniyu shcheli v spektre lokalizovannykh v kore vikhrya nizkoenergeticheskikh sostoyanii , kotoraya imeet poryadok velichiny E_g ~ Δ sqrt(R), chto uzhe pri ochen' malykh koeffitsientakh otrazheniya prevyshaet srednee rasstoyanie w_0 ~ Δ^2/E_F mezhdu urovnyami kiral'noi vetvi spektra. Shchel' maksimal'na, kogda vikhr' raspolozhen pryamo na defekte, umen'shaetsya po mere uvelicheniya rasstoyaniya b do defekta i zakryvaetsya pri k_F b ~ E_g/w_0. Issledovano takzhe obobshchenie zadachi na sluchai razlichnykh konfiguratsii s neskol'kimi granitsami (periodicheskie struktury, peresechenie dvukh lineinykh granits, «zvezda» s neskol'kimi luchami). Vo vsekh sluchayakh shchel' v spektre sokhranyaetsya, odnako v sluchae peresekayushchikhsya granits voznikaet sil'no vyrazhennyi effekt soizmerimosti, kogda velichina shcheli sushchestvenno zavisit ot togo, naskol'ko khorosho ugol peresecheniya (v edinitsakh polnoi okruzhnosti) approksimiruetsya ratsional'noi drob'yu.

We consider an interferometer based on artificially induced topological superconductivity and chiral 1D Majorana fermions. The (non-topological) superconducting island inducing the superconducting correlations in the topological substrate is assumed to be floating. This allows probing the physics of interfering Majorana modes via microwave response, i.e., the frequency dependent impedance between the island and the earth. Namely, charging and discharging of the island is controlled by the time-delayed interference of chiral Majorana excitations in both normal and Andreev channels. We argue that microwave measurements provide a direct way to observe the physics of 1D chiral Majorana modes.

In a quasi-one-dimensional system (a tube) with low concentration of defects $n$ the resistivity $\rho$ has peaks (van-Hove singularities) as a function of Fermi-energy. We show that due to non-Born scattering effects a deep narrow gap should appear just in the center of each peak. The resistivity at the bottom of a gap ($\rho_{\min}\propto n^2$) is dominated by scattering at rare ``twin-pairs'' of close defects, while scattering at solitary defects is suppressed. This effect is characteristic for multi-channel systems, it can not be observed in strictly one-dimensional one.

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Otlichnaya ot nulya ob'emnaya vyazkost' signaliziruet o narushenii masshtabnoi invariantnosti. My pokazali, chto besporyadok v dvumernom nevzaimodeistvuyushchem elektronnom gaze v perpendikulyarnom magnitnom pole privodit k nenulevoi ob'emnoi vyazkosti. Polucheno analiticheskoe vyrazhenie dlya usrednennoi po besporyadku ob'emnoi vyazkosti v bornovskom priblizhenii. Eta ostatochnaya ob'emnaya vyazkost' daet nizhnyuyu otsenku dlya ob'emnoi vyazkosti v dvumernykh elektronnykh sistemakh.

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Poslednee vremya nablyudaetsya bol'shoi eksperimental'nyi i teoreticheskii interes k geterostukturam, sostoyashchim iz ferromagnetika s magnitnymi skirmionami i sverkhprovodnika vtorogo roda. Obuslovleno eto perspektivoi sozdaniya ustoichivogo ob'ekta iz skirmiona i vikhrya s posleduyushchei vozmozhnost'yu manipulirovat' etoi sistemoi. V nashei rabote [1] izuchaetsya vzaimodeistvie neelevskogo skirmiona i pirlovskogo vikhrya za schet magnitnogo polya razmagnichivaniya. Nam udalos' pokazat', chto pri nekotorykh obstoyatel'stvakh pirlovskii vikhr' stremitsya raspolozhit'sya na nenulevom rasstoyanii ot tsentra skirmiona i chto etot effekt chuvstvitelen k kiral'nosti ferromagnetika. Pri etom kharakternyi razmer skirmiona uvelichivaetsya blagodarya vzaimodeistviyu s vikhrem. Takzhe nasha teoriya predskazyvaet vozmozhnost' spontannogo rozhdeniya pary vikhr'-antivikhr' v prisutstvii skirmiona, chto nakhoditsya v kachestvennom soglasii s rezul'tatami nedavnego eksperimenta [2].

[1] E.S. Andriyakhina. and I.S. Burmistrov “Interaction of a Néel–type skyrmion and a superconducting vortex” // arXiv: https://arxiv.org/abs/2102.05434.
[2] A.P. Petrović et al. “Skyrmion-(Anti)vortex coupling in a chiral magnet-superconductor heterostructure” // Phys.Rev. Lett.126, 117205 (2021).

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With the advent of large arrays of qubits coupled by high fidelity gates the possibility of forming a logical qubit from a large number of faulty physical ones becomes a reality. The problem of finding the probability of logical error, P(L), in a large system of size L ≫ 1 can be mapped into the statistical model, with P(L) that decreases to zero exponentially in the correctable phase. This decrease is sensitive to the probabilities of individual qubit errors, p, measurement errors, q, and error correlations, p_corr. Using a combination of numerical simulations and statistical physics arguments, we identify the regime in the parameter (p , q, p_corr) space in which error correction is possible and we find the logical error dependence on the system size. We argue that for surface code statistical models describing optimal error decoding at the Nishimori line, the critical exponent of the correlation length can be found exactly thereby allowing one to determine P(L) with limited numerical work. As the transition line is approached, we show that the dynamics in the models slows down dramatically due to Griffiths phase physics in these disordered systems, especially at large q. This result as well as the effect of p_corr show that at q ∼ p the error correction is much more difficult than for q ≪ p.

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V etom doklade ya predstavlyu perturbativnoe rassmotrenie, razrabotannoe dlya spetsial'nogo tipa kvantovykh skhem v prisutstvii shuma. Poslednie yavlyayutsya ob'ektom prakticheskogo interesa, poskol'ku oni dopuskayut estestvennuyu realizatsiyu na sushchestvuyushchikh kvantovykh ustroistvakh posredstvom posledovatel'nostei mikrovolnovykh impul'sov v sisteme sverkhprovodyashchikh kubitov. My rassmatrivaem odnomernye periodicheskie (Floke-) diskretnye skhemy, sostavlennye iz tak nazyvaemykh «dual-unitary» dvukhkubitnykh geitov, kotorye mogut byt' grubo opredeleny kak unitarnye kak vo vremennom, tak i v prostranstvennom napravleniyakh. Khotya nekotoroe ponimanie unitarnoi dinamiki v dannom tipe skhem sushchestvuet v literature, ochen' malo izvestno o vliyanii slabykh vozmushchenii, narushayushchikh svoistvo «dual-unitary», ne govorya uzhe pro effekt ot vneshnego shuma v sisteme. My predlagaem prostuyu model' s odnokubitnym shumom i provodim kak chislennyi, tak i analiticheskii analiz modeli, v osnovnom rassmatrivaya povedenie parnogo korrelyatora dvukh operatorov kak funktsii koordinat i vremeni. Poluchennye dannye predostavlyayut nekotoroe kachestvennoe ponimanie opisaniya dannykh neintegriruemykh sistem. Vazhno otmetit', chto razrabotannyi podkhod yavlyaetsya osnovoi dlya bolee detal'nogo izucheniya predlagaemoi modeli v razlichnykh rezhimakh. Nakonets, nashi rezul'taty mogut byt' ispol'zovany kak sposob kharakterizovat' lokal'nyi shum v fizicheskoi sisteme iz mnogikh kubitov.

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Recent demonstration of the first beyond classical quantum computation with a programmable quantum computer [1] opens the path to discovery of new quantum physics phenomena using these hardware systems. Gate model quantum computers used in [1] realize complex multi-qubit evolution in terms of discrete gates, elementary one and two qubit unitary operations, practically realized by a local time-dependent Hamiltonian. In this talk we present a theory and experimental data describing quantum circuit kinetics in such systems, which answers the following question: how does a system initialized in a product state generate highly entangled states and in the case of a non-integrable system approach universal random matrix statistics? We characterize circuit kinetics using time-dependent evolution of out-of-time-order correlators (OTOC) and their ensemble variance. We demonstrate that dynamics of an ensemble average OTOC can be mapped onto a classical population dynamics process, an analog of hydrodynamic description. OTOC variance on the other hand is subject to a “sign problem” and therefore evades efficient classical description. We use ensemble average OTOC to verify hardware output whereas OTOC variance provides a signature of operator entanglement generated in the system [2].

[1] Arute et. al. Nature, Vol 574, 505 (2019)
[2] Mi et. al. arXiv:2101.08870

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We study the propagation of stationary waves in disordered nonlinear media described by the nonlinear Schrödinger equation and show that, for given boundary conditions and a given coherent wave incident on the sample, the number of solutions of the equation increases exponentially with sample size. We also discuss the ballistic case, the sensitivity of the solutions to the change of external parameters, the similarity of this problem to the problem of spin glasses, and time-dependent solutions.

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We consider a noninteracting many-fermion system populating levels of a unitary random matrix ensemble —a generic model of single-particle quantum chaos. We study the corresponding many-particle level statistics by calculating the spectral form factor analytically using algebraic methods of random matrix theory, and match it with an exact numerical simulation. Despite the integrability of the theory, the many-body spectral rigidity is found to have a surprisingly rich landscape. In particular, we find a residual repulsion of distant many-body levels stemming from single-particle chaos, together with islands of level attraction. These results are encoded in an exponential ramp in the spectral form factor, which we show to be a universal feature of nonergodic many-fermion systems embedded in a chaotic medium.

We analyze the spatial distribution of the order parameter \Delta(r) in strongly disordered superconductors close to Superconductor-Insulator Transition. The analysis is based on a model of a superconductor on a locally loopless lattice with a pseudogap. We derive and solve a set of equations for the local distribution function P(\Delta) at zero temperature. The results are applicable both in the region of relatively small disorder corresponding to a Gaussian profile of P(\Delta) and in the region of strong fluctuation. The analytical results are in excellent agreement with the direct numerical solution of the self-consistency equations.

We study determininstic power-law quantum hopping model local Gaussian disorder in low dimensions d = 1, 2 under the condition d < β < 3d/2. We demonstrate unusual combination of exponentially decreasing density of the ”tail states” and localization-delocalization transition (as function of disorder strength w) pertinent to a small (vanishing in thermodynamic limit) fraction of eigenstates. In a broad range of parameters density of states ν(E) decays into the tail region E < 0 as simple exponential. We develop simple analytic theory which describes E0 dependence on power-law exponent β, dimensionality d and disorder strength W , and compare its predictions with exact diagonalization results. At low energies within the bare ”conduction band”, all eigenstates are localized due to strong quantum interference at d = 1, 2; however localization length grows fast with energy decrease, contrary to the case of usual Schrodinger equation with local disorder.

Postroena mikroskopicheskaya teoriya protsessov perenosa namagnichennosti, zatukhaniya Gil'berta i effektivnoi perenormirovki spina v dvumernom elektronnom gaze so spin-orbital'nym vzaimodeistviem Rashby v gryaznom predele. Pokazano, chto eti yavleniya imeyut sil'no vyrazhennuyu anizotropiyu. V sluchae dvukh chastichno zapolnennykh spinovykh podzon ustanovleno neozhidannoe sootnoshenie mezhdu tremya perechislennymi velichinami. Pri otsutstvii vneshnego magnitnogo polya i drugikh sil, deistvuyushchikh na namagnichennost', eto sootnoshenie predskazyvaet dvizhenie magnitnoi tekstury pod deistviem elektricheskogo toka s klassicheskoi skorost'yu dreifa elektronov provodimosti. Takzhe rassmotrena dinamika namagnichennosti pod deistviem vneshnego elektricheskogo polya (effekt Edel'shteina).
I.A. Ado, P.M. Ostrovsky, and M. Titov, Phys. Rev. B 101, 085405 (2020).

Predlozhena prostaya kvantovaya model' rasseyaniya na tochechnykh potentsial'nykh primesyakh pri proizvol'nom zakone dispersii. Eta model' obobshchaet standartnoe priblizhenie medlennykh chastits v kvantovoi mekhanike na anizotropnyi sluchai i pozvolyaet polnost'yu opisat' energeticheskuyu zavisimost' secheniya rasseyaniya pri pomoshchi odnogo fenomenologicheskogo parametra, analogichnogo faze rasseyaniya v s-kanale. Odnim iz neposredstvennykh sledstvii postroennoi teorii okazyvaetsya nezavisimost' vremeni svobodnogo probega nositelei v poluprovodnikakh ot ikh polozheniya na fermi-poverkhnosti.

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We developed a theory of electric and thermoelectric conductivity of lightly doped SrTiO3 in the non-degenerate region k_B T ≥ E_F , assuming that the major source of electron scattering is their interaction with soft transverse optical phonons present due to proximity to ferroelectric transition. We have used kinetic equation approach within relation-time approximation and we have determined energy-dependent transport relaxation time τ(E) by the iterative procedure. Using electron effective mass m and electron-transverse phonon coupling constant λ as two fitting parameters, we are able to describe quantitatively a large set of the measured temperature dependences of resistivity R(T) and Seebeck coefficient S(T) for a broad range of electron densities studied experimentally in recent paper by K.Behnia and his colleagues. In addition, we calculated Nernst ratio in the linear approximation over weak magnetic field in the same temperature range.

The multifractal superconducting state originates from the interplay of Anderson localization and interaction effects. In this article we overview the recent theory of the superconductivity enhancement by multifractality and extend it to describe the spectral properties of superconductors on the scales of the order of the superconducting gap. Specifically, using the approach based on renormalization group within the nonlinear sigma model, we develop the theory of a multifractal superconducting state in thin films. We derive a modified Usadel equation that incorporates the interplay of disorder and interactions at energy scales larger than the spectral gap and study the effect of such an interplay on the low-energy physics. We determine the spectral gap at zero temperature which occurs to be proportional to the multifracally enhanced superconducting transition temperature. The modified Usadel equation results in the disorder-averaged density of states that, near the spectral gap, resembles the one obtained in the model of a spatially random superconducting order parameter. We reveal strong mesoscopic fluctuations of the local density of states in the superconducting state. Such strong mesoscopic fluctuations imply that the interval of energies in which the superconducting gap establishes is parametrically large in systems with multifractally-enhanced superconductivity.

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Sostoyaniya, opisyvaemye neironnymi setyami, (NQS) privlekayut bol'shoe vnimanie v svyazi s ikh potentsialom stat' ochen' vyrazitel'nym variatsionnym priblizheniem dlya opisaniya kvantovykh mnogochastichnykh sistem. My issleduem faktory, kotorye opredelyayut primenimost' NQS k frustrirovannym magnetikam, obuchaya set' na osnovnykh sostoyaniyakh neskol'kikh Gamil'tonianov s ispol'zovaniem nebol'shogo podmnozhestva znachenii tochno naidennoi volnovoi funktsii. My pokazyvaem, chto sposobnost' seti k obobshcheniyu, -- sposobnost' vosstanovit' osnovnoe sostoyanie po nebol'shomu chislu amplitud i pravil'no predskazat' volnovuyu funktsiyu v ostal'noi chasti Gil'bertova prostranstva, rezko padaet s perekhodom vo frustrirovannyi rezhim. My demonstriruem, chto v nastoyashchii moment, dlya ispol'zovaniya NQS v izuchenii realistichnykh modelei, sushchestvenna imenno obobshchayushchaya sposobnost', a ne vyrazitel'nost' takogo anzatsa. Po rabote: T. Westerhout, N. Astrakhantsev, K. S. Tikhonov, M. I. Katsnelson, A. A. Bagrov, “Generalization properties of neural network approximations to frustrated magnet ground states”, Nature Communications 11, 1593 (2020).

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It is shown that hydrodynamic collision processes in undoped graphene can be described in terms of a Fokker-Planck equation with a fractional derivative, corresponding to Lévy flights in momentum space. Electron-electron collisions give rise to frequent small-angle scattering processes that are interrupted by rare large-angle events. The latter give rise to a superdiffusive phase-space dynamics whose importance for relaxation processes, charge and heat transport, as well as collective modes will be discussed. I will also comment on implications for experiments with surface acoustic waves in graphene-piezoelectric devices.

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V etoi rabote my izuchili nechetnoe po chastote sparivanie, sparivanie Berezinskogo, v neuporyadochennykh provodnikakh. V pervom primere nami byl rassmotren sluchai neuporyadochennoi sistemy vblizi ee perekhoda v izolyator. Tam sovmestnoe deistvie kulonovskogo vzaimodeistviya i rasseyaniya na primesyakh mozhet byt' istochnikom tripletnogo sparivaniya nechetnogo po chastote. V drugom rassmotrennom nami sluchae takoe sparivanie mozhet proiskhodit' vblizi sverkhprovodyashchego perekhoda. V svyazi s etim my rassmotreli sushchestvuyushchie eksperimenty i sdelali predpolozhenie, chto nechetnoe po chastote sparivanie privodit k dielektricheskomu sostoyaniyu. Takoe sostoyanie mozhet byt' rassmotreno kak nezavisimaya faza, sushchestvuyushchaya pered sverkhprovodyashchim perekhodom.

Po rabote Vladimir A. Zyuzin, Alexander M. Finkel’stein, "Odd-frequency spin-triplet instability in disordered electron liquid", arXiv:1912.04258

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We investigate inelastic microwave photon scattering by a transmon qubit embedded in a high-impedance circuit. The transmon undergoes a charge-localization (Schmid) transition upon the impedance reaching the critical value. Due to the unique transmon level structure, the fluorescence spectrum carries a signature of the transition point. At higher circuit impedance, quasi-elastic photon scattering may account for the main part of the inelastic scattering cross-section; we find its dependence on the qubit and circuit parameters. Our theory of total inelastic cross-section explains the measured quality factors of devices consisting of a transmon in a galvanic connection with a high-impedance Josephson junction array.

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Superconducting quantum wires with broken time-reversal and spin-rotation symmetries are emerging as a building block of a topological qubit. By varying the applied external magnetic field or chemical potential such wires may be tuned through the quantum critical point into the topological phase. We investigate signatures of this quantum phase transition in the dynamic response of a Josephson junction. To this end, we compute the finite-frequency admittance Y(ω) of the junction at the topological transition and in its vicinity. At the critical point, the dependence of the admittance on frequency and temperature is universal and determined by the symmetries of the system. We find that, despite the closing of the spectral gap at the transition, the dissipative response may remain weak: ReY(ω) ~ max(ω, T)². This unusual power-law behavior is markedly different from the electromagnetic response of a normal metal. Away from the critical point, a gap opens in the spectrum of the system. The dependence of the admittance on frequency, temperature, and spectral gap has a scaling form. We apply our universal theory to find the scaling functions for different combinations of symmetries.

Exchange coupling of magnetic adsorbates to a superconducting substrate leads to Yu-Shiba-Rusinov (YSR) states within the superconducting energy gap. These can be probed by scanning tunneling spectroscopy as a pair of resonances at positive and negative bias voltage and over a wide range of tunnel conductances. At low tunneling rates, the current is carried by single-electron processes, where each excitation is sufficiently quickly followed by a relaxation into the energetic continuum. Upon increasing the junction conductance, the relaxation rates suppress single-electron tunneling and resonant Andreev processes start to dominate the transport process. The cross-over of these processes is expressed in the variation of the ratio of YSR peak height at positive and negative bias voltage [1]. Here, we investigate these transport processes by photon-assisted tunneling. While applying highfrequency radiation to the tunneling junction, we record the differential conductance spectra in the low and high-conductance regime. At low conductance, the YSR states exhibit symmetrically spaced sidebands with their spacing directly evidencing single-electron tunneling. Surprisingly, at large junction conductance, the spacing remains the same while the patterns become asymmetric. We show that this asymmetry is direct evidence of a resonant Andreev reflection with tunneling threshold conditions imposed on its electron and hole component [2]. We suggest that photon-assisted tunneling can be a powerful tool for the determination of the nature of the charge carriers in a single tunneling event.
References
[1] M. Ruby, F. Pientka, Y. Peng, F. von Oppen, B.W. Heinrich, and K.J. Franke, "Tunneling Processes into Localized Subgap States in Superconductors", Phys. Rev. Lett. 115, 087001 (2015).
[2] O. Peters, N. Bogdanoff, S. Acero González, L. Melischek, J. Rika Simon, Gaël Reecht, C.B. Winkelmann, Felix von Oppen & K.J. Franke, "Resonant Andreev reflections probed by photon-assisted tunnelling at the atomic scale", Nat. Phys. (2020). https://doi.org/10.1038/s41567-020-0972-z; arXiv:2001.09534

Video

A brief overview of the main results of the experimental and theoretical works of the last ~ 10 years on quantum phase superconductor-insulator and superconductor-metal transitions will be done. In addition, it is supposed to provide some list of the main unsolved problems in this area.
B. Sacépé, M. Feigel'man, T.M. Klapwijk, Quantum breakdown of superconductivity in low-dimensional materials, Nature Physics 16, 734-746 (2020); arXiv:2007.15870

Sostoyaniya, opisyvaemye neironnymi setyami, (NQS) privlekayut bol'shoe vnimanie v svyazi s ikh potentsialom stat' ochen' vyrazitel'nym variatsionnym priblizheniem dlya opisaniya kvantovykh mnogochastichnykh sistem. My issleduem faktory, kotorye opredelyayut primenimost' NQS k frustrirovannym magnetikam, obuchaya set' na osnovnykh sostoyaniyakh neskol'kikh Gamil'tonianov s ispol'zovaniem nebol'shogo podmnozhestva znachenii tochno naidennoi volnovoi funktsii. My pokazyvaem, chto sposobnost' seti k obobshcheniyu, -- sposobnost' vosstanovit' osnovnoe sostoyanie po nebol'shomu chislu amplitud i pravil'no predskazat' volnovuyu funktsiyu v ostal'noi chasti Gil'bertova prostranstva, rezko padaet s perekhodom vo frustrirovannyi rezhim. My demonstriruem, chto v nastoyashchii moment, dlya ispol'zovaniya NQS v izuchenii realistichnykh modelei, sushchestvenna imenno obobshchayushchaya sposobnost', a ne vyrazitel'nost' takogo anzatsa.
Po rabote: T. Westerhout, N. Astrakhantsev, K. S. Tikhonov, M. I. Katsnelson, A. A. Bagrov, “Generalization properties of neural network approximations to frustrated magnet ground states”, Nature Communications, volume 11, Article number: 1593 (2020)

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Ya rasskazhu o zadachakh, nad kotorymi seichas rabotayu. Rabota nad chast'yu etikh zadach nakhoditsya na stadii podgotovki stat'i k publikatsii, nad nekotorymi – na etape formulirovki voprosa. Primernyi spisok:

1. Neravnovesnyi instanton Korshunova v real'nom vremeni (Ya. Rodionov, A. Dotdaev)
2. Elektronnaya defazirovka na poverkhnosti topologicheskogo izolyatora (I. Gornyi)
3. Eksponentsial'nye khvosty v lokalizatsii so stepennymi pryzhkami (M. Feigel'man, A. Ioselevich)
4. Eilerovskaya neustoichivost' s besporyadkom (S. Evseev, I. Burmistrov, V. Kachorovskii)
5. Korrelyatsii v rasseyannoi na dvukhurovnevoi sisteme volne (N. Masnev, Yu. Makhlin)
6. Sostoyaniya neironnykh setei dlya kvantovykh magnetikov (A. Bagrov, N. Astrakhantsev, T. Westerhout)

Plotnost' sostoyanii i soprotivlenie chistykh kvaziodnomernykh sistem obladayut osobennostyami Van Khova pri prokhozhdenii urovnya Fermi cherez dno podzony poperechnogo kvantovaniya. Odnako, uchet rasseyaniya na primesyakh dolzhen zamyvat' eti osobennosti. Kak bylo pokazano v nashei predydushchei rabote [Phys. Rev. B 99, 035414 (2019)] dlya sluchaya chistykh provodyashchikh trubok, kharakter zamytiya osobennostei sushchestvenno zavisit ot kontsentratsii primesei $n$. Dlya $n>n_c$ osobennosti prosto razmyvayutsya, v to vremya kak dlya $n < n_c$ iznachal'naya osobennost' asimmetrichno rasshcheplyaetsya v 2 pika dlya prityagivayushchikh primesei. Zdes' $n_c$ — kriticheskaya kontsentratsiya primesei. V dannoi rabote my obobshchaem eti rezul'taty dlya sluchaya «polosok» — kvaziodnomernykh struktur v dvumernykh provodnikakh. V etom sluchae pri $n < n_c$ takzhe imeet mesto asimmetrichnoe rasshcheplenie osobennosti v 2 pika. Odnako, v otlichii ot sluchaya trubki, amplitudy rasseyaniya na primesyakh zavisyat ot ikh pozitsii, i eti piki okazyvayutsya neodnorodno ushirennymi. Naibolee sil'no ushiryaetsya levyi maksimum, voznikayushchii (tol'ko dlya sluchaya prityagivayushchikh primesei) vsledstvie rasseyaniya na kvazistatsionarnykh urovnyakh. Dannye urovni, v svoyu ochered', obrazuyut otnositel'no shirokuyu primesnuyu zonu so slaboi osobennost'yu, pokhozhei na osobennost' Van Khova, na nizhnei granitse. Razlichnye uchastki zavisimosti soprotivleniya opredelyayutsya vkladami razlichnykh grupp primesei. Tak, vblizi minimuma soprotivleniya sil'nee vsego rasseivayut, chto udivitel'no, samye «slabye» primesi, raspolozhennye vblizi uzlov volnovoi funktsii. Oblast' kvazi-osobennosti Van Khova vblizi levogo maksimuma opredelyaetsya rasseyaniem na «sil'nykh» primesyakh, raspolozhennykh vblizi puchnostei volnovoi funktsii.

We present a full theory of the interacting insulating phases of twisted bilayer graphene around the first magic angle where the bandwidth of the “active” bands becomes very small. We show that the single particle Hamiltonian is fully anomalous: it contains stable topology for every set of bands. Furthermore, we analyze the Coulomb interaction and obtain exact insulating ground states as well as the full excitation spectrum in certain limits.

Video

We consider the semiclassical dynamics of electrons on complex Fermi surfaces in the presence of strong magnetic fields. The reconstructions of the general topological structure of such dynamics are accompanied by the appearance of closed extremal trajectories of a special form, closely related to geometry and topology of the Fermi surface. The study of oscillation phenomena on such trajectories allows, in particular, to propose a relatively simple method for refining the parameters of the dispersion relation in metals with complex Fermi surfaces.

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We derive the Casimir-Polder force and torque for an anisotropic molecule close to a conducting plane with a general tensorial conductivity. The results are then applied to study carbon dioxide CO2 molecule behaviour close to a Hall plane and to a free standing graphene. The Casimir-Polder torque acting on this linear molecule is found to favor the orientation of its main axis perpendicular to the surface, thus potentially facilitating penetration of the molecule through a membrane.

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Superconducting films of amorphous Indium Oxide (a:InO) thin films undergo a transition to insulation upon increasing disorder. This quantum phase transition is driven by the localization of preformation of Cooper pairs, which has been evidenced through various unusual spectroscopic properties. The continuous decrease of the critical temperature as the critical disorder approaches indicates a similarly continuous suppression of the superfluid density. In this talk I discuss the fate of the superfluid density in the vicinity of the transition to insulation in a:InO films. To access the superfluid density we conducted a systematic study of the whole plasmon dispersion spectrum of high quality factor microwave resonators made of a:InO, combined with DC resistivity measurements, as a function of disorder. Our main observations are a breakdown of the Mattis-Bardeen theory and a record kinetic inductance of 17nH per square for critical, superconducting samples. Surprisingly, we find that the superfluid density remains finite at the critical disorder. Besides providing new insights to understand the SIT in a:InO, these results may find applications in superconducting quantum circuits where very large inductances are highly desirable.

Suppression of the critical temperature in homogeneously disordered superconducting films is a consequence of the disorder-induced enhancement of Coulomb repulsion. We demonstrate that for the majority of thin films studied now this effect cannot be completely explained in the assumption of two-dimensional diffusive nature of electrons motion. The main contribution to the $T_c$ suppression arises from the correction to the electron-electron interaction constant coming from small scales of the order of the Fermi wavelength that leads to the critical temperature shift $\delta T_c/T_{c0} \sim - 1/k_Fl$, where $k_F$ is the Fermi momentum and $l$ is the mean free path. Thus almost for all superconducting films that follow the fermionic scenario of $T_c$ suppression with decreasing the film thickness, this effect is caused by the proximity to the three-dimensional Anderson localization threshold and is controlled by the parameter $k_Fl$ rather than the sheet resistance of the film.
D.S. Antonenko, M.A Skvortsov,. JETP Lett. (2020). https://doi.org/10.1134/S0021364020190017

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Dolinnyi effekt Kholla zaklyuchaetsya v poyavlenii dolinnogo potoka chastits – protivopolozhno napravlennykh potokov v dvukh dolinakh zony Brillyuena. Dolinnyi potok perpendikulyaren iskhodnomu potoku chastits po analogii s tem, kak v spinovom effekte Kholla spinovyi tok poperechen elektricheskomu. Iskhodnyi potok chastits mozhet byt' zadan vneshnim polem, a mozhet byt' obuslovlen uvlecheniem nositelei zaryada ili eksitonov fononami ili fotonami. Tsel' doklada – izlozhit' razvituyu v rabotakh [1,2] teoriyu dolinnogo effekta Kholla v dvumernykh kristallakh v usloviyakh effekta uvlecheniya.

Pokazano, chto imeetsya tri vklada v dolinnyi tok: (i) ot asimmetrichnogo (skew) rasseyaniya (vklyuchaya kogerentnoe rasseyanie na parakh primesyakh i dvukhfononnye protsessy asimmetrichnogo rasseyaniya) i anomal'nye vklady, obuslovlennye (ii) sdvigami volnovykh paketov pri rasseyanii i (iii) ikh anomal'noi skorost'yu. Prodemonstrirovana chastichnaya kompensatsiya anomal'nykh vkladov i ukazana ee fizicheskaya priroda. Vypolneno sopostavlenie dolinnykh tokov elektronov i eksitonov v usloviyakh effekta uvlecheniya s rezul'tatami dlya vneshnego staticheskogo polya i pri nalichii gradienta temperatury chastits (dolinnyi effekt Nernsta) i prodemonstrirovana chuvstvitel'nost' effekta k prirode tyanushchei sily. Dlya eksitonov takzhe provedeno obobshchenie dreifovo-diffuzionnoi modeli, uchityvayushchei dolinnye stepeni svobody, i rasschitany prostranstvennye profili eksitonnoi plotnosti i dolinnoi polyarizatsii.

[1] Valley Hall effect caused by the phonon and photon drag, M. M. Glazov and L. E. Golub, Phys. Rev. B 102, 155302 (1-16) (2020).
[2] Skew Scattering and Side Jump Drive Exciton Valley Hall Effect in Two-Dimensional Crystals, M. M. Glazov and L. E. Golub, Phys. Rev. Lett. 125, 157403 (1-7) (2020).

We report a complete analytical expression for the one-loop correction to the ac conductivity $\sigma(\omega)$ of a disordered two-dimensional electron system in the diffusive regime. The obtained expression includes the weak localization and Altshuler–Aronov corrections as well as the corrections due to superconducting fluctuations above superconducting transition temperature. The derived expression has no divergency in the static limit, $\omega\to 0$ , in agreement with general expectations for the normal state conductivity of a disordered electron system. The results are published in I.S. Burmistrov, Ann. Phys. 418, 168201 (2020).

1. Perevernutyi mayatnik i smezhnye zadachi (N. Stepanov)
2. Kvantovyi transport v maioranovskikh provodakh (D. Antonenko, P. Ostrovskii)
3. Vikhr' u ploskoi stenki (U. Khodaeva)
4. Kogerentnoe proskal'zyvanie fazy (A. Bun'kov, O. Astaf'ev)
5. Fluktuatsii v odnofotonnykh detektorakh (A. Semenov)
6. Neodnorodnyi sverkhtekuchii tok (M. Feigel'man, D. Fazlizhanova)

The interplay of interactions and disorder in two-dimensional (2D) electron systems has actively been studied for decades. The paradigmatic approach involves starting with a clean Fermi liquid and perturbing the system with both disorder and interactions. We instead start with a clean non-Fermi liquid near a 2D ferromagnetic quantum critical point and consider the effects of disorder. In contrast with the disordered Fermi liquid, we find that our model does not suffer from runaway flows to strong coupling and the system has a marginally stable fixed point with perfect conduction.

Disorder has different profound effects on superconducting thin films. For a large variety of materials, increasing disorder reduces electronic screening which enhances electron-electron repulsion. These fermionic effects lead to a mechanism described by Finkelstein: when disorder combined to electron-electron interactions increases, there is a global decrease of the superconducting energy gap Δ and of the critical temperature Tc, the ratio Δ/kBTc remaining roughly constant. In addition, in most films, an emergent granularity develops with increasing disorder and results in the formation of inhomogeneous superconducting puddles. These gap inhomogeneities are usually accompanied by the development of bosonic features: a pseudogap develops above the critical temperature Tc and the energy gap Δ starts decoupling from Tc. Thus the mechanism(s) driving the appearance of these gap inhomogeneities could result from a complicated interplay between fermionic and bosonic effects. By studying the local electronic properties of an NbN film with scanning tunneling spectroscopy (STS), we show that the inhomogeneous spatial distribution of Δ is locally strongly correlated to a large depletion in the local density of states (LDOS) around the Fermi level, associated to the Altshuler-Aronov effect induced by strong electronic interactions. By modeling quantitatively the measured LDOS suppression, we show that the latter can be interpreted as local variations of the film resistivity. This local change in resistivity leads to a local variation of Δ through a local Finkelstein mechanism. Our analysis furnishes a purely fermionic scenario explaining quantitatively the emergent superconducting inhomogeneities, while the precise origin of the latter remained unclear up to now.

We study numerically the critical behavior at the localization transition in the Anderson model on infinite Bethe lattice and on random regular graphs. As a first step, we carry out a precise determination of the critical disorder. After this, we determine the dependence of the correlation volume on disorder on the delocalized side of the transition by means of population dynamics. The asymptotic critical behavior is found to be in agreement with analytical prediction based on the stability analysis of the symmetry-broken solution near criticality.

We develop a theory of conductivity of type-II superconductors in the flux flow regime taking into account random spatial fluctuations of the system parameters, such as the gap magnitude Δ(r) and the diffusion coefficient D(r). We find a contribution to the conductivity that is proportional to the inelastic relaxation time τin, which is much longer than the elastic relaxation time. This new contribution is due to Debye-type relaxation, and it can be much larger than the conventional flux flow conductivity due to Bardeen and Stephen. The new contribution is expected to dominate in clean superconductors at low temperatures and in magnetic fields much smaller than Hc2.

1. Metallicheskoe povedenie, indutsirovannoe vzaimodeistviem, v dvumernoi neuporyadochennoi ne-Fermi zhidkosti (sovmestno s P. Nosov i S. Raghu)
2. Skirmiony i vikhri v geterostrukturakh sverkhprovodnik-kiral'nyi ferromagnetik (sovmestno s E. Andriyakhina)
3. Magnitnye primesi v neuporyadochennykh sverkhprovodnikakh (sovmestno s A. Lyublinskaya, S. Babkin, B. Pashinskii)
4. Mezoskopicheskie fluktuatsii plotnosti sostoyanii v neuporyadochennykh sverkhprovodnikakh (sovmestno s F. Evers, M. Stosiek)
5. Vyazkost' i svyazannye s nei transportnye koeffitsienty v dvumernom neuporyadochennom elektronom gaze v magnitnom pole (sovmestno s V. Zakharov, M. Goldstein)
6. Fluktuatsii izgiba palochki s uchetom besporyadka (sovmestno s S. Evseev, K. Tikhonov, V. Kachorovskii)

Seminar ochnyi, no s online translyatsiei dlya interesuyushchikhsya, no otsutstvuyushchikh: link na translyatsiyu

V mnogozonnykh sverkhprovodnikakh sushchestvuyut sostoyaniya s narushennoi simmetriei otnositel'no obrashcheniya vremeni. My rassmotreli sistemy takogo tipa i pokazali, chto funktsional Ginzburga-Landau imeet osnovnoe sostoyanie bez ``vnutrennego'' magnitnogo polya -- s nulevym znacheniem plotnosti toka. Osnovnoe sostoyanie bylo issledovano v teorii vozmushchenii po slaboi neodnorodnosti. Bylo pokazano, chto v otsutstvie vneshnego magnitnogo polya neodnorodnosti ne privodyat k vozniknoveniyu spontannogo vnutrennego magnitnogo polya. Rasshirenie funktsional'nogo prostranstva s vklyucheniem singulyarnykh reshenii imeet bol'shoe znachenie dlya ponimaniya eksperimental'noi situatsii v mnogozonnykh sverkhprovodnikakh.
doklad po stat'e: Yu.N. Ovchinnikov, D.V. Efremov, Singular ground state of multiband inhomogeneous superconductors, Phys. Rev. B 99, 224508 (2019)

Fail s prezentatsiei: zdes'

Investigation of Josephson effect, current flow in narrow superconducting stripes, dynamical states in superconductors lead to the necessity to deal with an important phenomenon: phase slip events. The study of the distribution of zeros for Riemann's Zeta function also requires an analisis of the same phenomenon.
It was found that, in addition to trivial zeros in points ($ z = -2N, N = 1, 2, ... $, natural numbers), the Riemann’s zeta function $\zeta(z)$ has zeros only on the line {$z = 1/2 + i t_0$, $t_0$ is real}. All zeros are numerated, and for each number, N, the positions of the non-overlap intervals with one zero inside are found. The simple equation for the determination of centers of intervals is obtained. The analytical function $\eta(z)$), leading to the possibility fix the zeros of the zeta function $\zeta(z)$, was estimated. To perform the analysis, the well-known phenomenon, phase-slip events, is used. This phenomenon is the key ingredient for the investigation of dynamical processes in solid-state physics, for example, if we are trying to solve the TDGLE (time-dependent Ginzburg-Landau equation).
J. Supercond. Novel Magn., 32(11), 3363-3368 (2019)

We study the SYK model with a weak quadratic perturbation, beyond the simplest perturbative limit considered previously. For intermediate values of the perturbation strength, fluctuations of the Schwarzian mode are suppressed, and the mean-field solution remains valid beyond the expected interval. Out-of-time-order correlation function displays at short time intervals exponential growth with maximal Lyapunov exponent 2\piT, but its prefactor scales as T at low temperatures

Issledovana prostranstvennaya i temperaturnaya zavisimost' parametra poryadka v tonkikh sverkhprovodyashchikh plenkakh v prodol'nom magnitnom pole i sil'nom spin-orbital'nom vzaimodeistvii obshchego vida v okrestnosti perekhoda v prostranstve: magnitnoe pole, spin-orbita, temperatura. Vblizi kriticheskoi poverkhnosti parametr poryadka est' neyavnaya funktsiya otnosheniya dvukh malykh parametrov: temperatury i samogo parametra poryadka. [1]
Issledovano vozmozhnoe obrazovanie poverkhnostnogo sostoyaniya v izolyatore s malym zazorom. Bylo podschitano, chto otvet zavisit ot real'nykh granichnykh uslovii na poverkhnosti. «Estestvennoe» granichnoe uslovie dlya obraztsa konechnogo razmera privodit k sokhraneniyu shcheli v spektre vozbuzhdeniya. [2]
[1] Yu.N. Ovchinnikov, Singular Temperature Dependence of the Equation of State of Superconductors with Spin-Orbit Interaction in Low-Temperature Region – II, J. Supercond. Novel Magn., 31(12), 3855–3866 (2018)
[2] Yu.N. Ovchinnikov, Topological Insulator: Surface localized States, J. Supercond. Novel Magn., 32 (5), 1327-1331 (2019)

We consider the statistical properties of a non-falling trajectory in the Whitney problem of an inverted pendulum excited by an external force. In the case when the external force is white noise, we recently found the instantaneous distribution function of the pendulum angle and velocity over an infinite time interval using a transfer-matrix analysis of the supersymmetric field theory. Here, we generalize our approach to the case of finite time intervals and multipoint correlation functions. Using the developed formalism, we calculate the Lyapunov exponent, which determines the decay rate of correlations on a non-falling trajectory.

Predlozhena stekol'naya model' pinninga vikhrei v tonkikh sverkhprovodyashchikh plenkakh s sil'nym besporyadkom v oblasti magnitnykh polei B « H$_{c2}$ i pri nizkikh temperaturakh. Ispol'zuetsya metod, podobnyi razvitomu v rabote Myullera i Ioffe (2004) dlya "kulonovskogo stekla" v modeli Efrosa-Shklovskogo dlya kulonovskoi shcheli. Stekol'noe sostoyanie opisyvaetsya v ramkakh priblizheniya "1-RSB", kotoroe okazyvaetsya ochen' khoroshim priblizheniem chislenno (khotya i yavlyaetsya, strogo govorya, neustoichivym), sootvetstvuyushchii parametr malosti imeet poryadok 10$^{-5}$. Raspredelenie effektivnykh lokal'nykh energii vikhrei P(h) yavlyaetsya, s toi zhe tochnost'yu, shchelevym, chto obespechivaet nalichie effektivnoi sverkhprovodyashchei plotnosti (konechnoi kineticheskoi induktivnosti) plenki v sil'nom magnitnom pole.

We study stochastic dynamics of an inverted pendulum subject to a random force in the horizontal direction. Considered at the entire time axis, the problem admits a unique solution which always remains in the upper half plane. We develop a new technique for treating statistical properties of this unique non-falling trajectory. In our approach based on the supersymmetric formalism of Parisi and Sourlas, statistics of the non-falling trajectory is expressed in terms of the zero mode of a corresponding transfer-matrix Hamiltonian. The emerging mathematical structure is similar to that of the Fokker-Planck equation, but it is rather written for the «square root» of the distribution function.
We derive the specific boundary conditions that correspond to the non-falling trajectory. Our results for the distribution function of the angle and its velocity at the non-falling trajectory are in perfect agreement with direct numerical simulations of the stochastic pendulum equation. In the limit of very strong noise, an exact analytical solution is obtained.

Webinar link: http://bbb2.itp.ac.ru/b/qme-erf-krk
Gaussian Rosenzweig-Porter (GRP) random matrix ensemble is the only one in which the robust multifractal phase have a status of a mathematical theorem. In this paper we suggest an extension of the GRP model, the LN-RP model, by adopting a logarithmically-normal (LN) distribution of off-diagonal matrix elements. We show that large matrix elements from the tail of this distribution give rise to a peculiar weakly-ergodic phase that replaces both the multifractal and the fully-ergodic phases present in GRP ensemble. A new phase is characterized by the broken basis-rotation symmetry which the fully-ergodic phase respects. Thus in addition to the localization and ergodic transitions in LN-RP model there exists also the FWT transition between the two ergodic phases. We formulate the criteria of the localization, ergodic and FWT transitions and obtain the phase diagram of the model. We also suggest a new criteria of stability of the non-ergodic phases and prove that the Anderson transition in LN-RP model is discontinuous, in contrast to its GRP counterpart.

Webinar link: http://bbb2.itp.ac.ru/b/qme-erf-krk
We study SYK_4 model with weak SYK_2 random terms of typical magnitude Γ beyond the simplest perturbative limit considered previously. In the intermediate range J/N << Γ << J/N^{1/2} of the perturbation strength Γ, fluctuations of the Schwarzian soft mode are suppressed and conformal mean-field solution for the Majorana Green function G(τ) is valid much beyond usual timescale t_∗ ∼ N/J characteristic for pure SYK_4 model. However, high momenta of the probability distribution of the Green function are shown to grow as ln([G(τ)]^p) ∝ p^2 at p >> 1, indicating log-normal shape of the distribution P[G(τ)] . Short-time decay of the out-of-time-order correlation function is characterized by the universal exponent 2πT/\hbar, while the pre-factor is much smaller than in pure SYK_4 model, and shows unusual temperature dependence.

Topological insulators combine an insulating bulk with gapless states at their surfaces. This talk introduces "higher-order topological insulators", which are crystalline insulators with a gapped bulk and gapped crystalline boundaries, but topologically protected gapless states at corners or at edges of the crystal. I'll show that such "higher-order boundary states" are a generic boundary manifestation of the nontrivial bulk topology, if the bulk topology relies on a crystalline symmetry for its protection.

Webinar link: http://bbb2.itp.ac.ru/b/qme-erf-krk
We develop a hydrodynamic description of the resistivity and magnetoresistance of an electron liquid in a smooth disorder potential. This approach is valid when the electron-electron scattering length is sufficiently short. In a broad range of temperatures, the dissipation is dominated by heat fluxes in the electron fluid, and the resistivity is inversely proportional to the thermal conductivity, κ. This is in striking contrast to the Stokes flow, in which the resistance is independent of κ and proportional to the fluid viscosity. We also identify a new hydrodynamic mechanism of spin magneto-resistance.

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.256804

Webinar: http://bbb2.itp.ac.ru/b/qme-erf-krk
Localization of wavefunctions is arguably the most familiar effect of disorder in quantum systems. It has been recently argued [V. Khemani, R. Nandkishore, and S. L. Sondhi, Nature Physics, 11, 560 (2015)] that, contrary to naive expectation, manipulation of a localized-site in the disordered medium may produce a disturbance over a length-scale much larger than the localization-length ξ. Here we report on the observation of this nonlocal phenomenon in electronic transport experiment. Being a wave property, visibility of this effect hinges upon quantum-coherence, and its spatial-scale may be ultimately limited by the phase-coherent length of the disordered insulator. Evidence for quantum coherence in the Anderson-insulating phase may be obtained from magneto-resistance measurements which however are useful mainly in thin-films. The technique used in this work offers an empirical method to measure this fundamental aspect of Anderson-insulators even in relatively thick samples.

In addition, it is recommended by the author to read the following two papers before the seminar:
[1] I. M. Lifshitz, & V. Y. Kirpichenkov, Tunnel transparency of disordered systems, Zh. Eksp. Teor. Fiz. 77, 989 (1979) [Sov. Phys. JETP 50, 499 (1979)].
[2] J. B. Pendry, Quasi-extended electron states in strongly disordered systems, J. Phys. C: Solid State Phys. 20, 733 (1987).

We develop a theory of quantum T=0 phase transition (q-SMT) between metal and superconducting ground states in a two-dimensional metal with frozen-in spatial fluctuations of the Cooper attraction constant. When strength of these fluctuations exceeds some critical magnitude, usual mean-field-like scenario of the q-SMT breaks down due to spontaneous formation of local droplets of superconducting phase. The density of these droplets grows exponentially with the increase of average attraction constant. Interaction between the droplet's order parameters is due to proximity effect via normal metal and scales with distance as inverse power of distance, with power exponent slightly larger than 2. We treat this interaction by means of strong-disorder real-space renormalization group and find the RG flow formally similar to the Berezinski-Kosterlitz-Thouless RG for 2D XY model. Line of fixed points of this RG corresponds to a Griffiths phase of a metal with large fractal clusters of strongly coupled superconducting islands. Superconducting side of the transition is characterized by a non-monotonic variation of physical properties with logarithm of the temperature T, which results of a very weak T-dependence in a broad temperature range.

Webinar: http://bbb2.itp.ac.ru/b/qme-erf-krk
Recent experiments on twisted bilayer graphene (TBG) near the magic angle have observed spontaneous integer quantum Hall states in the presence of an aligned hexagonal boron nitride (hBN) substrate. These states arise from valley ferromagnetism, and the complete filling of Chern bands. A natural question is whether fractional filling of the same bands would lead to fractional quantum Hall states, i.e. to fractional Chern insulators (FCIs). Using a variant of the continuum model for TBG with zero hopping between AA Moire cites we construct a Laughlin wave function on a real-space torus in full analogy with the Haldane and Rezayi construction for two-dimensional electrons at the lowest Landau-level on a torus.

One of the most exciting phenomena observed in crystalline disordered membranes, including a suspended graphene, is rippling, i.e. a formation of static flexural deformations. Despite an active research, it still remains unclear whether the rippled phase exists in the thermodynamic limit, or it is destroyed by thermal fluctuations. We demonstrate that a sufficiently strong short-range disorder stabilizes ripples, whereas in the case of a weak disorder the thermal flexural fluctuations dominate in the thermodynamic limit. The phase diagram of the disordered suspended graphene contains two separatrices: the crumpling transition line dividing the flat and crumpled phases and the rippling transition line demarking the rippled and clean phases. At the intersection of the separatrices there is the unstable, multicritical point which splits up all four phases. Most remarkably, rippled and clean flat phases are described by a single stable fixed point which belongs to the rippling transition line.

The ferroelectric instability in pristine strontium titanate is aborted by quantum fluctuations. Therefore, the static electric permittivity saturates to an extremely large value at low temperature and the effective Bohr radius approaches a micron. In this context, removing a tiny fraction of oxygen atoms turns the system to a dilute metal with a sharp Fermi surface and a superconducting instability. The focus of this talk will be charge and entropy transport by electrons in this dilute metal and their general implications.
The temperature dependence of the resistivity of this dilute metal at low-temperature implies that electron-electron scattering can generate a T-square resistivity even in absence of Umklapp scattering with a single Fermi pocket. The magnitude of resistivity at a low temperature would imply a mean-free-path too short to be physically plausible. Combined with the temperature dependence of the Seebeck coefficient, this implies that non-degenerate electrons become heavier with warming. We will see that these observations cannot be explained by available polaronic theories. There is a whole family of dilute metals emerging from doped quantum paraelectrics with similar properties.

Webinar: http://bbb2.itp.ac.ru/b/qme-erf-krk
Quantum information theory and strongly correlated electron systems share a common theme of macroscopic quantum entanglement. In both topological error correction codes and theories of quantum materials (spin liquid, heavy fermion and high-Tc systems) entanglement is implemented by means of an emergent gauge symmetry. Inspired by these connections, here we introduce a simple model for fermions moving in the deconfined phase of a Z2 gauge theory, by coupling Kitaev's toric code to mobile fermions. This permits us to exactly solve the ground state of this system and map out its phase diagram. By changing the sign of the plaquette term in the toric code, we are able to tune the groundstate between an orthogonal metal and an orthogonal semimetal, in which the single particle correlators of the original Fermi operators are gapped, despite the existence of gapless collective modes. The small-to-large Fermi surface transition between these two states occurs in a stepwise fashion with multiple intermediate phases. We are able to access the physics beyond the integrable point using a novel diagrammatic perturbation expansion, which allows us to examine various instabilities of the deconfined phase and to derive the Ising (XY) critical theory at the transition between deconfined and confined metal (semimetal). Finally, the connection to quantum information science allows to discuss an analogue quantum emulator (an array of Majorana Cooper pair boxes) for fermions in Z2 gauge theories. Analytical results for this minimal model pave the way for a better understanding of quantum materials with itinerant fermions and the connection to the toric code opens the potential for simulation using upcoming quantum information techniques.

We investigate spin-orbit torques on magnetization in an insulating ferromagnetic layer that is brought into close proximity to a topological insulator (TI). In addition to the well-known fieldlike spin-orbit torque, we identify an anisotropic anti-damping-like spin-orbit torque that originates in a diffusive motion of conduction electrons. This diffusive torque is vanishing in the limit of zero momentum (i.e., for a spatially homogeneous electric field or current), but it may, nevertheless, have a strong impact on spin-torque resonance at finite frequency provided the external field is neither parallel nor perpendicular to the TI surface. The required electric-field configuration can be created by a grated top gate.

The presence of both inversion (P) and time-reversal (T) symmetries in solids leads to a well-known double degeneracy of the electronic bands (Kramers degeneracy). When the degeneracy is lifted, spin textures can be directly observed in momentum space, as in topological insulators or in strong Rashba materials. The existence of spin textures with Kramers degeneracy, however, is very difficult to observe directly. Here, we use quantum interference measurements combined with first-principle band structure calculations to provide evidence for the existence of hidden entanglement between spin and momentum in the antiperovskite-type 3D Dirac material Sr3SnO. We find robust weak antilocalization (WAL) independent of the position of EF. The observed WAL signal at low doping is fitted using a single interference channel, which implies that the different Dirac valleys are mixed by disorder. Notably, this mixing does not suppress WAL, suggesting contrasting interference physics compared to graphene. We identify scattering among axially spin-momentum locked states as a key process that leads to a spin-orbital entanglement, giving rise to robust WAL. Our work sheds light on the subtle role of spin and pseudospin, when both could contribute to the same quantum effect.

A quantum magnetic impurity of spin $S$ at the edge of a two-dimensional time reversal invariant topological insulator may give rise to backscattering. We study here the shot noise associated with the backscattering current for arbitrary $S$. Our full analytical solution reveals that for $S>½$ the Fano factor may be arbitrarily large, reflecting bunching of large batches of electrons. By contrast, we rigorously prove that for $S=½$ the Fano factor is bounded between 1 and 2, generalizing earlier studies. Based on paper P.D. Kurilovich, V.D. Kurilovich, I.S. Burmistrov, Y. Gefen, M. Goldstein "Unrestricted electron bunching at the helical edge", Phys. Rev. Lett. 123, 056803 (2019).

V rabote izuchaetsya kvazichastichnyi transport v neuporyadochennykh topologicheskikh sverkhprovodyashchikh provolokakh klassa simmetrii D, kotorye mogut soderzhat' paru kraevykh Maioranovskikh sostoyanii. Rassmotren kriticheskii rezhim, realizuyushchiisya na granitse mezhdu topologicheskoi i trivial'noi fazami, pri kotorom zakryvaetsya ob'emnaya shchel', a para Maioranovskikh sostoyanii ischezaet. Ranee bylo pokazano, chto v kriticheskom rezhime srednii kondaktans na bol'shikh dlinakh L vedet sebya kak 1/\sqrt{L}. My vychislyaem dispersiyu kondaktansa var g s pomoshch'yu nelineinoi supersimmetrichnoi sigma-modeli s dvumya replikami, chto svoditsya k fur'e analizu na supermnogoobrazii sigma-modeli. S pomoshch'yu parametrizatsii Ivasavy postroeny sobstvennye funktsii sootvetstvuyushchego operatora Laplasa-Bel'trami. Poluchena yavnaya formula dlya var g pri proizvol'nykh L, opisyvayushchaya krossover ot rezhima drudevskoi provodimosti na malykh dlinakh k rezhimu shirokogo raspredeleniya kondaktansa pri bol'shikh dlinakh. Takzhe issledovan sluchai disbalansa levykh/pravykh kanalov v provoloke, opisyvaemyi sigma-model'yu s topologicheskim chlenom Vessa-Zumino-Vittena.

We develop a theory of quantum T = 0 phase transition (q-SMT) between metal and superconducting ground states in a two-dimensional metal with frozen-in spatial fluctuations δλ(r) of the Cooper attraction constant. When strength of fluctuations δλ(r) exceeds some critical magnitude, usual mean-field-like scenario of the q-SMT breaks down due to spontaneous formation of local droplets of superconducting phase. The density of these droplets grows exponentially with the increase of average attraction constant λ. Interaction between the droplet's order parameters is due to proximity effect via normal metal and scales with distance ∝ 1/rβ, with 2 < β ≤ 3. We account for this interaction by means of a real-space strong-disorder renormalization group (RG). Near the q-SMT the RG flow is, formally, a dual equivalent of the Kosterlitz-Thouless RG. The corresponding line of fixed points describes a Griffiths phase of a metal with large fractal clusters of superconducting islands. Superconducting side is described by a runaway of RG trajectories into the strong-coupling region. Close to the transition point on the SC side, 0 < −δ << 1, RG trajectories possess an extremum as function of the RG parameter ∼ |δ| 1/2 ln(1/T). It results in a very wide temperature range where physical properties are nearly T-independent. This observation may be relevant to the understanding of a ”strange metal” state frequently observed near q-SMT.

We theoretically find that finite size Fulde-Ferrell (FF) superconductor (which is characterized by spatially nonuniform ground state with Delta(r) ~ exp(-i q_{FF} r), where Delta is a superconducting order parameter) has paramagnetic Meissner, vortex and 'onion' ground states with spatially nonuniform |Delta|. These states are realized due to boundary effect when the lateral size of superconductor L ~ 1/q_{FF}. We argue, that predicted states could be observed in thin disc/square made from superconductor-ferromagnet-normal metal trilayer with L ~ 150-600 nm.

In this talk we review recent experiments on planar submicron superconductor/normal metal/superconductor junctions which have been performed in the Laboratory of superconductivity, ISSP recently. We investigated how quasiparticles and spins injected into leads and barrier of SNS junctions affect the critical current, phase difference inversion and non-local effects.

With the help of the magnetic decoration method, we investigate the structure of the magnetic flux in single-crystalline magnetic superconductors based on EuFeAs doped by phosphorus. In a single crystal of ferromagnetic superconductor EuFe2(As0:79P0:21)2 with superconducting transition temperature (Tsc=22K) by decoration technique we observe vortex structure in domains of spontaneous magnetic flux (vortex domains) near the temperature of ferromagnetic transition (TSurie= Tc =18K). In a narrow temperature interval (~1K) around Tc =18K we also observe Meissner domains, detected previously by the magnetic-force microscopy method. When temperature is lowered, we observe a domain structure (vortex domains) with changing direction of the magnetic flux.

An increase in disorder in a superconductor leads to the smearing of the coherence peak and appearance of localized quasiparticle states under the average gap. At a phenomenological level, the smeared density of states was calculated by Larkin and Ovchinnikov in 1971. I will overview further developments in this filed, both from a theoretical and experimental point of view.

Rassmatrivaetsya teoreticheskaya zadacha o rasprostranenii pary fotonov v odnomernom volnovode, v kotoryi pomeshchen periodicheskii massiv dvukhurovnevykh atomov. Otlichiem ot klassicheskoi modeli Dikke yavlyaetsya uchet konechnogo nenulevogo rasstoyaniya mezhdu atomami. Blagodarya fotonnoi blokade - nevozmozhnosti pogloshcheniya dvukh fotonov odnim atomom - mezhdu fotonami voznikaet effektivnoe ottalkivanie. Budet pokazano, chto eto ottalkivanie privodit k obrazovaniyu dvukhfotonnykh sostoyanii, kogda odin iz fotonov lokalizovan, a vtoroi obrazuet stoyachuyu volnu. Takie dvukhchastichnye mody mozhno rassmatrivat' kak analog indutsirovannykh vzaimodeistviem opticheskikh reshetok.

We consider a superconductor with surface suppression of the BCS pairing constant $\lambda(x)$. We analytically find the gap in the surface density of states (DOS), behavior of the DOS $\nu(E)$ above the gap, a ``vertical'' peculiarity of the DOS around an energy equal to the bulk order parameter $\Delta_0$, and a perturbative correction to the DOS at higher energies. The surface gap in the DOS is parametrically different from the surface value of the order parameter due to a difference between the spatial scale $r_c$, at which $\lambda(x)$ is suppressed, and the coherence length. The vertical peculiarity implies an infinite-derivative inflection point of the DOS curve at $E=\Delta_0$ with square-root behavior as $E$ deviates from $\Delta_0$. The coefficients of this dependence are different at $E < \Delta_0$ and $E > \Delta_0$, so the peculiarity is asymmetric. The talk is based on the paper [Ya.V. Fominov, A.A. Mazanik, M.V. Razumovskiy, Phys. Rev. B 100, 224513 (2019)].

Formation of unusual textures of polarization is imminent for nano-scale ferroelectric samples, films, rods, and granules, where the depolarization surface effects play the crucial role. The topologically protected stability of such textures and security of information storage is coming from polarization vorticity, provided by condition of absence of the energetically-unfavorable depolarization charge. The endurance of ferroelectric formations with respect to high-energy irradiation makes them ideal for the aerospace industry, and the periodic domain walls structures can be used as a platform for terahertz radiation generators and detection devices. Polarization domains that alternate the surface charge distribution can be formed in ferroelectric thin films as an effective mechanism to confine the depolarization field to the near-surface layer and diminish the depolarization energy. However their existence have long been considered as barely possible until the direct theoretical predictions [1-3] and experimental evidences [4-6] in thin oxide-based superlattices. Very recently we have demonstrated that the effective capacitance of ferroelectric layers with domains is negative [7]. This effect is explained by the opposite orientation of the depolarizing field with respect to the field-induced averaged polarization. This phenomenon is currently considered as the platform for realization of the dissipation-free high performance nano-circuits [8]. Moreover, in sub-THz region the resonance plasmonic effect can be induced by oscillating domain walls [9] and can be suitable for design of the ultra-small low-energy THz chips. Multi-vortex [10] and skyrmion [11] states can be formed inside ferroelectric cylindrical nano-dots and nanorods to reduce the depolarization energy. We study the stability of such states and demonstrate that the topological class of the most stable topological excitations can be driven by the geometrical and electrical parameters of the system, external field and temperature. We target the multi-domain and topological excitations in FE nanodots as a platform for IT-secured multivalued logic units, breaking ground for neuromorphic computing [12,13].

[1] A. M. Bratkovsky and A. P. Levanyuk, Phys. Rev. Lett. 84, 3177 (2000).
[2] V. A. Stephanovich, I. A. Luk'yanchuk, and M. G. Karkut, Phys. Rev. Lett., 94, 047601 (2005)
[3] I. Luk'yanchuk, L. Lahoche, and A. Sene, Phys. Rev. Lett., 102, 147601 (2009)
[4] S. K. Streiffer, J. A. Eastman, D. D. Fong et al., Phys. Rev. Lett. 89, 067601 (2002);
[5] S. O. Hruszkewycz, M. J. Highland, et al., Phys. Rev. Lett.110, 177601 (2013).
[6] Yadav, A. K., Nelson,et al.. Nature, 530 (7589), 198. (2016)
[7] P. Zubko, M. Hadjimichael, S. Fernandez-Pena, A. Sené, I. Luk’yanchuk, J.-M. Triscone & J. Íñiguez, Nature, 534, 524 (2016)
[8] Khan, A. I., Chatterjee, K., Wang B. et al. Nature Materials 14, 182–186 (2015).
[9] I. Luk'yanchuk, A.Pakhomov, A.Sené, A. Sidorkin, V. Vinokur, arXiv:1410.3124
[10] G. Pascoli L. Lahoche, I. Luk'yanchuk, Integrated Ferroelectrics, 99, 60 (2008)
[11] L Baudry, A Sené, IA Luk'yanchuk, L Lahoche, and JF Scott, Phys. Rev. B 90, 024102 (2014)
[12] P.-W. Martelli, S. M. Mefire, I. Luk'yanchuk, Europhys. Lett. 111, 50001 (2015)
[13] Baudry, L., Lukyanchuk, I. & Vinokur, V. M. Sci. Rep. 7: 42196 (2017)

Algoritm kvantovogo adiabaticheskogo nestrukturirovannogo poiska - odin iz nemnogikh algoritmov kvantovoi adiabaticheskoi optimizatsii, dlya kotorykh dokazany teoremy o tom, chto oni rabotayut znachitel'no bystree, chem ikh klassicheskie analogi. V svyazi s tem, chto dlya adiabaticheskikh kvantovykh vychislenii v nastoyashchee vremya otsutstvuyut teoremy ob otkazoustoichivosti, garantiruyushchie ustoichivost' takikh algoritmov k oshibkam, izuchenie vliyaniya vozmozhnykh defektov pri ikh vypolnenii na rezul'tat vychislenii imeet nauchnoe i prakticheskoe znachenie. My izuchaem ustoichivost' algoritma k sleduyushchim trem tipam defektov: netochnost' v vypolnenii interpolyatsionnogo grafika, nalichie gaussovogo shuma v gamil'toniane, vzaimodeistvie s teplovym okruzheniem. Pokazano, chto kvadratichnoe uskorenie algoritma nestrukturirovannogo poiska, voobshche govorya, ne yavlyaetsya ustoichivym pri nalichii lyubogo iz vysheperechislennykh defektov. V nekotorykh sluchayakh my nakhodim, chto ustoichivost' algoritma privodit k nerealistichnym trebovaniyam dlya zavisimosti sily istochnikov shuma ot razmera sistemy, neobkhodimoi dlya sokhraneniya kvadratichnogo uskoreniya.
[1] M. Slutskii, T. Albash, L. Barash, I. Hen, New Journal of Physics, 21, 113025 (2019), https://dx.doi.org/10.1088/1367-2630/ab51f9

Vychislenie plotnosti sostoyanii sistem s sil'no peresechennymi landshaftami svobodnoi energii yavlyaetsya izvestnoi slozhnoi i aktual'noi zadachei vo mnogikh oblastyakh fiziki, ot spinovykh stekol do biopolimerov. Takzhe, chislennoe opredelenie plotnosti sostoyanii nedavno stalo instrumentom dlya testirovaniya korrektnosti raboty ustroistv dlya kvantovogo otzhiga, pozvolyayushchikh delat' vyborku. Ispol'zovanie standartnykh podkhodov mozhet privodit' k lozhnoi skhodimosti vychislenii k metastabil'nym minimumam, i nalichie etoi problemy chrezvychaino slozhno obnaruzhit' v protsesse vychislenii. My predlagaem metod vyborki, osnovannyi na algoritme otzhiga populyatsii, usovershenstvovannom pri pomoshchi mul'ti-gistogrammnogo analiza. My issleduem proizvoditel'nost' predlozhennogo metoda dlya spinovykh stekol i demonstriruem vozmozhnost' v ryade sluchaev preodolet' problemu oshibochnogo opredeleniya plotnosti sostoyanii, prisushchuyu drugim metodam entropiinoi vyborki. Eto privodit v ryade sluchaev k znachitel'nomu preimushchestvu nashego metoda, pozvolyayushchemu poluchit' vernyi otvet za znachitel'no men'shee vremya, po sravneniyu s drugimi metodami, chto mozhet okazat'sya poleznym dlya obnaruzheniya novoi fiziki pri pomoshchi komp'yuternogo modelirovaniya. Novyi metod pozvolyaet izbezhat' ryada nedostatkov, prisushchikh izvestnym drugim metodam, i on mozhet byt' primenen k shirokomu klassu sistem bez dopolnitel'nykh razbienii na energeticheskie okna i sshivok. Sravnitel'noe testirovanie effektivnosti metodov opredeleniya plotnosti sostoyanii bylo proizvedeno pri pomoshchi primeneniya neskol'kikh skhem, pozvolyayushchikh tochno nakhodit' stepeni vyrozhdeniya energeticheskikh urovnei dlya testiruemykh obraztsov modeli Edvardsa-Andersona.
[1] L. Barash, J. Marshall, M. Weigel, I. Hen, New Journal of Physics, 21, 073065 (2019).

We study the low-energy physics of a chain of Majorana fermions in the presence of interaction and disorder, emphasizing the difference between Majoranas and conventional (complex) fermions. While in the noninteracting limit both models are equivalent (in particular, belong to the same symmetry class BDI and flow towards the same infinite-randomness critical fixed point), their behavior differs drastically once interaction is added. Our density-matrix renormalization group calculations show that the complex-fermion chain remains at the noninteracting fixed point. On the other hand, the Majorana fermion chain experiences a spontaneous symmetry breaking and localizes for repulsive interaction. To explain the instability of the critical Majorana chain with respect to a combined effect of interaction and disorder, we consider interaction as perturbation to the infinite-randomness fixed point and explore correlations of wave functions that enter interaction matrix elements. Our numerical and analytical results exhibit a rich structure of critical eigenstate correlations. This allows us to identify a relevant interaction operator that drives the Majorana chain away from the infinite-randomness fixed point. For the case of complex fermions, the interaction is irrelevant.

We will review the advances and challenges in the field of quantum combinatorial optimization and closely related problem of low-energy eigenstates and coherent dynamics in transverse field quantum spin glass models. We will discuss the role of collective spin tunneling that gives rise to bands of delocalized non-ergodic quantum states providing the coherent pathway for the population transfer (PT) algorithm: the quantum evolution under a constant transverse field that starts at a low-energy spin configuration and ends up in a superposition of spin configurations inside a narrow energy window. We study the transverse field induced quantum dynamics of the following spin model: zero energy of all spin configurations except for a small fraction of spin configuration that form a narrow band at large negative energy. We use the cavity method for heavy-tailed random matrices to obtain the statistical properties of the low-energy eigenstates in an explicit analytical form. In a broad interval of transverse fields, they are non-ergodic, albeit extended giving rise to a qualitatively new type of quantum dynamics. For large transverse fields »1 the typical runtime of PT algorithm $\sim \sqrt{2^n / \Omega e^r}$ scales with n and Ω as that of the Grover’s quantum search, except for the small correction to the exponent θ ≈ 1/(2). The model we consider is non-integrable. As a result, our PT protocol does not require any fine-tuning of and may be initialized in a computational basis state. We argue that our approach can be applied to study PT protocol in other optimization problems with the potential quantum advantage over classical algorithms.

A hallmark of the phase diagrams of quantum materials is the existence of multiple electronic ordered states. In many cases those are not independent, competing phases, but instead display a complex intertwinement. In this talk, we focus on a realization of intertwined orders with a fluctuation-driven vestigial phase characterized by a composite order parameter. In other words, we are investigating the condensation of fluctuations.
We demonstrate that this concept naturally explains the nematic state in iron-based superconductors and nematic superconductivity in doped topological insulators. In addition we propose a natural mechanism for charge 4e superconductivity with half flux quanta. We present a formalism that provides a framework to understand the complexity of quantum materials based on symmetry, largely without resorting to microscopic models.

Iz-za apparatnykh ogranichenii sushchestvuyushchie kvantovye protsessory sposobny proizvodit' lish' opredelennyi nabor unitarnykh operatsii nad odnim ili dvumya kvantovymi bitami v techenie konechnogo promezhutka vremeni, posle kotorogo ustroistvo teryaet kogerentnost'. Chtoby ispol'zovat' podobnye ustroistva dlya simulyatsii proizvol'nogo vida gamil'tonianov, neobkhodimo stroit' priblizheniya, pozvolyayushchie s pomoshch'yu dostupnykh operatsii vosproizvesti proizvol'nyi operator evolyutsii i pri etom ispol'zuyushchie kak mozhno men'she obrashchenii k kvantovomu ustroistvu.

Izvestno neskol'ko printsipial'no razlichnykh algoritmov postroeniya podobnykh priblizhenii, i v dannom obzore my rassmotrim naibolee aktivno izuchaemye:

• metod Suzuki-Trotter, osnovannyi na khoroshem priblizhenii eksponenty ot summy ermitovykh operatorov cherez eksponenty ot kazhdogo iz chlenov summy,
• pryamoe razlozhenie eksponenty operatora evolyutsii v ryad Teilora po vremeni evolyutsii,
• metod Quantum Signal Processing, osnovannyi na effektivnom metode simulyatsii polinomov ot zadannogo ermitovogo operatora, chto zatem ispol'zuetsya dlya polinomial'noi approksimatsii eksponenty ot operatora evolyutsii.

Razvitie tekhnologii proizvodstva i izmereniya sverkhprovodyashchikh kubitov v Rossii uzhe pozvolyaet sozdavat' mnogokubitnye svyazannye sistemy, iz kotorykh mozhno delat' razlichnye analogovye i tsifrovye simulyatory. Poluchennyi v sozdanii dvukhkubitnykh geitov opyt pokazal nam napravlenie dlya dal'neishego razvitiya v etoi sfere: kakie tipy geitov neobkhodimo ispol'zovat' i uluchshat', kak vyklyuchat' ostatochnoe ZZ vzaimodeistvie vo vremya prostaivaniya kubitov. Ya predstavlyu nashi rezul'taty i rasskazhu o potentsial'nykh sposobakh prodvizheniya v etikh oblastyakh.

We provide analytic formulas decribing the effect of small loss/gain on the recurrence of anomalous waves in the focusing Nonlinear Schrodinger equation. We show that very small loss or gain essentially affects the statistics and the character of the recurrence. In particular, our formulas explains the results of numerical simulations from the paper by O. Kimmoun, H.C. Hsu, H. Branger, M.S. Li, Y.Y. Chen, C. Kharif, M. Onorato, E.J.R. Kelleher, B. Kibler, N. Akhmediev, A. Chabchoub (2016).

In the talk, we focus on the physics of magneto-excitons in a quantum Hall insulator at the filling factor of 2. The simplest realizations are magneto-excitons formed by an electron promoted from the occupied zeroth Landau level to the empty first Landau level and by the vacancy under the Fermi level. There are two magneto-excitons: a spin-singlet with total spin S = 0; and a spin-triplet (CSFE) with total spin S = 1. The first one is magneto-plasmon which decays with the emission of a photon. In contrast, the CSFE is not radiatively active owing to electron spin conservation and its energy is lower than the cyclotron energy. Consequently, spin-triplet magneto-excitons exhibit relaxation time reaching up to 900 us. We also discovered condensation of excitons by measurement of exciton lifetime in a temperature range of 0.5–1.5 K. Here we report on spin exciton transfer at distance exceeding 200 μm by pump-probe photo-luminescence measurements and photo-resonant reflection. These effects exhibit threshold both in excitation power and temperature.

The experimental studies on CSFE ensembles that have to obey the Bose-Einstein statistics signal the emergence of an excitonic coherent phase. In the present paper, the theory is developed of the weakly interacting Bose gas of spin-cyclotron excitations in terms of a virial correction to the single magnetoexciton energy. The condition for a coherent-incoherent phase transition is discussed. It is expected to be strongly related to the studied long-distant inter-excitonic correlations. The results obtained theoretically are discussed in terms of their agreement with specific experimental data.

When an ultrashort laser pulse of visible light is absorbed by a solid, mainly the electrons in the material are excited. In metals, free electrons in the conduction band can directly absorb photons. In semiconductors and dielectrics, on the other hand, a band gap has to be overcome first, as almost no free electrons are present at room temperature in the unexcited material. Due to this excitation, the electronic system, or the so-called electron-hole plasma, is in a nonequilibrium state. A sequence of different relaxation processes transfers the material into a new equilibrium. Depending on the interaction associated with the particular relaxation process, it occurs on a characteristic timescale. On the basis of complete Boltzmann-type collision integrals, we calculate the transient distribution functions of electrons and phonons in different materials. We consider electron-electron interaction, different ionization processes, as well as electron-phonon coupling. By that we trace the relaxation cascade of nonequilibrium electrons after ultrafast heating. Distinct material properties enter through the density of states of the electrons in the conduction band. We study in particular noble metals, dielectrics and ferromagnets. In noble metals and ferromagnets, d-electrons play an important role, whereas in dielectrics two separated bands govern the dynamics and the ionization state may differ from. We show, that the electron distributions deviate from Fermi distributions for timescales up to a few picoseconds. While the initial thermalization within one band has an intrinsic timescale of typically only a few tens of femtoseconds, nonequilibrium occupations of the different bands as well as continous electron-phonon coupling can drive the conduction electrons out of equilibrium for much longer times [1, 2]. We present in detail the mutual influence of different interaction and relaxation processes.
[1] N. Brouwer and B. Rethfeld, Phys. Rev. B 95, 245139 (2017). [2] S.T. Weber and B. Rethfeld, Phys. Rev. B 99, 174314 (2019).

The report will provide an overview of the results so far obtained in the problem of describing the geometry of level lines of quasiperiodic functions on a plane and problems associated with it. In particular, we will consider cases of quasiperiodic functions on a plane with different numbers of quasiperiods, as well as features of the behavior of trajectories of dynamical systems associated with such functions (and also some of their generalizations). As can be shown, in many interesting cases, the trajectories of such systems can be represented by a finite number of different types corresponding to various nontrivial sets in the parameter space of such systems. As an example of dividing the parameter space into such sets, one can address to the division of the angular diagrams of the conductivity of metals in strong magnetic fields into a finite number of complexity classes.

Using the symmetry arguments we show that in many metals with antiferromagnetic ordering the effective g-factor of charge carries, measured from magnetic quantum oscillations, is exactly zero. The experimental study of this effect is performed in several compounds and compared with the proposed theory. We find that the Néel state of the layered organic conductor κ-(BETS)₂FeBr₄ shows no spin modulation of the Shubnikov-de Haas oscillations, contrary to the paramagnetic state of the same material. This is evidence of spin degeneracy of Landau levels -- a direct manifestation of the generic Zeeman spin-orbit coupling, predicted for antiferromagnetic conductors. Likewise, we find no spin modulation in the angle dependence of the slow Shubnikov-de Haas oscillations in the optimally electron-doped cuprate Nd_2−xCe_xCuO₄. This points to the presence of Néel order in this superconductor even at optimal doping.

We calculate the electron susceptibility of rare-earth tritelluride compounds RTe₃ as a function of temperature, wave vector, and electron-dispersion parameters. Comparison of the results obtained with the available experimental data on the transition temperature and on the wave vector of a charge-density wave in these compounds allowed us to make predictions about the evolution of electron-dispersion parameters with the variation of the atomic number of rare-earth elements (R). Our measurements of the Hall coefficient in RTe₃ compounds reveal a strong hysteresis between cooling and warming in the low temperature range where a second unidirectional charge density wave (CDW) occurs. We propose that this effect may result from the interplay between two instabilities: band crossing of the Te p_x and p_y orbitals at the Fermi level and CDW, which have a close energy gain and compete. Calculation of the electron susceptibility at the CDW wave vector with and without band anticrossing reconstruction of the electron spectrum yields a satisfactory estimation of the temperature range of the hysteresis in the Hall effect measurements.
[1] P.A. Vorobyev, P.D. Grigoriev, K.K. Kesharpu and V.V. Khovaylo, Materials 12, 2264 (2019).
[2] P.D. Grigoriev, A.A. Sinchenko, P.A. Vorobyev, A. Hadj-Azzem, P. Lejay, A. Bosak, P. Monceau, Phys. Rev. B 100, 081109(R) (2019).

Effekt blizosti v gibridnykh sistemakh sverkhprovodnik-normal'nyi metall okazyvaet sushchestvennoe vliyanie na kogerentnye kolebaniya sverkhprovodyashchego parametra poryadka Δ, izvestnye kak mody Khiggsa. Standartnaya moda Khiggsa s chastotoi 2Δ ispytyvaet zatukhanie iz-za utechki kvazichastits iz sverkhprovodnika v normal'nyi metall. Pomimo etogo iz-za kogerentnogo tunnelirovaniya elektronov mezhdu sverkhprovodnikom i normal'nym metallom poyavlyayutsya dve dopolnitel'nye khiggsovskie mody s chastotami, opredelyaemymi pervichnoi shchel'yu Δ i navedennoi shchel'yu v normal'nom metalle. Eti tri mody opredelyayut asimptoticheskoe povedenie sverkhprovodyashchego parametra poryadka, vozmushchennogo elektromagnitnym impul'som libo rezkim izmeneniem parametrov sistemy. Issledovanie mod Khiggsa v gibridnykh strukturakh vazhno dlya ponimaniya dinamicheskikh svoistv sverkhprovodyashchikh priborov, osnovannykh na effekte blizosti.

Motivated by recent experimental interest in 'random anti-lasing' (e.g. K. Pichler et al. Nature 567, 351 (2019)) I consider manifestations of zeroes of scattering matrices in wave-chaotic cavities. In particular, I will introduce the notion of Reflection Time Difference playing the same role for the S-matrix zeroes as the Wigner time delay plays for the S-matrix poles, and a possibility of its experimental measurement. I will then discuss how statistics of complex zeroes of scattering matrix entries can be described in the framework of RMT-based model of resonance scattering.
Presentation will be based on papers arXiv:1908.06920 and J. Phys. A 50, 30LT01 (2017).

The structure of the edge of a QHE edge is constrained, but not dictated, by the topology of the bulk. Particularly interesting is the class of hole-conjugate fractional QH states. For such states the edge hosts counter-propagating modes that are responsible for quantized electrical and thermal conductance. In the coherent quantum limit renormalized edge modes emerge, which may involve neutral modes with non-trivial exchange statistics. I will discuss the behavior of topology-influenced transport coefficient both in the coherent and the fully equilibrated regimes, topological classification of non-equilibrium shot noise, and the relation to recent experiments.

Otchet ob uchastii v konferentsii "NANO-2019: Limits of Nanoscience and Nanotechnologies" (Kishinev, Moldaviya).

Provedeno teoreticheskoe soprovozhdenie novoi serii eksperimentov po izucheniyu effekta sverkhprovodyashchego tripletnogo spinovogo klapana v sisteme tipa FFS (gde F — ferromagnetik, S — sverkhprovodnik). Effekt sostoit v tom, chto kriticheskaya temperatura T_c sistemy zavisit ot vzaimnoi orientatsii namagnichennostei dvukh ferromagnetikov. V eksperimente v kachestve srednego ili vneshnego F sloya byl vzyat splav Geislera Co₂Cr_1-xFe_xAl, magnitnye svoistva kotorogo zaviseli ot uslovii prigotovleniya. Dlya ob'yasneniya poluchennykh rezul'tatov byla sformulirovana teoriya, uchityvayushchaya proizvol'nye obmennye polya F sloev i proizvol'nye parametry granits v ramkakh kvaziklassiki v diffuznom predele.
Doklad osnovan na sleduyushchikh rabotakh:
[1] A.A. Kamashev, N.N. Garif’yanov, A.A. Validov, J. Schumann, V. Kataev, B. Büchner, Ya.V. Fominov, I.A. Garifullin, "Superconducting switching due to a triplet component in the Pb/Cu/Ni/Cu/ Co₂Cr_1-xFe_xAl _y spin-valve structure", Beilstein J. Nanotechnol. 10, 1458 (2019).
[2] A.A. Kamashev, N.N. Garif’yanov, A.A. Validov, J. Schumann, V. Kataev, B. Büchner, Ya.V. Fominov, I.A. Garifullin, "Superconducting spin-valve effect in heterostructures with ferromagnetic Heusler alloy layers", napravleno v Phys. Rev. B.
[3] A.A. Kamashev. N.N. Garif'yanov, A.A. Validov, I. Shumann, V. Kataev, B. Byukhner, Ya.V. Fominov, I.A. Garifullin, Pis'ma v ZhETF 110, 325 (2019).

We compute the absolute Poisson's ratio $\nu$ and the bending rigidity exponent $\eta$ of a free-standing two-dimensional crystalline membrane embedded into a space of large dimensionality $d = 2 + d_c$, $d_c \gg 1$. We demonstrate that, in the regime of anomalous Hooke's law, the absolute Poisson's ratio approaches material independent value determined solely by the spatial dimensionality $d_c$: $\nu = -1 +2/d_c-a/d_c^2+\dots$ where $a\approx 1.76\pm 0.02$. Also, we find the following expression for the exponent of the bending rigidity: $\eta = 2/d_c+(73-68\zeta(3))/(27 d_c^2)+\dots$. These results cannot be captured by self-consistent screening approximation.

It is shown that the anomalous elasticity of membranes affects the profile and thermodynamics of a bubble in van der Waals heterostructures. Our theory generalizes the non-linear plate theory as well as membrane theory of the pressurised blister test to incorporate the power-law scale dependence of the bending rigidity and Young's modulus of a two-dimensional crystalline membrane. This scale dependence caused by long-ranged interaction of relevant thermal fluctuations (flexural phonons), is responsible for the anomalous Hooke's law observed recently in graphene. It is shown that this anomalous elasticity affects dependence of the maximal height of the bubble on its radius and temperature. We identify the characteristic temperature above which the anomalous elasticity is important. It is suggested that for graphene-based van der Waals heterostructures the predicted anomalous regime is experimentally accessible at the room temperature.

The weakly dissipating dielectric spheres (glass, quartz, etc.) permit to realize high order Fano resonances for internal Mie modes. These resonances for specific values of the size parameter yield field-intensity enhancement factors on the order of 10⁴–10⁷, which can be directly obtained from analytical calculations. These “super-resonances” provides magnetic nanojets with giant magnetic fields, which is attractive for many applications.

Classical many body interacting systems are typically chaotic (nonzero Lyapunov exponents) and their microcanonical dynamics ensures that time averages and phase space averages are identical (ergodic hypothesis). In proximity to an integrable limit the long- or short-range properties of the network of nonintegrable action space perturbations define the finite time relaxation properties of the system towards Gibbs equilibrium. I will touch upon few analytical results including the KAM theorem, and review a number of computational studies which originate from the pioneering work of Enrico Fermi, John Pasta, Stanislaw Ulam and Mary Tsingou. I will then focus on short range networks which lead to a dynamical glass (DG), using a classical Josephson junction chain in the limit of large energy densities or small Josephson energies. Close to these limits the Josephson coupling between the superconducting grains induces a short-range nonintegrable network in the corresponding action space. I will introduce a set of quantitative measures which lead to the Lyapunov time TΛ, the ergodization time TE, and to a diffusion constant D. In the DG the system fragments into large patches of nonresonant ’integrable’ grains of size l separated by triplets of resonant chaotic patches, all surviving over large times. TE sets the time scale for chaotic dynamics in the triplets. Contrary, TE ≈ l2/D is the much larger time scale of slow diffusion of chaotic triplets. The DG is a generic feature of weakly non-integrable systems with a short range coupling network in action space, and expected to be related to nonergodic quantum metallic states of quantum many-body systems in proximity to a many-body localization phase.

One-dimensional quantum liquids are commonly treated using the Luttinger liquid theory, which neglects elementary excitations with high energies. In this approximation, in addition to the number of particles, energy, and momentum the liquid possesses another conserved quantity - J, which may be interpreted as the difference between the numbers of right- and left- moving particles. Beyond the Luttinger liquid approximation J is no longer conserved, but its relaxation time is exponentially long at low temperatures. I will show that as a result, one-dimensional quantum liquids exhibit two-fluid behavior. In particular in a wide frequency interval they support two sound modes that are similar to the first and second sound in superfluid He.

We show that derivatives of thermal Hall conductance of a 2d lattice quantum system with respect to parameters of the Hamiltonian are well-defined bulk quantities provided correlators of local observables are short-range. This is despite the fact that thermal Hall conductance itself has no meaning as a bulk transport coefficient. We use this to define a relative topological invariant for gapped 2d lattice quantum systems at zero temperature. Up to a numerical factor, it can be identified with the difference of chiral central charges for the corresponding edge modes. This establishes bulk-boundary correspondence for the chiral central charge. We also show that for Local Commuting Projector Hamiltonians relative thermal Hall conductance vanishes identically, while for free fermionic systems it is related to the electric Hall conductance via the Wiedemann-Franz law.

Hydrodynamic charge transport is at the center of recent research efforts. Of particular interest is the nondissipative Hall viscosity, which conveys topological information in clean gapped systems. The prevalence of disorder in the real world calls for a study of its effect on viscosity. Here we address this question, both analytically and numerically, in the context of a disordered noninteracting 2D electrons. Analytically, we employ the self-consistent Born approximation, explicitly taking into account the modification of the single-particle density of states and the elastic transport time due to the Landau quantization. The reported results interpolate smoothly between the limiting cases of weak (strong) magnetic field and strong (weak) disorder. In the regime of weak magnetic field our results describes the quantum (Shubnikov-de Haas type) oscillations of the dissipative and Hall viscosity. For strong magnetic fields we characterize the effects of the disorder-induced broadening of the Landau levels on the viscosity coefficients. This is supplemented by numerical calculations for a few filled Landau levels. Our results show that the Hall viscosity is surprisingly robust to disorder.

At a superconductor interface with a ferromagnetic insulator (FI), the FI acts to induce a local exchange field within the S layer, which in the presence of spin-orbit interaction promotes a phase- modulated superconducting state. Here we demonstrate that within a thin superconducting loop that is partially proximitized by a FI, spontaneous currents form with a magnetization-orientation-dependent chirality with sizable shifts in LittleParks oscillations. Furthermore, the critical temperature of the loop is also magnetization-orientation-dependent and conversely, the superconducting transition itself may influence the magnetization direction. More generally, the superconducting region above the FI serves as a “phase battery” and so offers a new device concept for superconducting spintronics.

Venue: NUST MISIS, conference hall № B-734 (Main Building, 7th floor)

Entrance for seminar participants who are not students, graduate students or employee of MISIS, will be provided upon presentation of the passport upon prior registration for the seminar. Registration is opened till 14:00 June, 5.

To register https://smm.misis.ru/en/event/xxi-shmidt-seminar-on-superconductivity/

In the 90’s, an impressive series of works by theoreticians from the Landau Institute on electrons shot noise in quantum conductors [1] and on the statistics of transfer of electrons [2] has leaded to the emergence of the beautiful concept of minimal excitation states [3-5]. These minimal excitation states can be generated by applying voltage pulses on the contact of a conductor to inject short single electron pulses. These states show minimal noise and provide a convenient and clean single electron source for electron optics whose aim is to perform quantum optics tasks with electrons instead of photons. The minimal excitations states, now called levitons, have been produced in recent experiments [6] and have triggered a large number of theoretical works. They have enabled Hong Ou Mandel like experiments [6] with electrons and single electron quantum Tomography [7]. Extension to fractionally charged anyons is possible.
At the root of the minimal excitation property is a specific single side band modulation of the electron wave by the Lorentzian voltage pulse. This property can be applied to classical electromagnetic or acoustic waves for applications in digital communication [8] or in music sound synthesis.
[1] G. B. Lesovik, JETP Letters, 49 (9), 592-594 (1989).
[2] L.S. Levitov, G.B. Lesovik, Charge-transport statistics in quantum conductors, JETP Lett., 55 (9), 555-559 (1992).
[3] A. Ivanov, H.W. Lee, L.S. Levitov, Coherent states of alternating current, Phys. Rev. B 56(11), 6839-6850 (1997); cond-mat/9501040
[4] L.S. Levitov, H. Lee, G.B. Lesovik, Electron Counting Statistics and Coherent States of Electric Current, J. Math. Phys., 37(10), 4845-4866 (1996); cond-mat/9607137.
[5] J. Keeling, I. Klich, and L. S. Levitov, Minimal Excitation States of Electrons in One-Dimensional Wires, Phys. Rev. Lett. 97, 116403 (2006).
[6] Minimal-excitation states for electron quantum optics using levitons, J. Dubois, T. Jullien, F. Portier, P. Roche, A. Cavanna, Y. Jin, W. Wegscheider, P. Roulleau & D. C. Glattli, Nature, 502, 659–663 (2013).
[7] Quantum tomography of an electron, T. Jullien, P. Roulleau, B. Roche, A. Cavanna, Y. Jin & D. C. Glattli, Nature, 514, 603–607 (2014).
[8] Power Spectrum Density of Single Side Band CPM Using Lorenztian Frequency Pulses, Haïfa Farès, D. Christian Glattli, Yves Louet, Jacques Palicot, Preden Roulleau, and Christophe Moy, IEEE Wireless Communications Letters, 6 (6), 786-789, (2017).

Anyons occur in two-dimensional electron systems as excitations with fractional charge in the topologically ordered states of the fractional quantum Hall effect (FQHE). Their dynamics are of utmost importance for topological quantum phases and possible decoherence-free quantum information approaches, but observing these dynamics experimentally is challenging. Here, we report on a dynamical property of anyons: the long-predicted [1] Josephson relation f_J = e*V/h for charges e* = e/3 and e/5, where e is the charge of the electron and h is Planck’s constant [2].

The relation manifests itself as marked signatures in the dependence of photo-assisted shot noise (PASN) [3-4] on voltage V when irradiating contacts at microwaves frequency f_J [4]. The validation of FQHE PASN models indicates a path toward realizing time-resolved anyon sources based on levitons. The method may be of interest to provide a demonstration of anyonic statistics, a pre-requisite for topological quantum computing.

[1] X. G. Wen, Edge transport properties of the fractional quantum Hall states and weak-impurity scattering of a one-dimensional charge-density wave, Phys. Rev. B 44, 5708–5719 (1991). [2] M. Kapfer, P. Roulleau, M. Santin, I. Farrer, D. A. Ritchie, and D. C. Glattli, A Josephson relation for fractionally charged anyons, Science 363, 846–849 (2019). [3] G. B. Lesovik and L. S. Levitov, Noise in an ac biased junction: Nonstationary Aharonov-Bohm effect, Phys. Rev. Lett. 72, 538–541 (1994). [4] C. de C. Chamon, D. E. Freed, and X. G. Wen, Tunneling and quantum noise in one-dimensional Luttinger liquids, Phys. Rev. B 51, 2363–2379 (1995).

Kvantovye vychisleniya v poslednee vremya yavlyayutsya aktivno razvivayushcheisya oblast'yu prikladnoi fiziki i teorii informatsii. Odnim iz mnogoobeshchayushchikh primenenii vozmozhnostei segodnyashnikh kvantovykh komp'yuterov yavlyayutsya kvantovyi simulyatsii fizicheskikh sistem na sistemakh kubitov. Odnako, sushchestvennymi problemami na puti k fizicheski korrektnym simulyatsiyam yavlyayutsya trotterovskaya oshibka diskretizatsii i razlichnye effekty shuma. V etom doklade budet predlozhena prostaya tochno reshaemaya model' sistemy spinov, pozvolyayushchaya izuchit' osnovnye effekty trotterovskoi oshibki i dayushchaya vozmozhnost' dlya izucheniya effektov shuma.

The last few years have seen an explosion of interest in hydrodynamic effects in interacting electron systems in ultra-pure materials. One such material, graphene, is not only an excellent platform for the experimental realization of the hydrodynamic flow of electrons, but also allows for a controlled derivation of the hydrodynamic equations on the basis of kinetic theory. The resulting hydrodynamic theory of electronic transport in graphene yields quantitative predictions for experimentally relevant quantities, e.g. viscosity, electrical conductivity, etc. In this talk I will review recent theoretical advances in the field, compare the hydrodynamic theory of charge carriers in graphene with relativistic hydrodynamics and recent experiments, and discuss applications of hydrodynamic approach to novel materials beyond graphene.

Video (v svyazi s oshibkoi video zapisano ne do kontsa)

Pokazano, chto topologicheskoe sverkhtekuchee sostoyanie s p-sparivaniem (p_x + i p_y) mozhet byt' realizovano v dvumernoi opticheskoi reshetke fermionnykh polyarnykh molekul. Dlya sistem s odnosloinoi i dvukhsloinoi geometriei vychislennye temperatury fazovykh perekhodov v sverkhtekuchee sostoyanie okazalis' eksperimental'no dostizhimymi, poryadka desyatkov nanokel'vinov. [A.K. Fedorov, S.I. Matveenko, V. I. Yudson, G.V. Shlyapnikov , "Novel p-wave superfluids of fermionic polar molecules", Sci. Rep. 6, 27448; (2016).]
Issledovana chislenno i analiticheski fazovaya diagramma dvusloinoi sistemy fermionnykh polyarnykh molekul s disbalansom molekulyarnykh plotnostei v sloyakh. Dlya disbalansa (effektivnogo magnitnogo polya), prevyshayushchego kriticheskoe znachenie, sistema perekhodit pri dostatochno nizkikh temperaturakh iz sostoyaniya odnorodnoi sverkhtekuchei zhidkosti v sostoyaniya Larkina-Ovchinnikova-Ful'de-Ferrella s periodicheskoi strukturoi parametra poryadka. V otlichie ot sluchaya kontaktnogo vzaimodeistviya s singletnym sparivaniem, dipol'-dipol'noe vzaimodeistvie generiruet nenulevuyu tripletnuyu sostavlyayushchuyu parametra poryadka. [Hao Lee, S. I. Matveenko, Daw-Wei Wang, G. V. Shlyapnikov, "Fulde-Ferrell-Larkin-Ovchinnikov state in bilayer dipolar systems", Phys.Rev. A, 96, 061602(R) (2017)].
Issledovana odnomernoi model' dvukhkomponentnogo fermionnogo gaza s sil'nym kontaktnym ottalkivaniem chastits s protivopolozhnym spinom i nelokal'nym prityazheniem fermionov s odinakovym spinom. Model' mozhet byt' eksperimental'no realizovana v sisteme kholodnykh atomov. Pri etom parametry vzaimodeistviya mogut izmenyat'sya v shirokom diapazone s pomoshch'yu vneshnego magnitnogo polya. Ispol'zuya metody bozonizatsii i renormgruppy, naideno osnovnoe sostoyanie sistemy v zavisimosti ot parametrov vzaimodeistviya. Pokazano, chto pri kriticheskom znachenii nelokal'nogo vzaimodeistviya proiskhodit fazovyi perekhod pervogo roda v sostoyanie s nenulevoi namagnichennost'yu. [D. V. Kurlov, S. I. Matveenko, V. Gritsev, G. V. Shlyapnikov, "One-dimensional two-component fermions with contact even-wave repulsion and SU(2) breaking near-resonant odd-wave attraction", Phys. Rev. A, (prinyata v pechat')].

I consider the problem of reconstructing a source vector from its encrypted image corrupted by an additive Gaussian noise. Assuming encryption to be given by a random Gaussian mapping, the reconstruction problem in the framework of the Least Square Scheme turns out to be equivalent to finding the configuration of minimal energy in a certain version of spherical spin glass model. As a measure of the quality of the signal reconstruction one can use the mean overlap between the original signal and its recovered image. Thi overlap is analysed in the framework of Parisi scheme of Replica Symmetry Breaking. If the mapping is quadratic, there exists a threshold in the noise-to-signal ratio beyond which the reconstruction is impossible. The behaviour close to the threshold is controlled by the replica symmetry breaking mechanism and is characterized by a nontrivial exponent 3/4.

Video

We consider an elastic manifold of internal dimension d and length L pinned in a N dimensional random potential and confined by an additional parabolic potential of curvature μ. First we consider N = d = 1 case of a directed polymer and show how counting stationary points of its energy provides an upper bound on the strength of the depinning force. Then we consider a mean-filed limit: first N→∞ at fixed L^d, and then L→∞, and find the mean spectral density ρ(λ) of the Hessian matrix K at the absolute minimum of the energy functional. We show that for a confinement curvature μ exceeding a critical value, the so-called "Larkin mass", the system is replica-symmetric and the Hessian spectrum is always gapped (from zero). The gap vanishes quadratically at approaching the Larkin mass. For smaller curvatures the replica symmetry breaking (RSB) occurs and the Hessian spectrum is either gapped or extends down to zero, depending on whether RSB is 1-step or full. In the 1-RSB case the gap vanishes in all d as fourth power of the distance to the transition. In the full RSB case the gap is identically zero.

The presentation will be based on Y.V. Fyodorov et al., Ann. Phys. 397, 1–64 (2018) and Y.V. Fyodorov and P. Le Doussal, arXiv:1903.07159.

We determine the noise of charge current that is generated by a precessing magnetization of a small itinerant ferromagnet, which is driven by ferromagnetic resonance (FMR) and tunnel-coupled to two normal metal leads. Even when the leads are in equilibrium with each other, i.e. neither voltage nor thermal bias is applied, the electron system is driven out of equilibrium by the precessing magnetization. In turn, a non-equilibrium electron distribution develops in the small ferromagnet. This distribution is governed by the dynamics of the magnetization and determines the (zero-frequency) noise of charge current. We show that this noise can be used to gain information about the magnetization dynamics.

Conventional Anderson localization is due to destructive interference of matter waves described by local random Hamiltonians. Correlations in random diagonal elements of such a Hamiltonian are known to favor delocalization. Recently systems with non-local Hamiltonians become experimentally accessible. We consider two families of such random matrix Hamiltonians with correlations in the long-range hopping terms and demonstrate that localization is enhanced and the wave function ergodicity is progressively degrading as the correlations become stronger.

We review the localization/delocalization criteria of Mott and Anderson and show that the former is the sufficient criterion of weak ergodicity and the latter is the sufficient criterion of localization. The fact that these two criteria are not complimentary is the reason why the non-ergodic extended (multifractal) states may exist when neither the Mott, nor the Anderson criterion is fulfilled.
We suggest a new class of random matrix models (Toeplitz RMT) with translation-invariant hopping integrals and identify the character of eigenfunction and eigenvalue statistics in them. We formulate the principles of level statistics if the type of eigenfunction statistics is known both in the coordinate and in the momentum basis and demonstrate that for the Toeplitz RMT the ergodic delocalization in the coordinate space may coexist with the Poisson level statistics.
Finally, we suggest a matrix-inversion trick that allows to identify uniquely the type of eigenfunction statistics and prove the absence of delocalized states in the bulk of spectrum of long-range Hamiltonians with deterministic (fully correlated) hopping.

Video

My rassmotrim samye obshchie osobennosti uglovykh diagramm provodimosti v normal'nykh metallakh so slozhnymi poverkhnostyami Fermi v prisutstvii sil'nykh magnitnykh polei. Opisanie takikh osobennostei budet osnovano na topologicheskom opisanii dinamicheskoi sistemy, voznikayushchei dlya evolyutsii elektronnykh sostoyanii na poverkhnosti Fermi v prisutstvii vneshnego magnitnogo polya. My rassmotrim uglovye diagrammy provodimosti dlya normal'nykh (monokristallicheskikh) metallov so slozhnymi poverkhnostyami Fermi v prisutstvii sil'nykh magnitnykh polei. Povedenie provodimosti v etom sluchae sil'no zavisit ot napravleniya magnitnogo polya i ustoichivye netrivial'nye rezhimy takogo povedeniya sootvetstvuyut pri etom spetsial'nym zonam ustoichivosti na uglovoi diagramme, otvechayushchim opredelennym (topologicheskim) svoistvam tenzora provodimosti. Kak my pokazhem, v obshchem sluchae mozhno razdelit' takie diagrammy na dva obshchikh tipa, prostye (tip A) i slozhnye (tip B). Nas budut interesovat' pri etom diagrammy vtorogo tipa, obladayushchie ryadom spetsificheskikh osobennostei (beskonechnoe chislo zon ustoichivosti, nalichie khaoticheskikh rezhimov i t.p.), kotorye my rassmotrim bolee podrobno. Po rezul'tatam rabot: ZhETF, t. 151, vyp. 5, 944-973 (2017); ZhETF, t. 152, vyp. 5(11), 1053-1064 (2017) , ZhETF, 154(6), 1183-1210 (2018)

V doklade obsuzhdaetsya svyaz' spetsial'nykh kharakteristik dinamicheskikh sistem na poverkhnostyakh (indeksov Zoricha - Kontsevicha - Forni) s povedeniem provodimosti v metallakh v sil'nykh magnitnykh polyakh. Dannoe rassmotrenie yavlyaetsya vazhnym v sluchae vozniknoveniya naibolee slozhnykh (khaoticheskikh) elektronnykh traektorii na poverkhnosti Fermi, vozmozhnom dlya dostatochno slozhnykh poverkhnostei i spetsial'nykh napravlenii magnitnogo polya. Kak mozhno pokazat', upomyanutye kharakteristiki imeyut neposredstvennoe otnoshenie k povedeniyu magnitoprovodimosti, takim obrazom, mozhno v printsipe govorit' o vozmozhnosti ikh eksperimental'nogo opredeleniya v sootvetstvuyushchikh sluchayakh. Po rezul'tatam raboty: Trudy MIAN, tom 302, (2018) str. 296–315

(po motivam izucheniya stat'i A.Yu. Kitaeva)

Model' SYK (Sachedev-Ye-Kitaev) opisyvaet sistemu sluchaino vzaimodeistvuyushchikh maioranovskikh fermionov bez kvadratichnykh chlenov v gamil'toniane. V predele bol'shogo chisla fermionov (N) i nizkikh temperaturakh (T « J, gde J - kharakternyi masshtab vzaimodeistviya) funktsiya Grina modeli, v sedlovom priblizhenii, imeet ne fermi-zhidkostnoe povedenie G(t) ~ t^(-1/2). Odnako, sedlovye uravneniya obladayut vysokoi simmetriei i dopuskayut zamenu t na proizvol'nuyu monotonnuyu funktsiyu f(t). Takoe reshenie imeet tol'ko SL(2,R) simmetriyu. Ponizhenie simmetrii ot polnoi gruppy reparametrizatsii do SL(2,R) privodit k sushchestovaniyu myagkoi mody, kotoraya stanovitsya sushchestvenna pri NT « J . Funktsiya Grina na samykh bol'shikh vremenakh menyaet svoyu asimptotiku na G(t) ~ t^(-3/2).
V nashei rabote my issleduem vliyanie kvadratichnogo vozmushcheniya na eto povedenie. Naivnoe rassmotrenie sedlovykh uravnenie pokazyvaet, chto na bol'shikh vremenakh fermi-zhidkostnoe povedenie dolzhno vosstanavlivat'sya. Odnako, voznikaet vopros: chto, proizoidet esli eti vremena budut stol' bol'shimi, chto nuzhno uchityvat' fluktuatsii myagkoi mody? Rassmatrivaya vtoroi poryadok teorii vozmushcheniya my pokazyvaem, chto sushchestvuet nenulevoi interval amplitud vozmushchenii, kogda povedenie funktsii Grina ne menyaetsya, sokhranyaya asimptotiku G(t) ~ t^(-3/2). Eto pozvolyaet nadeyat'sya na ispol'zovanie modeli SYK dlya postroeniya kontroliruemoi teorii ne-fermizhidkostnogo povedeniya sil'no vzaimodeistvuyushchikh fermionov.

Postroena teoriya, opisyvayushchaya vzaimodeistvie elektromagnitnogo polya s drozhashchei dispergiruyushchei sredoi. V pervom poryadke po mekhanicheskomu smeshcheniyu vychislena popravka k polyarizuemosti sredy, obuslovlennaya drozhaniem. Pokazano, chto dvizhenie v prostranstve elektricheskogo dipolya privodit k poyavleniyu magnitnogo dipol'nogo i elektricheskogo kvadrupol'nogo momentov. Teoriya primenena dlya opisaniya neuprugogo rasseyaniya sveta na drozhashchikh chastitsakh i membranakh. Ustanovleno, chto kharakter interferentsii elektromagnitnykh voln, izluchennykh razlichnymi mul'tipolyami, opredelyaetsya chastotnoi zavisimost'yu dielektricheskoi pronitsaemosti. V sluchae, kogda ona imeet rezonans, vblizi nego svet rasseivaetsya preimushchestvenno vpered, a vdali ot nego — nazad. Takzhe opisana konversiya polyarizatsii sveta v protsesse neuprugogo rasseyaniya.

A. V. Poshakinskiy and A. N. Poddubny, Phys. Rev. X 9, 011008 (2019).

Pokazano, chto fazovaya diagramma odnoi iz prosteishikh modelei kvantovogo spinovogo stekla – kvantovogo obobshcheniya modeli Derridy sluchainykh urovnei energii – obladaet neergodicheskoi delokalizovannoi fazoi s vremenem relaksatsii, eksponentsial'no dlinnym po chislu spinov n. Kak vremya relaksatsii, tak i ob'em Gil'bertova prostranstva, zanimaemyi mnogochastichnoi volnovoi funktsiei, yavlyayutsya stepennymi funktsiyami polnoi razmernosti Gil'bertova prostranstva N = 2^n. Oba eti pokazateli stepeni naideny v ramkakh priblizhennoi analiticheskoi teorii, poluchennye dlya nikh otvety neplokho soglasuyutsya s rezul'tatami pryamoi chislennoi diagonalizatsii. Poluchennye rezul'taty mogut byt' polezny dlya fizicheskoi realizatsii kvantovogo simulyatora dlya resheniya zadach algoritmicheskoi optimizatsii tipa number partitioning.

The quantum Hall effects belong to the most striking phenomena in condensed matter physics. Despite of intensive theoretical efforts over the last three decades, important aspects of the quantum Hall transitions are still not fully understood. In particular, there is still no consensus concerning the critical field theory and the corresponding scaling properties of the observables near and at the plateau transition.
Notwithstanding this status, the last ten years have seen considerable progress in understanding basic properties of scaling near localization-delocalization transitions that have implications also for the quantum Hall transition. These concern, e.g., the important topic of corrections to scaling, the wavefunction statistics and higher-order multifractality. A brief review of these developments will be offered in the first part of the talk.
The second part of the talk will be devoted to the spin quantum Hall effect, which is a variant of the integer quantum Hall effect (class A) taking place in the Altland-Zirnbauer class C. For this transition several critical exponents are known analytically and can serve as reference points. Therefore, this transition provides an ideal testbed for the qualitative predictions made by analytical theories. Analytical predictions will be confronted with most recent numerical results.

Video

V doklade budet obsuzhdat'sya zadacha ob anomal'nom skeilinge v turbulentnosti. Eto yavlenie proyavlyaetsya v singulyarnom (vozmozhno stepennom) povedenii razlichnykh statisticheskikh velichin, zavisyashchikh ot integral'nogo masshtaba turbulentnosti s beskonechnym kolichestvom nezavisimykh anomal'nykh pokazatelei. I eksperimenty, i chislennoe modelirovanie pokazyvayut, chto otkloneniya ot klassicheskoi teorii Kolmogorova bolee yarko vyrazheny dlya passivnogo perenosa skalyarnykh polei (naprimer, polya temperatury ili plotnosti primesi), chem dlya samogo polya skorosti. Samyi znachitel'nyi progress byl dostignut dlya modeli Kreichnana, gde pole skorostei perenosa yavlyaetsya gaussovym, ne korrelirovannym po vremeni. V protsesse doklada budet podrobno obsuzhdat'sya metod renormgruppy v primenenii k etoi modeli, a takzhe k bolee slozhnym i realistichnym modelyam perenosa.

V ramkakh diagrammnoi tekhniki vyvoditsya analiticheskoe vyrazhenie dlya dispersii kondaktansa neuporyadochennogo obraztsa cherez propagatory, podchinyayushchiesya transportnomu uravneniyu. Vychisleniya osnovany na sootnosheniyakh dlya vershiny Khikami bez ispol'zovaniya diffuzionnogo (gradientnogo) razlozheniya i bornovskogo priblizheniya dlya odnotsentrovogo rasseyaniya. Obsuzhdayutsya prichiny usileniya fluktuatsii pri perekhode ot kvaziballisticheskogo k diffuzionnomu rezhimu transporta.

We consider angular conductivity diagrams for normal (single-crystal) metals with complex Fermi surfaces in the presence of strong magnetic fields. The behavior of conductivity in this case strongly depends on the direction of the magnetic field and the stable nontrivial regimes of this behavior correspond to special zones of stability on the angular diagram corresponding to certain (topological) properties of the conductivity tensor. As we show, in the general case such diagrams can be divided into two general types, simple (type A) and complex (type B). We will be interested in the diagrams of the second type, which have a number of specific features (an infinite number of stability zones, the presence of chaotic regimes, etc.), which we will consider in more detail.

V doklade obsuzhdaetsya svyaz' spetsial'nykh kharakteristik dinamicheskikh sistem na poverkhnostyakh (indeksov Zoricha - Kontsevicha - Forni) s povedeniem provodimosti v metallakh v sil'nykh magnitnykh polyakh. Dannoe rassmotrenie yavlyaetsya vazhnym v sluchae vozniknoveniya naibolee slozhnykh (khaoticheskikh) elektronnykh traektorii na poverkhnosti Fermi, vozmozhnom dlya dostatochno slozhnykh poverkhnostei i spetsial'nykh napravlenii magnitnogo polya. Kak mozhno pokazat', upomyanutye kharakteristiki imeyut neposredstvennoe otnoshenie k povedeniyu magnitoprovodimosti, takim obrazom, mozhno v printsipe govorit' o vozmozhnosti ikh eksperimental'nogo opredeleniya v sootvetstvuyushchikh sluchayakh.

My rassmotrim samye obshchie osobennosti uglovykh diagramm provodimosti v normal'nykh metallakh so slozhnymi poverkhnostyami Fermi v prisutstvii sil'nykh magnitnykh polei. Opisanie takikh osobennostei budet osnovano na topologicheskom opisanii dinamicheskoi sistemy, voznikayushchei dlya evolyutsii elektronnykh sostoyanii na poverkhnosti Fermi v prisutstvii vneshnego magnitnogo polya.
Po rezul'tatam rabot: ZhETF, t. 151, vyp. 5, 944-973 (2017); ZhETF, t. 152, vyp. 5(11), 1053-1064 (2017)

Issledovana dinamika plazmonnogo lazera s raspredelennoi obratnoi svyaz'yu (DFB lazera) na osnove dvumernoi perforirovannoi metallicheskoi plenki. Dlya takoi struktury mozhno vydelit' dva kharakternykh tipa mod. K pervomu iz nikh otnosyatsya mody, chastota kotorykh nakhoditsya v razreshennoi zone, imeyushchie bol'shie izluchatel'nye poteri i vysokii porog generatsii (svetlye mody). Ko vtoromu tipu otnosyatsya mody, chastota kotorykh nakhoditsya na krayu razreshennoi zony, imeyushchie nizkie izluchatel'nye poteri i nizkii porog generatsii (temnye mody). Pokazano, chto kogda pyatno nakachki men'she razmera poverkhnosti DFB lazera, nelineinoe vzaimodeistvie mezhdu modami periodicheskoi plazmonnoi struktury cherez aktivnuyu sredu privodit k novomu effektu, a imenno k kooperatsii mod [1]. Kooperatsiya mod proyavlyaetsya kak generatsiya svetlykh mod s vysokimi poteryami vmesto generatsii temnykh mod s nizkimi poteryami. Pokazano, chto etot effekt imeet mesto v dvumernykh DFB lazerakh i ne proyavlyaetsya v odnomernykh DFB lazerakh. Vzaimodeistvie svetlykh mod voznikaet iz-za neortogonal'nosti lazernykh mod v oblasti nakachki, gde svetlye mody stanovyatsya sinkhronizirovannymi po faze. Kak sledstvie, voznikaet ikh konstruktivnaya interferentsiya. Prodemonstrirovano, chto vsledstvie kooperatsii mod imeet mesto ushirenie diagrammy napravlennosti vyshe poroga generatsii, chto nablyudalos' v nedavnikh eksperimentakh [2].

[1] N.E. Nefedkin, A.A. Zyablovsky, E.S. Andrianov, A.A. Pukhov, and A. P. Vinogradov, ACS Photonics 2018 5(8): p. 3031-3039.
[2] Tenner, V.T., M.J.A. de Dood, and M.P. van Exter, Measurement of the phase and intensity profile of surface plasmon laser emission. ACS Photonics, 2016. 3: p. 942−946.

We analyze the experimental data on inelastic neutron scattering by a thin ~5-atomic-layer film of liquid helium at three different temperatures: T=0.4K, 0.98K and 1.3K. The neutron scattering intensity plots, in addition to the previously know dispersion of phonons and ripplons, suggest a branch of gapped surface excitations with activation energy ~4.5K and the dispersion similar to that expected for surfons -- the bound quantum states of helium atoms above liquid helium surface, proposed and investigated theoretically. These data, probably, provide the first direct experimental confirmation of surfons. Before these surface excitations received only indirect experimental substantiation, based on the temperature dependence of surface tension coefficient and on their interaction with surface electrons. The existence of surfons as an additional type of surface excitations, although being debated yet, is very important for various physical properties of He surface. We also analyze previous numerical results on excitations in liquid helium and argue that surface excitations similar to surfons have been previously obtained by numerical calculations and called resonance interface states.

The magnetoresistance of a TbTe3 two-dimensional conductor with a charge-density wave (CDW) has been measured in a wide temperature range and in magnetic fields of up to 17 T. At temperatures well below the Peierls transition temperature and in high magnetic fields, the magnetoresistance exhibits a linear dependence on the magnetic field caused by the scattering of normal charge carriers by “hot” spots of the Fermi surface. In the sliding CDW regime in low magnetic fields, a qualitative change in the magnetoresistance has been observed associated with the strong scattering of carriers by the sliding CDW.
[1] A.V. Frolov, A.P. Orlov, P.D. Grigoriev, V.N. Zverev, A.A. Sinchenko, P. Monceau, Magnetoresistance of a Two-Dimensional TbTe3 Conductor in the Sliding Charge-Density Wave Regime, JETP Lett., 107(8), 488-492 (2018)

Doklad po predstavlyaemoi k zashchite doktorskoi dissertatsii.

V doklade budet predstavlen odin iz metodov dlya opisaniya gidrodinamicheskikh plazmennykh effektov v dvumernykh elektronnykh sistemakh (DES). A imenno, budet primenen operatornyi podkhod k uravneniyam elektronnoi gidrodinamiki i postroen analog kvantovo-mekhanicheskoi teorii vozmushchenii. Razrabotannaya teoriya pozvolit poluchit' vyrazhenie dlya pervoi popravki k sobstvennoi chastote plazmonov v prisutstvie slabogo dreifa nositelei, magnitnogo polya, vyazkosti i rasseyaniya na primesyakh. Na model'nykh primerakh budet vyyavlen kharakter vliyaniya etikh vozmushchenii na spektr i ustoichivost' plazmennykh voln v razlichnykh strukturakh. Tak, budut opredeleny: (1) obshchie svoistva tokovykh neustoichivostei v ogranichennykh DES, (2) vliyanie dreifa nositelei na spektr plazmonov v periodicheskikh DES (usilennyi effekt Doplera), i (3) mekhanizmy vozbuzhdeniya kraevykh mod postoyannym tokom.

We study the quantum corrections to the conductivity of the two-dimensional disordered interacting electron system in the diffusive regime due to inelastic scattering off rare magnetic impurities. We focus on the case of very different g factors for electrons and magnetic impurities. Within the Born approximation for the inelastic scattering off magnetic impurities we find additional temperature-dependent corrections to the conductivity of the Altshuler-Aronov type.
The talk is based on I. S. Burmistrov and E. V. Repin, Phys. Rev. B 98, 045414 (2018)

I report about theoretical support of experimental data on the measurement of the magnetic properties of thin films of bismuth selenide doped with europium atoms, which form flat inclusions. The magnitudes of the various mechanisms of magnetic ordering are theoretically estimated. The estimates obtained are in satisfactory agreement with the experimental data.
Report is based on the paper: L.N. Oveshnikov, Ya.I. Rodionov, K.I. Kugel, I.A. Karateev, A.L. Vasiliev, Yu.G. Selivanov, E.G. Chizhevskii, I.S. Burmistrov and B.A. Aronzon, "Magnetism of Bi2Se3 Thin Films with Eu-rich flat inclusions", J. Phys .: Condens. Matter 30, 445801 (2018)

Razvita teoriya opticheskoi spektroskopii neravnovesnykh spinovykh i zaryadovykh fluktuatsii v kvantovoi tochke, pomeshchennoi v mikrorezonator. Pokazano, chto v rezhime sil'noi svyazi fotonnoi mody mikrorezonatora s trionnym rezonansom kvantovoi tochki fluktuatsii koeffitsienta prokhozhdeniya sveta cherez mikrorezonator soderzhat informatsiyu kak o spinovoi dinamike sistemy, tak i o statistike fotonov v mikrorezonatore. V rezhime slaboi svyazi vozmozhno formirovanie "odetykh fotonami" sostoyanii, chto pozvolyaet opredelyat' parametry spinovoi spinovoi dinamiki ne tol'ko dlya osnovnogo, no i dlya vozbuzhdennogo sostoyaniya kvantovoi tochki po fluktuatsiyam opticheskikh signalov Faradeya ili Kerra. Prilozhenie k sisteme prodol'nogo magnitnogo polya privodit k vozmozhnosti detektirovaniya zaryadovykh fluktuatsii v kvantovoi tochke.

I report theoretical support of the data on measuring the spin susceptibility at different temperatures and electron concentrations in a two-dimensional electron system based on a silicon field-effect transistor in the group of V.M. Pudalov (Lebedev Institute).
The short talk is based on the work of V. M. Pudalov, A. Yu. Kuntsevich, M.E. Gershenson, I.S. Burmistrov, and M. Reznikov, Phys. Rev. B 98, 155109 (2018).

We consider a small itinerant ferromagnet exposed to an external magnetic field and strongly driven by a thermally induced spin current. For this model, we derive the quasi-classical equations of motion for the magnetization where the effects of a dynamical non-equilibrium distribution function are taken into account self-consistently. We obtain the Landau-Lifshitz-Gilbert equation supplemented by a spin-transfer torque term of Slonczewski form. We identify a regime of persistent precessions in which we find an enhancement of the thermoelectric current by the pumping current.
The talk is based on T. Ludwig, I.S. Burmistrov, Y. Gefen, A. Shnirman, "A thermally driven spin-transfer-torque system far from equilibrium: enhancement of the thermoelectric current via pumping current", arxiv:1808.01192

The spread of the Cooper pairs into the ferromagnet in proximity coupled superconductor – ferromagnet (SF) structures is shown to cause a strong inverse electrodynamic phenomenon, namely, the long-range transfer of the magnetic field from the ferromagnet to the superconductor. Contrary to the previously investigated inverse proximity effect resulting from the spin polarization of superconducting surface layer, we found a very generic orbital mechanism of the magnetic moment transfer from a ferromagnet to a superconductor which is unavoidable in S/F hybrids. It is related with the fact that the common superconducting wave function in S and F (near the interface) does not permit to exclude the vector-potential of the magnetization by gauge transformation. From the experimental point of view, this phenomenon reminds the Aharonov-Bohm effect since the current inside the attached superconductor is induced by the ferromagnetic layer which cannot create the magnetic field in the outside in the absence of such superconducting environment. At the same time, the true physical key point is that the wave function penetrating the ferromagnet is responsible for this effect. Let us stress that the characteristic length of the above proposed inverse electrodynamic effect is of the order of the London penetration depth.

This will include e.g. works like
[1] R. Klees, G. Rastelli, J.C. Cuevas, and W. Belzig, "Quantum Geometry of Josephson Matter" (submitted to Science Advances, not on arxiv yet).
[2] Tomohiro Yokoyama, Johannes Reutlinger, Wolfgang Belzig, and Yuli V. Nazarov, "Order, disorder and tunable gaps in the spectrum of Andreev bound states in a multiterminal superconducting device", Phys. Rev. B 95, 045411 (2017) [arXiv:1609.05455].
[3] J. Reutlinger, L. Glazman, Yu. V. Nazarov, and W. Belzig, ""Smile" gap in the density of states of a cavity between superconductors", Phys. Rev. Lett. 112, 067001 (2014) [arXiv:1308.2529].

Presentations: 1.QuantumGeomJJ.pdf, 2.SmileTopo.pdf

Weak, almost non-invasive quantum measurements differ from the standard text book example of strongly invasive, projective measurements, since they leave the measured system basically unchanged. This opens the path to measure e.g. non-commuting observables and at the same time poses several open questions: Which order of operators is measured? Can quantum tests like Bell or Leggett-Garg be reformulated? What time scales are involved in the measurement process? We will address some basic properties of weak measurements leading to surprises like apparent spontaneous time-reversal symmetry breaking or the possibility of engineered detectors to tailor the measured quantum correlations.

Exotic quasiparticles have been observed in complex spin systems exhibiting spin ice rules, skyrmions and so on. Here, we discuss the emergence of novel quasiparticles, mediated by magnetic dipolar interactions that have been hiding in simpler spin systems with uniformly ordered ground states. Amongst other properties, these quasiparticles exhibit a spin ranging from zero to above 1ℏ [1]. Of particular interest is our finding that the eigenmodes in an easy-axis antiferromagnet are spin-zero quasiparticles instead of the widely believed spin-1 magnons [2]. These unusual properties originate from a competition between quantum mechanical squeezing (increasing the spin) and hybridization (decreasing the spin).
We then present a theoretical study of spin transport across a ferrimagnet/non-magnetic conductor interface, when a magnetic eigenmode is driven into a coherent state. In the simple case of ferromagnets with non-integer “effective spin” above 1ℏ, we show that spin-current noise measurement can reveal this fundamental quantum phenomenon [1]. This is in full analogy to the effective charge known e.g. in the fractional quantum Hall regime, which has been experimentally determined via shot noise measurements.
Furthermore, we extend our model to continuously encompasses systems from ferromagnets to antiferromagnets [3] and include novel dissipation terms [4], thereby allowing analytical results for the full range of materials within a unified description. We also allow arbitrary interfaces (disordered and asymmetric). The obtained spin current expression includes intra- as well as cross-sublattice terms. We find that the cross-sublattice terms, disregarded in previous studies, play an important role and result in qualitative changes to our understanding of spin pumping in antiferromagnets. The dc current is found to be sensitive to the asymmetry in interfacial coupling between the two sublattice magnetizations and the mobile electrons, especially for antiferromagnets.
References:
[1] A. Kamra and W. Belzig, Super-Poissonian shot noise of squeezed-magnon mediated spin transport, Phys. Rev. Lett. 116, 146601 (2016).
[2] A. Kamra, U. Agrawal, and W. Belzig, Noninteger-spin magnonic excitations in untextured magnets, Phys. Rev. B 96, 020411(R) (2017).
[3] A. Kamra and W. Belzig, Spin pumping and shot noise in ferrimagnets: bridging ferro- and antiferromagnets, Phys. Rev. Lett. 119, 197201 (2017).
[4] A. Kamra, R. E. Troncoso, W. Belzig, and A. Brataas, Gilbert damping phenomenology for two-sublattice magnets, arXiv:1808.04385 (to appear in Phys. Rev. B).

Sposoby dostizheniya temperatur urovnya nanokel'vinov v atomnykh gazakh stanut pervoi temoi doklada. Dalee budut privedeny primery interesnykh eksperimentov s kvantovymi gazami. V to zhe vremya rech' poidet o slozhnostyakh, kotorye vstrechayutsya v eksperimentakh i o vozmozhnykh, eshche ne realizovannykh, putyakh ikh preodoleniya. V zaklyuchenii podrobno budet obsuzhdat'sya neopublikovannyi eksperiment po interferentsii tsepochki boze-kondensatov, v kotorom voznikaet prostranstvenno periodicheskaya interferentsionnaya kartina, nesmotrya na to, chto otnositel'nye fazy kondensatov sluchainy.
Video

We study the supercurrent in quasi-one-dimensional Josephson junctions with a weak link involving magnetism, either via magnetic impurities or via ferromagnetism. In the case of weak links longer than the magnetic pair-breaking length, the Josephson effect is dominated by mesoscopic fluctuations. We establish the supercurrent-phase relation (CPR) along with statistics of its sample-dependent properties in junctions with transparent contacts between leads and link. High transparency gives rise to the inverse proximity effect, while the direct proximity effect is suppressed by magnetism in the link. We find that all harmonics are present in the CPR. Each harmonic has its own sample-dependent amplitude and phase shift with no correlation between different harmonics. Depending on the type of magnetic weak link, the system can realize a \varphi_0 or \varphi junction in the fluctuational regime. Full supercurrent statistics is obtained at arbitrary relation between temperature, superconducting gap, and the Thouless energy of the weak link.

Dynamical and spatial correlations of eigenfunctions as well as energy level correlations in the Anderson model on random regular graphs (RRG) are studied. We consider the critical point of the Anderson transition and the delocalized phase. In the delocalized phase near the transition point, the observables show a broad critical regime for system sizes below the correlation volume and then cross over to the ergodic behavior. Eigenstate correlations allow us to visualize the correlation length that controls the finite-size scaling near the transition. The critical-to-ergodic crossover is very peculiar, since the critical point is similar to the localized phase, whereas the ergodic regime is characterized by very fast diffusion which is similar to the ballistic transport. In particular, the return probability crosses over from a logarithmically slow variation with time in the critical regime to an exponentially fast decay in the ergodic regime. We find a perfect agreement between results of exact diagonalization and those resulting from the solution of the self-consistency equation obtained within the saddle-point analysis of the effective supersymmetric action. We show that the RRG model can be viewed as an intricate limit of the Anderson model in spatial dimensions.

Mesa structures made of Bi₂Sr₂CaCu₂O_8+δ high-temperature superconductor represent stacks of atomic scale intrinsic Josephson junctions. When voltage is applied to such mesas, they can generate various types of waves (photons, phonons, polaritons, magnons, plasmons) in a variety of different ways. In this talk I will overview both Josephson and non-Josephson mechanisms of emission, including the standard ac-Josephson effect for emission of electromagnetic waves [1], segnetoelectric effect for emission of phonons and polaritons [2] and non-equilibrium quasiparticle relaxation and recombination for emission of any type of bosons, having strong electron-boson interaction and participating in pairing [3]. Those effects are important both for applied research, e.g., creation of tunable, compact, continuous wave and monochromatic THz source with a frequency span in the whole THz gap region and beyond 0.1-15 THz [1,2], and for fundamental understanding of the mechanism of pairing in high-temperature superconductors [3].
References:
[1] E. A. Borodianskyi and V.M. Krasnov, Josephson emission with frequency span 1–11 THz from small Bi₂Sr₂CaCu₂O_8+δ mesa structures, Nature Commun. 8, 1742 (2017).
[2] S. O. Katterwe, H. Motzkau, A. Rydh, and V. M. Krasnov, Coherent generation of phonon-polaritons in Bi₂Sr₂CaCu₂O_8+x intrinsic Josephson junctions, Phys. Rev. B 83, 100510(R) (2011).
[3] V.M. Krasnov, S.O. Katterwe, & A. Rydh, Signatures of the electronic nature of pairing in high-Tc superconductors obtained by non-equilibrium boson spectroscopy, Nature Commun. 4, 2970 (2013).

Vychislena lokal'naya kompleksnaya provodimost' i obuslovlennyi eyu poverkhnostnyi impedans na diffuznoi granitse kiral'nogo p-volnovogo sverkhprovodnika. Imenno kiral'noe p-volnovoe sostoyanie schitaetsya naibolee veroyatnym v sverkhprovodyashchem rutenate strontsiya Sr₂RuO₄. Ono anizotropnoe i pri etom polnost'yu shchelevoe (modul' parametra poryadka fiksirovan, a faza zavisit ot napravleniya). My rassmatrivaem otklik na vneshnee elektromagnitnoe pole kak na podshchelevykh, tak i na nadshchelevykh chastotakh. Izucheny anomal'nye osobennosti poverkhnostnogo impedansa, svyazannye s generatsiei vblizi granitsy nechetnykh po chastote sverkhprovodyashchikh korrelyatsii (sostoyanie tipa sverkhprovodimosti Berezinskogo). Teoreticheskie rezul'taty sopostavleny s izmereniyami poverkhnostnogo impedansa Sr₂RuO₄, provedennymi v IFTT. Nablyudaetsya kachestvennoe soglasie teorii i eksperimenta.
Doklad osnovan na rabote S. V. Bakurskiy, Ya. V. Fominov, A. F. Shevchun, Y. Asano, Y. Tanaka, M. Yu. Kupriyanov, A. A. Golubov, M. R. Trunin, H. Kashiwaya, S. Kashiwaya, and Y. Maeno, "Local impedance on a rough surface of a chiral p-wave superconductor", Phys. Rev. B 98, 134508 (2018); https://arxiv.org/pdf/1807.11735.pdf

Provedeno teoreticheskoe soprovozhdenie eksperimentov po izmereniyu effekta sverkhprovodyashchego spinovogo klapana v sisteme tipa FFS (gde F — ferromagnetik, S — sverkhprovodnik). Effekt sostoit v tom, chto kriticheskaya temperatura T_c sistemy zavisit ot vzaimnoi orientatsii namagnichennostei dvukh ferromagnetikov. V eksperimente v kachestve srednego F sloya byl vzyat splav Geislera Co₂Cr_1-xFe_xAl, i eto pozvolilo usilit' effekt (raznost' T_c pri parallel'noi i antiparallel'noi orientatsii) po sravneniyu s ranee issledovannymi sistemami s zhelezom. Znak effekta zavisit ot tolshchiny sloya. Teoriya ob'yasnyaet poluchennye rezul'taty. Usilenie effekta okazyvaetsya svyazano s umen'shennoi velichinoi obmennogo polya v splave Geislera.
Doklad osnovan na sleduyushchikh rabotakh:
[1] A. Kamashev, A. Validov, N. Garif’yanov, Ya. Fominov, P. Leksin, J. Schumann, J. Thomas, V. Kataev, B. Büchner, I. Garifullin, "Isolation of proximity-induced triplet pairing channel in a superconductor/ferromagnet spin valve", EPJ Web of Conferences 185, 08001 (2018).
[2] A.A. Kamashev, A.A. Validov, J. Schumann, V. Kataev, B. Büchner, Ya.V. Fominov, I.A. Garifullin, "Increasing the performance of a superconducting spin valve using a Heusler alloy", Beilstein J. Nanotechnol. 9, 1764 (2018).

We report the experimental manifestation of even-odd parity effects in the transport characteristics of insulating Josephson junction chains, which occur as the superconducting gap is suppressed by applied magnetic fields at millikelvin temperatures. The primary signature is a non-monotonic dependence of the critical voltage, Vc, for the onset of charge transport through the chain, with the parity crossover indicated by a maximum of Vc at the parity field B*, We also observe a distinctive change in the transport characteristics across the parity transition, indicative of Cooper-pair dominated transport below B*, giving way to single-electron dominated transport above B*, For fields applied in the plane of the superconducting aluminum films, the parity effect is found to occur at the field, B*||, such that the superconducting gap equals the single-electron charging energy, Δ(B*||)=EC. On the contrary, the parity effect for perpendicularly applied fields can occur at relatively lower fields, B*⊥≃ 2Φ0/AI, depending only on island area, AI. In this case, the parity effect occurs in sync with formation of the single-vortex state of the islands in the chain. Our results suggest a novel explanation for the insulating peak observed in disordered superconducting films and one-dimensional strips patterned from such films, which occurs at a finite magnetic field.

The joint statistical properties of two free energies computed at two different temperatures in the same sample of (1+1) directed polymers is studied in terms of the replica technique. The scaling dependence of the free energies differenceon the two temperatures $T_{1}$ and $T_{2}$ is derived. In particular, it is shown that if the two temperatures $T_{1} < T_{2}$ are close to each other the typical value of the fluctuating part of the free energies difference is proportional to $(1 - T_{1}/T_{2})^{1/3}$. It is also shown that the left tail asymptotics of this free energy difference probability distribution function coincides with the corresponding tail of the Tracy-Widom distribution.
Europhysics Letters, 116, 40004 (2016); arXiv:1703.04305

Quasi-one-dimensional systems demonstrate Van Hove singularities in the density of states $\nu_F$ and the resistivity $\rho$, occurring when the Fermi level $E$ crosses a bottom $E_N$ of some subband of transverse quantization. We demonstrate that the character of smearing of the singularities crucially depends on the concentration of impurities. There is a crossover concentration $n_c\propto |\lambda|$, $\lambda\ll 1$ being the dimensionless amplitude of scattering. For $n\gg n_c$ the singularities are simply rounded at $\varepsilon\equiv E-E_N\sim \tau^{-1}$ – the Born scattering rate. For $n\ll n_c$ the non-Born effects in scattering become essential, despite $\lambda\ll 1$. The peak of the resistivity is split: for $\varepsilon>0$ there is a broad maximum at $\varepsilon\propto \lambda^2$. For $\varepsilon\lt 0$ there is a deep minimum at $|\varepsilon|\propto n^2\ll \lambda^2$. The behaviour of $\rho$ below the minimum depends on the sign of $\lambda$. In case of repulsion $\rho$ monotonically grows with $|\varepsilon|$ and saturates for $|\varepsilon| \gg \lambda^2$. In case of attraction $\rho$ has sharp maximum at $|\varepsilon| \propto \lambda^2$. The latter feature is due to resonant scattering by quasistationary bound states that inevitably arise just below the bottom of each subband for any attracting impurity.

A theory for electron-phonon energy exchange in Anderson insulators with long localization length is developed. The major contribution to the cooling power as a function of electron temperature is shown to be directly related to the correlation function of the local density of electron states, which is enhanced near the localization transition by multi-fractality and by the presence of Mott's resonant pairs of states. The theory we develop explains huge enhancement of the cooling power observed in insulating Indium Oxide films as compared to predictions of standard theory for disordered metals

The problem of one-dimensional randomly forced Burgers turbulence is considered in terms of (1+1) directed polymers. In the limit of strong turbulence (which corresponds to the zero temperature limit for the directed polymer system) using the replica technique a general explicit expression for the joint distribution function of two velocities separated by a finite distance is derived. In particular, it is shown that at length scales much smaller than the injection length of the Burgers random force the moments of the velocity increment exhibit typical strong intermittency behavior. Literature: J.Stat.Mech., 083302 (2018); arXiv:1804.08294.

Quantum-critical strongly correlated systems feature universal collision-dominated collective transport. Viscous electronics is an emerging field dealing with systems in which strongly interacting electrons flow like a fluid. Such flows have some remarkable properties never seen before. I shall describe recent theoretical and experimental works devoted, in particular, to a striking macroscopic DC transport behavior: viscous friction can drive electric current against an applied field, resulting in a negative resistance, recently measured experimentally in graphene. I shall also describe conductance exceeding the fundamental quantum-ballistic limit, field-theoretical anomalies and other wonders of viscous electronics. Strongly interacting electron-hole plasma in high-mobility graphene affords a unique link between quantum-critical electron transport and the wealth of fluid mechanics phenomena.

The Markov chain Monte Carlo method traditionally consists in exploring large configuration spaces using a reversible random walk where moves are accepted or rejected based on an energy criterion. In this talk, I will present recent progress on irreversible Markov chains that challenge this picture. In one-dimensional particle systems, the new algorithms are related to the TASEP (totally asymmetric simple exclusion model). We can rigorously prove that they mix on much shorter time scales than the reversible Metropolis algorithms. I will then show how these algorithms sample the Boltzmann distribution (and thus explore configuration space) without computing the energy. In long-range interacting systems, where the computation of the energy is time-consuming, this provides a key advantage for the new method. For locally charge-neutral systems in three dimensions, we obtain a highly efficient algorithm, of N log N complexity in the number N of particles. I discuss the main paradox of this method: How is it possible to sample the Boltzmann distribution without computing the energy, and then review some recent successes as well as prospects and challenges for irreversible Markov chains in statistical physics.
References:
S. C. Kapfer, W. Krauth, Physical Review Letters 119, 240603 (2017)
Z. Lei, W. Krauth, arXiv:1806.06786 (2018)
M. F. Faulkner, L. Qin, A. C. Maggs, W. Krauth, arXiv:1804.05795 (2018)

Since 2006, it has been found experimentally that superconductivity spontaneously breaks time-reversal symmetry (TRS) in certain materials, such as Sr2RuO4, UPt3, URu2Si2, and Bi/Ni bilayers. In the latter case, we argue that the superconducting order parameter has the winding number of +-2 around the Fermi surface, thus making Bi/Ni bilayers a rare example of intrinsic 2D topological superconductivity [1]. The experimental evidence for TRS breaking comes from the polar Kerr effect, which is rotation of polarization of normally incident light upon reflection from the sample. Theoretical studies indicate that this effect is possible only if a superconductor has more than one band. To clarify these conditions, we study a model of chiral TRS-breaking superconductivity on the honeycomb lattice [2]. We consider superconducting pairing on the neighboring sites belonging to different sublattices. The matrix of this superconducting pairing is non-unitary and does not commute with the normal-state Hamiltonian. We find that the latter condition is necessary for experimental manifestations of the TRS breaking. We show that such superconducting pairing generates persistent loop currents around each lattice site and opens a topological mass gap at the Dirac points with the corresponding chiral edge states, as in Haldane's model of the quantum anomalous Hall effect. We calculate the intrinsic ac Hall conductivity in the absence of an external magnetic field, which determines the polar Kerr effect, and show that it is proportional to the loop-current order parameter.
[1] X. Gong, M. Kargarian, A. Stern, D. Yue, H. Zhou, X. Jin, V. M. Galitski, V. M. Yakovenko, and J. Xia, Science Advances 3, e1602579 (2017), arXiv:1609.08538
[2] P. M. R. Brydon, D. S. L. Abergel, D. F. Agterberg, and V. M. Yakovenko, arXiv:1802.02280

Since 2006, it has been found experimentally that superconductivity spontaneously breaks time-reversal symmetry (TRS) in certain materials, such as Sr2RuO4, UPt3, URu2Si2, and Bi/Ni bilayers. In the latter case, we argue that the superconducting order parameter has the winding number of +-2 around the Fermi surface, thus making Bi/Ni bilayers a rare example of intrinsic 2D topological superconductivity [1]. The experimental evidence for TRS breaking comes from the polar Kerr effect, which is rotation of polarization of normally incident light upon reflection from the sample. Theoretical studies indicate that this effect is possible only if a superconductor has more than one band. To clarify these conditions, we study a model of chiral TRS-breaking superconductivity on the honeycomb lattice [2]. We consider superconducting pairing on the neighboring sites belonging to different sublattices. The matrix of this superconducting pairing is non-unitary and does not commute with the normal-state Hamiltonian. We find that the latter condition is necessary for experimental manifestations of the TRS breaking. We show that such superconducting pairing generates persistent loop currents around each lattice site and opens a topological mass gap at the Dirac points with the corresponding chiral edge states, as in Haldane's model of the quantum anomalous Hall effect. We calculate the intrinsic ac Hall conductivity in the absence of an external magnetic field, which determines the polar Kerr effect, and show that it is proportional to the loop-current order parameter.
References:

• [1] X. Gong, M. Kargarian, A. Stern, D. Yue, H. Zhou, X. Jin, V. M. Galitski, V. M. Yakovenko, and J. Xia, Science Advances 3, e1602579 (2017), arXiv:1609.08538
• [2] P. M. R. Brydon, D. S. L. Abergel, D. F. Agterberg, and V. M. Yakovenko, arXiv:1802.02280

Rassmatrivaemaya zadacha voznikla pri izuchenii modeli SYK, kotoraya sostoit iz bol'shogo chisla vzaimodeistvuyushchikh fermionov (vzaimodeistvie «vse so vsemi», t.e. effektivnaya razmernost' sistemy — 0+1). Pri nizkoi temperature vazhnuyu rol' igraet myagkaya moda s deistviem, vyrazhayushchimsya cherez shvartsian. Eto deistvie ekvivalento dvumernoi gravitatsii s dilatonom v opredelennom predele. Pervaya chast' doklada posvyashchena obzoru upomyanutykh rezul'tatov. Zatem shvartsiannaya moda (ili dvumernaya gravitatsiya) budet rassmotrena kak otdel'naya kvantovaya sistema. Statsumma v etoi modeli imeet neobychnoe vyrazhenie: Z = tr(e^-βHP), gde P — opredelennyi operator, kommutiruyushchii s gamil'tonianom.

Video

Recent experimental progress with ultracold atomic gases has made it possible to investigate in exquisite detail the far out-of-equilibrium many-body quantum dynamics of isolated systems. This dynamics necessarily generates interferences beyond an Ehrenfest time scale, where quantum and classical expectation values diverge. Theoretically speaking, the heavily-relied-upon truncated Wigner approximation leaves out these interferences.

In this talk, I will present a semiclassical theory which bridges classical and quantum concepts in many-body bosonic systems and properly incorporates such missing quantum effects. For mesoscopically populated Bose-Hubbard systems, this theory captures post-Ehrenfest quantum interference phenomena very accurately.

Topological states, such as the quantum Hall state or the quantum spin Hall state, are usually bulk insulators, with helical edge states that may carry current. The edge structure of such two dimensional systems is usually studied with sharp boundary conditions in spite of the fact that the confining potential in physical systems is expected to be smooth. It is shown that such a smooth confining potential may lead to edge reconstruction and formation of additional edge states. This is demonstrated explicitly for the case of integer and fractional quantum Hall systems, explaining several recent experimental puzzles. Moreover, the effect is also manifested in two-dimensional topological insulators (TIs), which are predicted to support helical edge modes that come in counter-propagating pairs, due to the time-reversal symmetry (TRS). The TRS protection of these edge states led to various suggested applications of TIs, ranging from spintronics to quantum computation. Here edge reconstruction leads to spontaneous TRS breaking, a finite Hall resistance at zero magnetic field and possible spin current. Such spontaneous TRS breaking may have important implications on transport properties and possible applications.

Spin liquid phases are insulating states of matter with unique properties. In certain cases the phase hosts edge modes, end modes, and emergent non-abelian quasiparticles. The latter is a key element in several suggestions for topological quantum computation. In this talk, I`ll describe a proposal to construct a platform for creating effective spin models using semiconductor nanowires. The wires are tuned to the topological regime; with Majorana zero modes on each end. We group them into three-wires building blocks called hexons, each containing six Majorana zero modes. In the presence of a strong charging energy, the hexon becomes a Cooper box that is equivalent to two spin-1/2 degrees of freedom. This structure enables a flexible control (using local gates only) of the couplings between the Majorana zero modes. This tuning of the Hamiltonian governing the low energy effective spins, provides us with a path of simulating interacting spin-models in one- and two-dimensions. I will describe several examples including realizations of different phases of 1/2 Heisenberg spin chains, topological spin phases on a two dimensional Fisher lattice and their experimental signature.

The ongoing development of superconducting qubits has brought some basic questions of many-body physics to the research forefront, and in some cases helped solving them. I will address two effects in quantum condensed matter highlighted by the development of a fluxonium qubit. The first one is the so-called cosine-phi problem stemming from the seminal paper of Brian Josephson: the predicted there phase dependence of the dissipative current across a Josephson junction was observed in a fluxonium, after nearly 50 years of unsuccessful attempts by other techniques. The second one is the dynamics of a weakly-pinned charge density wave: we predict that the dynamics may be revealed in measurements of microwave reflection off a superinductor, which is a key element of the fluxonium.

Khal'kogenidy vismuta yavlyayutsya topologicheskimi izolyatorami s naibol'shimi shirinami zapreshchennoi zony. Pri dopirovanii Bi₂Se₃ med'yu, strontsiem ili niobiem Bi₂Se₃ stanovitsya sverkhprovodyashchim (predpolozhitel'no, nematicheskim topologicheskim sverkhprovodnikom).

V doklade budet dan obzor imeyushchikhsya na segodnyashnii den' dannykh o nematicheskoi sverkhprovodimosti dannogo materiala, v tom chisle i nashi rezul'taty o korrelyatsii nematichnosti so strukturnymi iskazheniyami [arXiv:1801.09287].

Takzhe ya rasskazhu o chasto obsuzhdaemom v literature izmerenii fazy Berri iz magnitoostsillyatsii. Nami privedeny prostye makroskopicheskie argumenty [Phys. Rev. B 97, 195431 (2018)], pochemu v real'nykh topologicheskikh izolyatorakh eta faza mozhet sil'no otlichat'sya ot teoreticheski ozhidaemogo znacheniya.

The Kardar-Parisi-Zhang (KPZ) equation describes an important universality class of nonequilibrium stochastic growth. There has been a surge of recent interest in the one-point probability distribution P(H,t) of height H of the evolving interface at time t in one dimension. I will show how one can use the optimal fluctuation method (OFM) to evaluate P(H,t) for different initial conditions and in different dimensions.

In one dimension the central part of the short-time height distribution is Gaussian, but the tails are non-Gaussian and strongly asymmetric. One interesting initial condition is an ensemble of Brownian interfaces, where we found a singularity of the large deviation function of the height at a critical value of |H|. This singularity results from a breakdown of mirror symmetry of the optimal path of the system, and it has the character of a second-order phase transition. At d>2 the OFM is valid, in the weak-coupling regime, at all times. Here the long-time height distribution P(H) is time-independent, and we use the OFM to determine the Gaussian body and strongly asymmetric non-Gaussian tails of P(H).

Transport in systems with many particles experiencing frequent mutual collisions (such as gases or liquids) has been studied for more than two centuries and is accurately described by the theory of hydrodynamics. It has been argued theoretically for a long time that the collective behavior of charge carriers in solids can also be treated by the hydrodynamic approach. However, despite many attempts, very little evidence of hydrodynamic electron transport has been found so far. Graphene encapsulated between hexagonal boron nitride (hBN) offers an ideal platform to study electron hydrodynamics as it hosts an ultra-clean electronic system with the electron-electron mean free path being the shortest lengths scale in the problem. In the first part of my talk we will discuss why electron hydrodynamics has not been observed before and how it manifests itself in electron transport. Furthermore, it will be shown that electrons in graphene can behave as a very viscous fluid (more viscous than honey) forming vortices of applied electron current [1]. In the second part, we will discuss the measurements of the viscosity of an electron fluid by its superballistic flow through graphene point contacts [2]. Then we will talk about the behavior of electron fluids in the presence of magnetic field where I will report the experimental measurements of the Hall viscosity in two dimensions [3]. This dissipationless transport coefficient has been widely discussed in theoretical literature on fluid mechanics, plasma physics and condensed matter physics, yet, until now, any experimental evidence has been lacking, making the phenomenon truly a unicorn. Last but not least, we will discuss how electron hydrodynamics can be used for the development of resonant terahertz photodetectors.

References: [1] D.A. Bandurin, A. Principi, G.H. Auton, E. Khestanova, K.S. Novoselov, I.V Grigorieva, L.A. Ponomarenko, A.K. Geim, and M. Polini, Science 351, 1055 (2016). [2] R.K. Kumar, D.A. Bandurin, F.M.D. Pellegrino, Y. Cao, A. Principi, H. Guo, G.H. Auton, M. Ben Shalom, L.A. Ponomarenko, G. Falkovich, I.V. Grigorieva, L.S. Levitov, M. Polini, and A.K. Geim, Nat. Phys. 13, 1182 (2017). [3] A.I. Berdyugin, S.G. Xu, F.M.D. Pellegrino, R. Krishna Kumar, A. Principi, I. Torre, M. Ben Shalom, T. Taniguchi, K. Watanabe, I.V. Grigorieva, M. Polini, A.K. Geim, and D.A. Bandurin, to appear on arxiv soon.

(seminar provoditsya sovmestno s laboratoriei FKS VShE)

Using a combination of analytic and numerical methods, we study the polarizability of a (non-interacting) Anderson insulator in one, two, and three dimensions and demonstrate that, in a wide range of parameters, it scales proportionally to the square of the localization length, contrary to earlier claims based on the effective-medium approximation. We further analyze the effect of electron-electron interactions on the dielectric constant in quasi-1D, quasi-2D and 3D materials with large localization length, including both Coulomb repulsion and phonon-mediated attraction. The phonon-mediated attraction (in the pseudogapped state on the insulating side of the Superconductor-Insulator Transition) produces a correction to the dielectric constant, which may be detected from a linear response of a dielectric constant to an external magnetic field.
M.V. Feigel’man, D.A. Ivanov, E. Cuevas, Dielectric response of Anderson and pseudogapped insulators, New J. Phys. 20, 053045 (2018); arXiv:1711.05972

Interactions between the surface and the bulk in a topological insulator (TI) cause a finite quasiparticle lifetime of the topological surface states (TSS) as shown by the recent experiments for Bi2X3 (X=Se,Te). Previously, hexagonally warped topological band has been detected and other anomalies related to warping have been reported. The most remarkable among which is the 6-fold periodic spin canting anomaly (SCA) of the in-plane spin around the spin-1/2 vortex.

This talk is focused on understanding this SCA from an interaction point of view between the TSS and the bulk. We first device a general scheme based on interactions and the spin-off-diagonal component of the self energy. It is shown that, the spin-off diagonal interaction channel is topology preserving. Then the effective interaction strength, strong spin-orbit coupling and the Fermi surface warping is shown to cooperate in giving rise to the periodic spin canting anomaly. Our result points at the presence of the topology friendly interaction channels in strong TIs.

KAK POPAST' NA SEMINAR: Na fizfake MGU propusknoi rezhim, zhelatel'no imet' s soboi pasport. Organizatory vstretyat uchastnikov. Telefon organizatora: +7-911-703-2266 (Mikhail Evgen'evich Zhuravlev).

We develop the theory of transverse magnetoresistance in layered quasi-two-dimensional metals. Using the Kubo formula and harmonic expansion we calculate intralayer conductivity in a magnetic field perpendicular to conducting layers. The analytical expressions for the amplitudes and phases of magnetic quantum oscillations (MQO) and of the so-called slow oscillations (SlO) are derived and applied to analyze their behavior as a function of several parameters: magnetic field strength, interlayer transfer integral and the Landau-level width. Both the MQO and SlO of intralayer and interlayer conductivity have approximately opposite phase in weak magnetic field and the same phase in strong field. The amplitude of SlO of intralayer conductivity changes sign at $\omega_c\tau\approx\sqrt{3}$. There are several other qualitative differences between magnetic oscillations of in-plane and out-of-plane conductivity. The results obtained are useful to analyze experimental data on magnetoresistance oscillations in various strongly anisotropic quasi-2D metals.

I will review the concept of non-equilibrium phase transitions in rare events statistics as well as a recent dramatic progress in studies of 1D KPZ. The focus of my talk is on the reflection symmetry breaking phase transition recently found stationary KPZ problem: https://arxiv.org/abs/1606.08738

The weak Dzyaloshinskii-Moriya interaction in chiral cubic magnets like MnSi, FeGe or Cu₂OSeO₃ twists the magnetization on long length scales resulting in spatially periodic magnetic textures — magnetic crystals. There exist especially magnetic crystals with a one- and two-dimensional periodicity corresponding to the magnetic helix and the topologically non-trivial skyrmion lattice, respectively. In this talk, we provide an overview of their properties. In particular, we discuss the crystallization process of these magnetic crystals that is characterized by strongly correlated chiral paramagnons that drive the transition first-order [1,2]. This fluctuation-induced first-order transition is well described by a theory put forward by Brazovskii. We will introduce the magnon band structure and their non-reciprocal properties in the presence of a magnetic field [3,4]. For the skyrmion lattice, this band structure is topological and characterized by finite Chern numbers that can be attributed to the formation of magnon Landau levels due to an emergent orbital magnetic field [5,6,7]. Finally, we will discuss domain walls of helimagnets that share similarities with grain boundaries consisting of disclination and dislocation defects of the helimagnetic order [8].

References: [1] M. Janoschek et al. Phys. Rev. B 87, 134407 (2013). [2] A. Bauer, M. Garst and C. Pfleiderer, Phys. Rev. Lett. 110, 177207 (2013). [3] M. Kugler et al. Phys. Rev. Lett. 115, 097203 (2015) [4] T. Weber et al. arXiv:1708.02098 [5] C. Schütte and M. Garst, Phys. Rev. B 90, 094423 (2014). [6] T. Schwarze, J. Waizner, M. Garst, A. Bauer, I. Stasinopoulos, H. Berger, C. Pfleiderer, and D. Grundler, Nat. Mater. 14, 478 (2015). [7] M. Garst J. Waizner, and D. Grundler, J. Phys. D: Appl. Phys. 50, 293002 (2017) [8] P. Schoenherr et al. Nat. Phys. in press, arXiv:1704.06288

The transport of excitations between pinned particles in many physical systems may be mapped to single-particle models with power-law hopping, 1/r^α. For randomly spaced particles, these models present an effective peculiar disorder that leads to surprising localization properties. We show that in one-dimensional systems almost all eigenstates (except for a few states close to the ground state) are power-law localized for any value of α > 0. Moreover, we show that our model is an example of a new universality class of models with power-law hopping, characterized by a duality between systems with long-range hops (α < 1) and short-range hops (α > 1), in which the wave function amplitude falls off algebraically with the same power γ from the localization center.

The paper has just been published: X. Deng, V. E. Kravtsov, G. V. Shlyapnikov, and L. Santos, Phys. Rev. Lett. 120, 110602 (2018).

We compute analytically the differential Poisson's ratio of a suspended two-dimensional crystalline membrane embedded into a space of large dimensionality $d \gg 1$. We demonstrate that, in the regime of anomalous Hooke's law, the differential Poisson's ratio approaches a universal value determined solely by the spatial dimensionality $d_c$, with a power-law expansion $\nu = -1/3 + 0.016/d_c + O(1/d_c^2)$, where $d_c=d-2$. Thus, the value $-1/3$ predicted in previous literature holds only in the limit $d_c\to \infty$.

Here we present the first quantum simulator for an impurity scattering in interacting 1D wires. The simulator consists of a transmission line made out of more than 30,000 Josephson junctions serving as a high-impedance media for microwave photons and a small phase slip Josephson junction playing the role of a back-scattering impurity. The system can be described by a boundary sine-Gordon model where the interaction strength is defined as g = Z/R_q with Z being the transmission line impedance and R_q = 6.5 kOhm the resistance quantum. By measuring scattering amplitudes and a spectrum of inelastically scattered microwave photons we can find the first and higher order correlation functions related to an AC conductance of the impurity. The controllability of the transmission line parameters and the finite size of the system allow us to fabricate lines with impedances exceeding R_q while keeping the phase slip rate of the line’s junctions very low. It gives us the unique opportunity to test Luttinger liquid physics at both sides of the critical point g = 1. A similar experimental setup can be used to simulate a Kondo impurity.

We derive the generalized Ambegaokar-Eckern-Schon action which governs the dynamics of the charge and spin degrees of freedom for the quantum dot described by the universal Hamiltonian and tunnel coupled to a reservoir. Contrary to previous works, we derive this dissipative action without the following assumptions (i) the absolute value of the spin is not aected by the tunneling coupling to a reservoir and (ii) the spin rotates slowly such that the adiabatic approximation holds. We use the derived dissipative action for analysis of stability of the mesoscopic Stoner phenomenon with respect to the electron tunneling to a reservoir. We nd that at nite temperature the electron tunneling suppresses the mesoscopic Stoner instability at tunneling conductance which depends on temperature. At zero temperature we predict the existence of the quantum phase transition between the mesoscopic Stoner phase and the paramagnetic phase.

Issledovany otkloneniya ot zakona Arkhimeda dlya sfericheskikh chastits radiusa R₀, vypolnennykh iz molekulyarnogo vodoroda u poverkhnosti zhidkogo He⁴. Klassicheskii zakon Arkhimeda imeet mesto, esli R₀ bol'she kapillyarnoi dliny geliya L_k ≅ 500 µm. Pri etom velichina vozvysheniya chastitsy nad zhidkost'yu h₊ ~ R₀. V oblasti 30 < R₀ < 500 µm sila Arkhimeda podavlyaetsya siloi poverkhnostnogo natyazheniya i h₊~ R₀³⁄L_k². Pri R₀ < 30 µm chastitsa nakhoditsya pod poverkhnost'yu zhidkosti. Zdes' sila Arkhimeda konkuriruet s siloi Kazimira, kotoraya ottalkivaet chastitsu ot poverkhnosti vglub' zhidkosti. Rasstoyanie chastitsy do poverkhnosti h_- ~ R_s^5⁄3⁄R₀^2⁄3, esli R₀ > R_s. Zdes' R_s – masshtab, nabrannyi, v osnovnom, iz mirovykh postoyannykh, R_s ≈ (ℏc/ϱg)^1⁄5 ≈ 1µm. (ℏ - postoyannaya Planka, c - skorost' sveta, g – uskorenie svobodnogo padeniya, ϱ_He – plotnost' geliya). Dlya ochen' malen'kikh chastits ( R₀ < R_s) rasstoyanie do poverkhnosti zhidkosti h_- ne zavisit ot ikh razmera h_- = R_s.

Nablyudaemye magnitnykh kvantovye ostsillyatsii (MKO) v vysokotemperaturnykh sverkhprovodnikakh YBCO (YBa₂Cu₃O_{6 +x} i YBa₂Cu₄O₈) imeyut dovol'no neobychnyi sostav garmonik. Preobrazovanie Fur'e etikh MKO soderzhit tri blizkikh ravnoudalennykh pika pri dostatochno nizkikh chastotakh ~530T i 530+-90T, chto sootvetstvuet okolo 2% zony Brillyuena, prichem tsentral'nyi pik imeet amplitudu v ~2 raza vyshe, chem dva pika s kazhdoi iz storon. Obshcheprinyatoe ob'yasnenie takikh kvantovykh ostsillyatsii predpolagaet perestroiku iskhodnoi bol'shoi poverkhnosti Fermi iz-za fluktuiruyushchei volny zaryadovoi plotnosti (VZP). Odnako takoe ob'yasnenie imeet ryad sushchestvennykh nedostatkov. Naprimer, ono predpolagaet takzhe nabor drugikh blizkikh chastot MKO, kotorye ne nablyudayutsya eksperimental'no. Krome etogo, v etoi modeli nablyudaemye chastoty MKO dolzhny sil'no zaviset' ot urovnya dopirovaniya, chto takzhe ne nablyudaetsya v eksperimente. My predlagaem al'ternativnuyu interpretatsiyu nablyudaemykh magnitnykh ostsillyatsii v YBCO, kotoraya dovol'no estestvennym obrazom ob'yasnyaet nablyudaemuyu kartinu bez dopolnitel'nykh podgonochnykh parametrov. Eta predlagaemaya model' MKO uchityvaet dvukhsloinuyu kristallicheskuyu strukturu YBCO i vklyuchaet sootvetstvuyushchee rasshcheplenie elektronnogo spektra i dispersiyu elektronov perpendikulyarno provodyashchim sloyam. Pri etom osnovnaya nablyudaemaya chastota ~530T sootvetstvuet velichine bisloinogo rasshchepleniya, a ne malomu karmanu poverkhnosti Fermi (PF), vyzvannomu ee perestroikoi iz-za VZP. Takie "medlennye" magnitnye ostsillyatsii poyavlyayutsya dazhe bez perestroiki PF i pochti ne zavisyat ot urovnya dopirovaniya. Krome togo, v otlichie ot obychnykh MKO, eti "medlennye" ostsillyatsii ne podavlyayutsya dlinnovolnovoi prostranstvennoi neodnorodnost'yu obraztsa, tipichnoi dlya VTSP kristallov i privodyashchei k razmytiyu urovnya Fermi vdol' obraztsa. Poetomu oni legche nablyudayutsya v eksperimente. Predlozhennaya interpretatsiya pozvolyaet razreshit' «protivorechie» dannykh ARPES i MKO, a takzhe ob'yasnyaet nekotorye drugie osobennosti nablyudaemykh MKO v YBCO, kotorye dovol'no slozhno ob'yasnit' stsenariem perestroiki PF vyzvannoi VZP.

We consider the effects of electron scattering on a quantum magnetic impurity on the current-voltage characteristics of the helical edge of a two-dimensional topological insulator. We compute the backscattering contribution to the current along the edge for a general form of the exchange interaction matrix and arbitrary value of the magnetic impurity spin. We find that the differential conductance might be a non-monotonous function of the voltage with several extrema. Effects of magnetic anisotropy for the impurity are considered.

V poslednie desyat' let voznik interes k izucheniyu fluktuatsii spinov elektronov i elektron-dyrochnykh kompleksov v poluprovodnikakh i poluprovodnikovykh nanosistemakh. V doklade predstavlena teoriya spinovykh fluktuatsii elektronov, lokalizovannykh v poluprovodnikovykh kvantovykh tochkakh, ili svyazannykh na donorakh v ob'emnom poluprovodnike, uchityvayushchaya sverkhtonkoe vzaimodeistvie spinov nositelei zaryada so spinami yader osnovnoi reshetki. Pokazano, chto spektr spinovykh shumov neset informatsiyu kak o funktsii raspredeleniya yadernykh polei, tak i o pryzhkakh elektronov mezhdu tsentrami lokalizatsii. Analiziruyutsya proyavleniya v spektre shumov obmennogo vzaimodeistviya mezhdu elektronami, lokalizovannymi na sosednikh tsentrakh. Rezul'taty teorii sopostavleny s dannymi eksperimentov.

Literatura: [1] M. M. Glazov and E. L. Ivchenko, Spin noise in quantum dot ensembles, Phys. Rev. B 86, 115308 (2012). [2] D.S. Smirnov, M.M. Glazov, E.L. Ivchenko, Vliyanie obmennogo vzaimodeistviya na spinovye fluktuatsii lokalizovannykh elektronov, FTT 54, 254 (2014). [3] M. M. Glazov, Spin noise of localized electrons: Interplay of hopping and hyperfine interaction, Phys. Rev. B 91, 195301 (2015). [4] A. V. Shumilin, E. Ya. Sherman, and M. M. Glazov, Spin dynamics of hopping electrons in quantum wires: Algebraic decay and noise, Phys. Rev. B 94, 125305 (2016). [5] Ph. Glasenapp, D. S. Smirnov, A. Greilich, J. Hackmann, M. M. Glazov, F. B. Anders, and M. Bayer, Spin noise of electrons and holes in (In,Ga)As quantum dots: Experiment and theory, Phys. Rev. B 93, 205429 (2016).

We consider ballistic SQUIDs with spin filtering inside half-metallic ferromagnetic arms. A singlet Cooper pair cannot pass through an arm in this case, so the Josephson current is entirely due to the Cooper pair splitting, with two electrons going to different interferometer arms. In order to elucidate the mechanisms of Josephson transport due to split Cooper pairs, we assume the arms to be single-channel wires in the short-junction limit. Different geometries of the system (determined by the length of the arms and the phases acquired by quasiparticles during splitting between the arms) lead to qualitatively different behavior of the SQUID characteristics (the Andreev levels, the current-phase relation, and the critical Josephson current) as a function of two control parameters, the external magnetic flux and misorientation of the two spin filters. The current-phase relation can change its amplitude and shape, in particular, turning to a pi-junction form or acquiring additional zero crossings. The critical current can become a nonmonotonic function of the misorientation of the spin filters and the magnetic flux (on half of period). Periodicity with respect to the magnetic flux is doubled, in comparison to conventional SQUIDs.

Predlozhena osnova teorii kollektivnykh mod v sil'no neuporyadochennykh sverkhprovodnikakh, nakhodyashchikhsya vblizi kvantovogo perekhoda v dielektricheskoe sostoyanie. Pokazano, chto s priblizheniem parametrov sverkhprovodnika k kvantovoi kriticheskoi tochke, v spektre vozbuzhdenii s neizbezhnost'yu voznikaet nenulevaya plotnost' nizkolezhashchikh (s energiyami sushchestvenno nizhe sverkhprovodyashchei shcheli) sostoyanii. Pri eshche bol'shem besporyadke eti podshchelevye sostoyaniya okazyvayutsya delokalizovannymi, chto dolzhno privodit' k zametnoi dissipatsii v mikrovolnovom otklike.

We calculate Aslamazov-Larkin paraconductity for a model of strongly disordered superconductors (dimensions d=2,3) with a large pseudogap whose magnitude strongly exceeds transition temperature T_c. We show that, within Gaussian approximation over Cooper-pair fluctuations, paraconductivity is just twice larger that the classical AL result at the same ε = (T-T_c)/T_c. Upon decreasing ε, Gaussian approximation is violated due to local fluctuations of pairing fields that become relevant at ε < ε₁ « 1. Characteristic scale ε₁ is much larger than the width ε₂ of the thermodynamical critical region, that is determined via the Ginzburg criterion, ε₂ ≈ ε₁^d. We argue that in the intermediate region ε₂ < ε < ε₁ paraconductivity follows the same AL power law, albeit with another (yet unknown) numerical prefactor. At further decrease of the temperature, all kinds of fluctuational corrections become strong at ε < ε₂; in particular, conductivity occurs to be strongly inhomogenuous in real space.

Dlya modeli Kitaeva na shestiugol'noi reshetki s razlichnymi tipami vozmushchenii byl razrabotan metod podscheta korrelyatsionnoi funktsii spin-spin v infrakrasnom predele. Bylo pokazano, chto zadacha o podschete dannoi funktsii mozhet byt' svedena k zadache o nakhozhdenii korrelyatsionnoi funktsii kvadratichnykh operatorov, sostoyashchikh iz svobodnykh Maioranovskikh fermionov. Pri etom vklad vysshikh poryadkov teorii vozmushchenii dlya iskhodnoi zadachi mozhet byt' uchten kak kvadratichnoe vozmushchenie dlya etikh fermionov. V kachestve prilozhenii rassmotreny sleduyushchie vozmushcheniya: magnitnoe pole, DM vzaimodeistvie cherez odnogo.

We consider a one-dimensional single channel quantum wire with a spin gap but gapless charge excitations. We show that the spin gap can be generated in two different ways, one of which has non-trivial topological properties. This topology manifests itself in two ways - firstly in the existence of gapless single-particle edge states, and secondly in an insensitivity of the wire to weak impurities reminiscent of the helical edge states of two dimensional topological insulators. We will demonstrate a number of ways such a phase of matter can be engineered, including spin-orbit quantum wires or two coupled helical edge states. If time permits, we will also touch on recent work concerning strong impurities in such systems.

References: [1] Kairanis and Carr, PRB 92, 035139 (2015). [2] Santos, Gutman and Carr, PRB 93, 235436 (2016). [3] Kainaris, Santos, Gutman and Carr, Forschr. Phys. 1600054 (2017). [4] Kainaris, Carr and Mirlin, coming soon.

Electric and thermal transport properties of a ν=2/3 fractional quantum Hall junction are analyzed. We investigate the evolution of the electric and thermal two-terminal conductances, G and G_Q, with system size L and temperature T. This is done both for the case of strong interaction between the 1 and 1/3 modes (when the low-temperature physics of the interacting segment of the device is controlled by the vicinity of the strong-disorder Kane-Fisher-Polchinski fixed point) and for relatively weak interaction, for which the disorder is irrelevant at T=0 in the renormalization-group sense. The transport properties in both cases are similar in several respects. In particular, G(L) is close to 4/3 (in units of e2/h) and G_Q to 2 (in units of πT/6ℏ) for small L, independently of the interaction strength. For large L the system is in an incoherent regime, with G given by 2/3 and GQ showing the Ohmic scaling, G_Q\sim 1/L, again for any interaction strength. The hallmark of the strong-disorder fixed point is the emergence of an intermediate range of L, in which the electric conductance shows strong mesoscopic fluctuations and the thermal conductance is G_Q=1. The analysis is extended also to a device with floating 1/3 mode, as studied in a recent experiment [A. Grivnin et al, Phys. Rev. Lett. 113, 266803 (2014)].

Referativnyi doklad po rabote http://www.nature.com/nature/journal/v484/n7394/full/nature10930.html

Recent measurements of the conductivity of nanoperforated graphene are interpreted in terms of edges states existing near the edge of each nanohole. The perimetric quantization of edge states should result in the formation of a quasi-equidistant ladder of quasistationary energy levels. Dirac fermions filling this ladder rotate about each nanohole in the direction determined by the valley index. We show that the irradiation of this system by circularly polarized terahertz radiation leads to a resonance in absorption in one of the valleys. The magnitude of absorption at the resonance frequency can be controlled by means of gate voltage.

Privodyatsya teoreticheskie i eksperimental'nye rezul'taty po elektroprovodnosti shirokikh ballisticheskikh kontaktov v dvumernom elektronnom gaze pri nalichii elektron-elektronnogo rasseyaniya za predelami gidrodinamicheskogo priblizheniya. Obsuzhdayutsya lineinaya zavisimost' popravki k elektroprovodnosti ot temperatury i polozhitel'noe magnetosoprotivlenie v slabykh polyakh. Rassmatrivaetsya takzhe protivopolozhnyi sluchai dlinnogo kanala s gladkimi stenkami.

Generic states of non-interacting electrons in disordered wires are localized, and the DC conductivity of a wire vanishes at zero temperature. However, the AC conductivity is non-vanishing, and its general asymptotic form at low frequency was obtained by Mott who used intuitive qualitative arguments. Then this formula was rigorously derived by Berezinsky for a strictly one-dimensional (1D) disordered system. Later Hayn and John have re-derived the Mott-Berezinsky formula applying instanton techniques to localized states in the Lifshits tails (at large negative energies). We revisit the instanton approach and apply it to the statistics of wave functions and AC transport, calculating exactly the integral over gaussian fluctuations around the exact two-instanton solution. We demonstrate that quite generically the contribution of zero modes to the fluctuation determinant exactly cancels the Jacobian that appears when the collective variable are introduced. Thus, we derive the correlations between eigenfunctions at different energies beyond the leading order in small energy difference. This allows us to calculate the leading corrections to the Mott-Berezinsky law. We also extend this approach to quasi-1D wires.

Formation of unusual textures of polarization is imminent for nano-scale ferroelectric samples, films, rods, and granules, where the depolarization surface effects play the crucial role. We consider the unconventional topological polarization textures in several nano-scale systems, in which they were either already directly observed or can be yet discovered. Polarization domains that alternate the surface charge distribution, first proposed by Landau (1935) in contents of ferromagnetism can be formed in ferroelectric thin films as an effective mechanism to confine the depolarization field to the near-surface layer and diminish the depolarization energy. Very recently we have demonstrated that the few-nanometer thick ferroelectric/paraelectric superlattices with periodic domain structures exhibit the striking feature. The effective capacitance of ferroelectric layers is negative. This effect is explained by the opposite orientation of the depolarizing field with respect to the field-induced averaged polarization. Moreover, in sub-THz region the real part of the dielectric constant becomes positive, passing through zero at frequency ~0.3-3THz, inducing the resonance effect, suitable for the design of the ultra-small low-energy THz chips. Multi-vortex and skyrmion states are formed inside ferroelectric cylindrical nano-dots and nanorods to reduce the depolarization energy. We study the stability of such states and calculate the phase diagram of the system. We demonstrate that the topological class of the most stable topological excitations can be driven by the geometrical and electrical parameters of the system, external field, and temperature. We target the multi-domain and topological excitations in FE nanodots as a platform for multivalued logic units, for neuromorphic computing.

V doklade dan obzor eksperimental'nykh issledovanii dvumernykh i trekhmernykh topologicheskikh izolyatorov (TI) na osnove HgTe kvantovykh yam i plenok. On sostoit iz dvukh chastei: pervaya posvyashchena dvumernomu TI na osnove HgTe yam s inversnym spektrom, a vtoraya trekhmernomu TI na osnove napryazhennoi plenki HgTe. V pervoi chasti osoboe vnimanie udeleno opisaniyu eksperimentov, imeyushchikh klyuchevoe znachenie dlya detektirovaniya kraevykh tokovykh sostoyanii. Podrobno opisyvaetsya polevaya tranzistornaya struktura, pozvolyayushchaya upravlyat' polozheniem urovnya Fermi kak dvumernogo, tak i trekhmernogo topologicheskogo izolyatora. Privodyatsya naibolee interesnye eksperimental'nye rezul'taty, poluchennye s ee pomoshch'yu. Esli govorit' o svoistvakh dvumernogo TI, to k nim mozhno otnesti nablyudenie nelokal'nogo ballisticheskogo i diffuzionnogo transporta v dvumernykh TI, magnitnyi proboi dvumernogo TI i anomal'nuyu temperaturnuyu zavisimost' soprotivleniya kraevykh kanalov. Esli zhe govorit' o trekhmernom TI, to eto dostizhenie rekordno vysokoi podvizhnosti poverkhnostnykh dvumernykh dirakovskikh fermionov i opredelenie blagodarya etomu vsekh ego osnovnykh parametrov (ob'emnoi shcheli, kontsentratsii dirakovskikh fermionov na obeikh ego poverkhnostyakh), a takzhe poluchenie informatsii o faze shubnikovskikh ostsillyatsii, svidetel'stvuyushchei o zhestkoi svyazi ikh spina i impul'sa. V zaklyuchenie obsuzhdayutsya perspektivy novykh eksperimentov.

Naideno i kolichestvenno opisano obshchee svoistvo: esli neodnorodnaya sverkhprovodimost' v anizotropnom provodnike poyavlyaetsya v vide izolirovannykh sverkhprovodyashchikh ostrovkov, ona umen'shaet elektricheskoe soprotivlenie anizotropno s maksimal'nym effektom vdol' osi s naimen'shei provodimost'yu. Eto svoistvo daet prostoi i ochen' obshchii instrument dlya izucheniya neodnorodnoi (ostrovkovoi) sverkhprovodimosti v razlichnykh anizotropnykh soedineniyakh i pozvolyaet otsenit' velichinu i temperaturnuyu zavisimost' ob'emnoi doli sverkhprovodyashchei fazy. Yavlenie nablyudaetsya v razlichnykh vysokotemperaturnykh sverkhprovodnikakh i v organicheskikh metallakh.

C pomoshch'yu opisannogo svoistva i izmerenii elektronnoi provodimosti i diamagnetizma vpervye pokazano poyavlenie neodnorodnoi sverkhprovodimosti v ob'emnom soedineniya FeSe pri atmosfernom davlenii i pri temperature v 5 raz vyshe, chem izvestnaya ranee temperatura sverkhprovodyashchego perekhoda T_c=8K, sootvetstvuyushchaya nulevomu soprotivleniyu. Eto otkrytie pomogaet ponyat' mnogochislennye neobychnye sverkhprovodyashchie svoistva FeSe, takie kak pyatikratnoe povyshenie T_c pri uvelichenii davleniya do neskol'kikh kilobar. Obsuzhdaetsya vozmozhnost' primeneniya etogo svoistva dlya obnaruzheniya prostranstvenno neodnorodnoi sverkhprovodimosti v drugikh anizotropnykh soedineniyakh, takikh kak kupraty i organicheskie metally.

Strongly interacting electrons can move in a neatly coordinated way, reminiscent of the movement of viscous fluids. In viscous electron flows interactions give rise to a collective behavior, facilitating transport and allowing conductance to exceed the fundamental Sharvin-Landauer ballistic limit G_ball. This talk will describe a theory of the ballistic-to-viscous crossover in a constriction exhibiting the ballistic transport at T = 0 but governed by electron hydrodynamics at elevated temperatures. An approach based on quasi-hydrodynamic variables predicts an additive relation G = G_ball + G_vis, where the viscous contribution G_vis dominates over G_ball in the hydrodynamic limit. We will also discuss recent measurements of electron transport through graphene constrictions, finding that conductance below 150 K increases with increasing temperature. The measurements help to identify the conductance contribution arising due to electron viscosity and determine its temperature dependence. Besides fundamental interest, this work shows that viscous effects can facilitate high-mobility transport at elevated temperatures, a potentially useful behavior for designing graphene-based devices.

When different materials are interfaced/jointed with each other, the resulted hybrid systems often manifest fascinating physical properties that do not exist in nature. Among the many artificial hybrids (sometimes addressed as meta-materials or hetero-structures), nano-hybrid made with low-dimensional materials and other functional materials is attracting tremendous attentions in recent years. In this talk, we will mainly go through a couple of examples of our recent progresses on the graphene/superconducting-islands, and the 2D materials/h-Boron-Nitride nano-hybrid systems. In the former, the superconducting behavior is successfully coupled to the gate-tunable feature of graphene, leading to a metal-superconducting quantum phase transition at the ground state. While in the later, ultra-flat and ultra-clean interface allow ballistic electronic transport, opening new path to realize the paradigm of electron optics. Our recent experimental progresses on MoS2/h-BN hetero-structures will also be discussed. We expect that artificial nano-hybrids and their quantum properties can be expanded into many research areas that are important for both fundamental studies and future applications.

The impact of the nonanalytic reconstruction of vortex cores on static vortex structures inweakly coupled superfluids is considered. It is shown that, in rotating two-dimensional systems, the Abrikosov vortex lattice is unstable to vortex core deformation: Each zero of the wave function becomes a cut of finite length. The directors characterizing the orientations of the cuts are themselves ordered in superstructures due either to surface effects or to interaction with shear deformations of the lattice (spiral structure). Similar instability may also be observable in clean superconducting films.

We study exciton radiative decay in a two-dimensional material, taking into account large thermal population in the nonradiative states, from which excitons are scattered into the radiative states by acoustic phonons. We find an analytical solution of the kinetic equation for the nonequilibrium distribution function of excitons in the radiative states. Our estimates for bright excitons in transition-metal dichalcogenides indicate a strong depletion of radiative state population due to insufficient exciton-phonon scattering rate at low temperatures.

We study the entanglement entropy and particle number cumulants for a system of disordered noninteracting fermions in d dimensions. We show, both analytically and numerically, that for a weak disorder the entanglement entropy and the second cumulant (particle number variance) are proportional to each other with a universal coefficient. The corresponding expressions are analogous to those in the clean case but with a logarithmic factor regularized by the mean free path rather than by the system size. We also determine the scaling of higher cumulants by analytical (weak disorder) and numerical means. Finally, we predict that the particle number variance and the entanglement entropy are nonanalytic functions of disorder at the Anderson transition.

V svoem doklade ya rasskazhu ob obnaruzhennom nami effekte, voznikayushchem v kvantovom sverkhprovodyashchem metamateriale v predele sil'noi svyazi. Metamaterial sostoit iz tsepochki meta-atomov (kubitov), kazhdyi iz kotorykh soderzhit dva sverkhprovodyashchikh kol'tsa, soedinennykh tunnel'nym perekhodom. Elektromagnitnye svoistva takogo materiala mogut byt' opisany kvantovoi induktivnost'yu kazhdogo atoma, kotoroi mozhno upravlyat' v shirokom chastotnom diapazone pri pomoshchi izmeneniya vneshnego magnitnogo polya. Rezkoe podavlenie prokhozhdeniya mikrovolnovogo izlucheniya cherez takoi metamaterial chereduetsya s ego rezonansnym usileniem, voznikayushchim iz-za rasshchepleniya mezhdu vyrozhdennymi potokovymi sostoyaniyami. Osnovnoe sostoyanie sistemy mozhet byt' pereklyucheno v sostoyanie superpozitsii dvukh potokovykh sostoyanii, prilozheniem k obraztsu magnitnogo polya opredelennoi velichiny. Budet predstavleno neskol'ko kvantovykh modelei povedeniya takoi sistemy, kotorye mogut opisat' poluchennye eksperimental'nye dannye.

We formulate general criteria for localized, extended ergodic and extended non-ergodic (multifractal) phases in disordered quantum systems and apply these criteria to the problem of Anderson localization on Bethe lattice, random regular graphs and generalized Rosenzweig-Porter random matrix ensemble. We focus on the replica symmetry breaking approach to the problem and show how this approach provides a natural classification of phases and phase transitions.

We investigate the interplay of ferroelectricity and quantum electron transport at the nanoscale in the regime of Coulomb blockade. Ferroelectric polarization in this case is no longer the external parameter but should be self-consistently calculated along with electron hopping probabilities leading to new physical transport phenomena.

We study the temperature dependence of the electrical conductance of a clean strongly interacting quantum wire in the presence of a helical nuclear spin order. The nuclear spin helix opens a temperature-dependent partial gap in the electron spectrum. Using a bosonization framework we describe the gapped electron modes by sine-Gordon-like kinks. We predict an internal resistivity caused by an Ohmic-like friction these kinks experience via interacting with gapless excitations. As a result, the conductance rises from G=e^2/h at temperatures below the critical temperature when nuclear spins are fully polarized to G=2e^2/h at higher temperatures when the order is destroyed, featuring a relatively wide plateau in the intermediate regime. The theoretical results are compared with the experimental data for GaAs quantum wires obtained recently by Scheller et al. [Phys. Rev. Lett. 112, 066801 (2014)]. (arXiv:1611.10238)

Ya planiruyu obsudit' kratko dve raboty, svyazannye obshchei ideologiei o podschete chisla tochek ravnovesiya v neuporyadochennykh sistemakh. V pervoi chasti, sleduya rabote ArXiv:1610.04831, ya opishu, kak takaya zadacha reshaetsya dlya nerelaksatsionnoi dinamiki v modeli tipa spinovogo stekla na sfere bol'shoi razmernosti, i obsuzhu fazovyi perekhod v rezhim eksponentsial'no bol'shogo chisla tochek ravnovesiya. Vo vtoroi chasti (osnovannoi na eshche ne zavershennoi rabote s P. Le Doussal i C. Texier) ya kratko obrisuyu podschet chisla tochek ravnovesiya dlya napravlennogo polimera v sluchainom potentsiale, gde zadacha svoditsya k izucheniyu fluktuatsii pokazatelya Lyapunova v odnomernoi lokalizatsii v rezhime lifshitsevskogo khvosta.

Results of detailed study of the topological insulator Bi₂Se₃ surface state energy structure in the vicinity of surface steps by scanning tunneling microscopy (STM) and spectroscopy (STS) methods are described. Increase of the chemical potential in the vicinity of the step edge is observed. The value of the increase is found to correlate with the step height and is caused by redistribution of electron wave functions between outer and inner edges of surface steps, as it is known for usual metals, as well as by presence of dangling bonds on the step. Smaller value of the shift and its larger characteristic length reflect specifics of the helical surface states. This increase is accompanied by enhancement of the relative value of the differential tunneling conductance, dI/dV, at the Dirac point and thereby produces an illusion of appearance of edge states. We show that the enhancement is reproduced in the framework of the tunneling model, which takes into account the dependence of the tunneling gap transparency on the voltage. References: [1] N.I. Fedotov, S.V. Zaitsev-Zotov, JETP Letters, 104, #11 (2016) (in press); arXiv:1609.08294. [2] N.I. Fedotov, S.V. Zaitsev-Zotov, arXiv:1609.08911.

Manipulating small spin textures that can serve as bits of information by electric and spin currents is one of the main challenges in the field of spintronics. Ferromagnetic skyrmions recently attracted a lot of attention because they are small in size and are better than domain walls at avoiding pinning sites while moved by electric current. Nevertheless, ferromagnetic skyrmions also have certain disadvantages, such as the presence of stray fields and transverse dynamics, making them harder to employ in spintronic devices. To avoid these unwanted effects, we propose a novel topological object: the antiferromagnetic (AFM) skyrmion and explore its properties using analytical theory based on generalized Thiele equation and micromagnetic simulations. This topological texture has no stray fields and we show that its dynamics are faster compared to its ferromagnetic analogue. We obtain the range of stability and the dependence of AFM skyrmion radius on the strength of Dzyaloshinskii-Moriya interaction coming from relativistic spin-orbit effects. Moreover, we study the temperature effects on the stability and mobility of AFM skyrmions. We find that the thermal properties, e.g. such as the antiferromagnetic skyrmion radius and diffusion constant, are rather different from those for ferromagnetic skyrmions. More importantly, we show that due to unusual topology the AFM skyrmions do not have a velocity component transverse to the current (no topological Hall effect), and thus may be interesting candidates for spintronic memory and logic applications.

We develop the two-instanton approximation to the current-voltage characteristic of a single electron transistor within the Ambegaokar-Eckern-Sch\"on model. We determine the temperature and gate voltage dependence of the Coulomb blockade oscillations of the conductance and the effective charge. We find that a small (in comparison with the charging energy) bias voltage leads to significant suppression of the Coulomb blockade oscillations and to appearance of the bias-dependent phase shift.

Pokazano, chto elektrony provodimosti v poluprovodnikovykh strukturakh so spin-orbital'nym vzaimodeistviem vo vneshnem magnitnom pole ispytyvayut drozhanie. Drozhashchee dvizhenie (Zitterbewegung) voznikaet v otsutstvie peremennoi sily, ego priroda analogichna prirode Zitterbewegung svobodnykh dirakovskikh elektronov. V doklade obsuzhdayutsya rezul'taty pervogo eksperimental'nogo i teoreticheskogo issledovaniya kogerentnogo drozhaniya elektronov, indutsirovannogo opticheskoi orientatsiei ansamblya elektronov v odinakovoe spinovoe sostoyanie.

Using the two-loop analysis and the background field method we demonstrate that the local pure scaling operators without derivatives in the Finkel'stein nonlinear sigma model can be constructed by straightforward generalization of the corresponding operators for the noninteracting case. These pure scaling operators demonstrate multifractal behavior and describe mesoscopic fluctuations of the single-particle Green's function. We determine anomalous dimensions of all such pure scaling operators in the interacting theory within the two-loop approximation.

V doklade budet rasskazano o rezul'tatakh, poluchennykh v nedavnikh rabotakh: 1) N-teorema v kvantovoi fizike [G.B. Lesovik, A.V. Lebedev, I.A. Sadovskyy, M.V. Suslov, V.M. Vinokur, H-theorem in quantum physics, Sci. Rep. (Nature Publishing Group) 6, 32815 (2016)]. 2)Trading coherence and entropy by a quantum Maxwell demon [A. V. Lebedev, D. Oehri, G. B. Lesovik, G. Blatter (PRA 2016)]. 3) Phase Estimation Algorithms for Quantum Metrology with a Single Qubit [S. Danilin, A. Vepsalainen, A. V. Lebedev, G. B. Lesovik, G. Blatter, G. S. Paraoanu, in preparation)].

It has recently been realized that driven-dissipative dynamics, which usually tends to destroy subtle quantum interference and correlation effects, could actually be used as a resource. By proper engineering of the reservoirs and their couplings, one may drive a system towards a desired quantum-correlated steady state, even in the absence of internal Hamiltonian dynamics. An intriguing class of quantum phases is characterized by topology, including the quantum Hall effect and topological insulators and superconductors. Which of these noninteracting topological states can be achieved as the result of purely dissipative Lindblad-type dynamics? Recent studies have only provided partial answers to this question. In this talk, I will present a general recipe for the creation, classification, and detection of states of the integer quantum Hall and 2D topological insulator type as the outcomes of coupling a system to reservoirs, and show how the recipe can be realized with ultracold atoms and other quantum simulators. The mixed states so created can be made arbitrarily close to pure states, and the construction may be generalized to other topological phases.

Questions on the nature of edge reconstruction and ‘where does the current flow’ in the quantum Hall effect (QHE) have been debated for years. Moreover, the recent observation of proliferation of ‘upstream’ neutral modes in the fractional QHE raised doubts about the present models of edge channels. I will focus on the hole-conjugate state \nu=2/3 , and present a new picture of edge reconstruction. For example, while the hitherto accepted model for \nu=2/3 consists of a single downstream charge channel with conductance 2/3 and an upstream neutral mode, it has been recently predicted theoretically and found experimentally that the current is carried by two separate downstream edge channels, each with conductance 1/3 accompanied by upstream neutral mode(s). We find that if the two downstream channels are not equilibrated, inter-mode equilibration (via particle exchange) is accompanied by an excitation of upstream neutral modes. In turn, the counter-propagating neutral modes, moving in close proximity to the charge modes, fragment into propagating charges, inducing thus downstream current fluctuations with zero net current – a novel mechanism for non-equilibrium noise. The latter is shot noise with quantized Fano factors, which does not involve beam partitioning.

Weyl semimetals are recently discovered materials in which the valence and conduction bands touch at isolated points (Weyl nodes) in the Brillouin zone. This gives rise to unusual electronic properties of these materials. In particular, Weyl semimetals host peculiar surface electron states whose Fermi lines are shaped as open arcs. I will show that static electric fields that are necessarily present near the crystal surface result in a spiraling structure of Fermi arcs. The winding angle of the spiral is controlled by the chirality of the Weyl node and the magnitude of the surface potential. I will also discuss magnetoresistance of a pn-junction in a Weyl semimetal.

While phonons are routinely used to describe low-energy properties of quantum superfluids, repulsive bosons in one dimension are special: their low energy excitations allow for an alternative decription in terms of fermionic quasiparticles. In my talk I will present the quasiclassical theory of these excitations which allows calculation of the dynamical structure factor in a generic 1D Bose liquid. In this theory the main role is played by singular kink-like configurations of the bosonic field. I will demonstrate that it is the kinetics of these quasiparticles rather than hydrodynamics which provides an effective description of dynamics of 1D interacting bosons.

Amorphous materials as diverse as foams, emulsions, colloidal suspensions and granular media can jam into a solid-like disordered state. In this state each particle has a certain equilibrium position and can vibrate around it.

In this talk, I will show that the dynamical matrix M describing harmonic oscillations in such media can be represented in the form M = AA^T. The rows of the matrix A correspond to the degrees of freedom of individual granules and its columns correspond to elastic contacts between granules. This representation allows to apply the random matrix theory and estimate the vibrational density of states. The resulting vibrational density of states is approximately constant over a wide frequency range which is determined mostly by the ratio of the number of degrees of freedom and the total number of elastic contacts in the system. The results are in a good agreement with numerical experiments performed by various authors.

Izucheno dvizhenie elektrona v membrane pod vliyaniem ravnovesnykh izgibnykh kolebanii, korrelyator kotorykh ubyvaet s rasstoyaniem po zakonu r^{-2\eta}. Podrobno rassmotren sluchai \eta<1/2, kogda dazhe pri skol' ugodno slabom vzaimodeistvii teoriya vozmushchenii neprimenima. Pokazano, chto v etom sluchae obratnoe kvantovoe vremya proportsional'no g^{1/(1-\eta)} T^{(2-\eta)/(2-2\eta)}, gde g - konstanta elektron-fononnogo vzaimodeistviya, a T - temperatura. Razvityi metod prilozhen k vychisleniyu plotnosti sostoyanii elektrona v perpendikulyarnom k membrane magnitnom pole. Pokazano, v chastnosti, chto v rezhime slaboushirennykh besporyadkom urovnei Landau oni imeyut gaussovu formu s shirinoi, zavisyashchei ot magnitnogo polya po zakonu B^\eta. Krome togo, vychisleno vremya sboya fazy volnovoi funktsii elektrona za schet ego vzaimodeistviya s izgibnymi fononami v sluchae \eta<1/2. Pokazano, chto imeetsya neskol'ko temperaturnykh intervalov, v kotorykh vremya sboya fazy vyrazhaetsya razlichnymi stepennymi funktsiyami ot konstanty elektron-fononnogo vzaimodeistviya, temperatury i energii elektrona.

We describe theoretically the depairing effect of a microwave field on diffusive s-wave superconductors. The ground state of the superconductor is altered qualitatively in analogy to the depairing due to a dc current. In contrast to dc-depairing the density of states acquires, for microwaves with frequency \omega_0, steps at multiples of the photon energy \Delta \pm n\hbar\omega_0 and shows an exponential-like tail in the subgap regime. We show that this ac-depairing explains the measured frequency shift of a superconducting resonator at high microwave power and low temperatures.

My rassmatrivaem 2D vzaimodeistvuyushchie elektrony s dispersiei tipa "obez'yan'e sedlo" (OS), $\propto p_x^3-3p_xp_y^2$. Podobnaya dispersiya estestvenno voznikaet pri sliyanii trekh obychnykh sedel (osobennostei van Khova) v elementarnoi katastrofe tipa ellipticheskoi ombiliki. My pokazyvaem, chto takaya dispersiya voznikaet v dvukhsloinom grafene v poperechnom elektricheskom pole, prichem s tochki zreniya topologii poverkhnosti Fermi podobnaya singulyarnost' yavlyaetsya chetvernoi tochkoi Lifshitsa. Tochka Lifshitsa etogo tipa obladaet kharakternym povedeniem urovnei Landau $E_m\propto (Bm)^{3/2}$ i svyazannykh ostsillyatsii v termodinamicheskikh i transportnykh svoistvakh, takikh kak ostsillyatsii de-Gaaza-van-Al'fena i Shubnikova-de-Gaaza, chei period utraivaetsya pri peresechenii singulyarnosti. My demonstriruem, chto dlya izolirovannogo OS teoriya, opisyvayushchaya nevzaimodeistvuyushchie elektrony, neustoichiva po otnosheniyu k renormgruppovomu potoku, i v sisteme libo voznikaet sverkhprovodyashchaya neustoichivost', libo ne-Fermi-zhidkostnoe povedenie. V dvukhsloinom grafene, v kotorom imeetsya dva OS okolo $K$ i $K^\prime$ tochek, voznikaet konkurentsiya neustoichivostei, a imenno ferromagnetizma, voln spinovoi i zaryadovoi plotnostei, i nematichnosti.

We study the generation of Majorana fermions in a two-dimensional topological superconductor placed in a transverse magnetic field B. A topological insulator/superconductor heterostructure and a two-dimensional p-wave superconductor are discussed. It is demonstrated that in these systems a single vortex creates two Majorana fermions, one hosted at the vortex core. The wave function of the second Majorana state is localized in the superconductor volume along a circle of radius r^∗∝B⁻¹ centered at the vortex core. In the case of many vortices, the sensitivity of r^∗ to the magnetic field B may be used to control the coupling between the Majorana fermions. The latter property could be an asset for quantum computations.

Odinochnye nanorazmernye chastitsy, takie kak kolloidnye poluprovodnikovye nanokristally, nanosterzhni (nanorods), nanoprovoloki (nanowires) demonstriruyut fluktuatsii intensivnosti fluorestsentsii (mertsanie) na shirochaishem spektre vremennykh masshtabov, ot dolei millisekund do chasov. V doklade budut obsuzhdat'sya sushchestvuyushchie teoreticheskie mekhanizmy i modeli mertsaniya nanochastits, vklyuchaya model' Efrosa/Rozena [Al.L. Efros & M. Rosen, Phys. Rev. Lett. 78, 1110 (1997)] i Multiple recombination center model [P.A. Frantsuzov, S. Volkan-Kacso & B. Janko, Phys. Rev. Lett. 103, 207402 (2009)].

Kvantovyi turniket predstavlyaet soboi nanoelektronnoe ustroistvo, kontroliruemym obrazom perenosyashchee elektrony po odnomu mezhdu dvumya sverkhprovodyashchimi elektrodami putem podachi peremennogo napryazheniya na metallicheskuyu nanochastitsu, raspolozhennuyu mezhdu dvumya elektrodami. Okazyvaetsya, chto kogerentnaya svyaz' mezhdu elektronnymi sostoyaniyami v nanochastitse i kvazichastichnymi sostoyaniyami v sverkhprovodnikakh nakladyvaet fundamental'nye ogranicheniya na rabotu ustroistva.

I will report on experimental results obtained at Molenkamp’s group in Würzburg on ‘missing odd’ Shapiro steps and on emission of Josephson radiation. It is known that as a consequence of the Josephson equations, a strong relation exists between the voltage V measured across a Josephson junction and the characteristic frequency fJ =2eV/h of the current flowing in it. By applying microwave radiation steps occur at integer values of the voltage. Alternatively, ’listening’ to the rf signal radiated by the circulating supercurrent is a passive way of probing its properties. The data provide compelling evidence for the presence of a substantial 4\pi Josephson-current as would be expected from zero-enegry states. The results are available on the arxiv at: arXiv:1603.09611, arXiv:1601.08055, arXiv:1503.05591

Work done by: J.Wiedenmann, E.Bocquillon, R. Deacon, T.M.Klapwijk and various co-authors.
The research is supported by a 2014 Alexander von Humboldt prize.

Dvumernye monosloi soedinenii MoS₂, MoSe₂, WS₂, WSe₂ yavlyayutsya pryamoshchelevymi poluprovodnikami s opticheskoi (eksitonnoi) shchel'yu v vidimom diapazone. Shchel' nakhoditsya v dvukh elektronnykh dolinakh, svyazannykh simmetriei obrashcheniya vremeni. Iz-za sil'nogo spin-orbital'nogo vzaimodeistviya zony rasshchepleny po spinu. Znaki rasshchepleniya v raznykh dolinakh protivopolozhny. Iz 16 vozmozhnykh eksitonnykh sostoyanii s raznymi kombinatsiyami spinovykh i dolinnykh indeksov elektrona i dyrki, tol'ko 4 mogut annigilirovat' bez perevorota spina i/ili doliny. Ostal'nye sostoyaniya nazyvayutsya temnymi. V dannoi rabote rassmatrivayutsya temnye eksitony, raspad kotorykh razreshen po doline, no zapreshchen po spinu.

Referativnyi doklad po rabote D. M. Silevitch, T. F. Rosenbaum and G. Aeppli, Eur. Phys. J. Special Topics 224, 25 (2015)

Traditional simulated annealing uses thermal fluctuations for convergence in optimization problems. Quantum tunneling provides a different mechanism for moving between states, with the potential for reduced time scales and different outcomes. Thermal and quan- tum annealing are compared in two concentration regimes of a model disordered magnet, where the effects of quantum mechanics can be tuned both by varying an applied magnetic field and by controlling the strength of thermal coupling between the magnet and an external heat bath. The results indicate that quantum annealing hastens convergence to the final state, and that the quantum character of the final state can be engineered thermodynamically.

Polnaya statistika perenosa kvantovykh chastits, kvantovaya metrologiya i sozdanie zaputannykh sostoyanii" V dissertatsii s pomoshch'yu formalizma pervichnogo kvantovaniya avtorom polucheny novye vyrazheniya dlya kharakteristicheskoi funktsii polnoi statistiki perenosa, uchityvayushchie energeticheskuyu zavisimost', zavisimost' ot vremeni, a takzhe obmennye effekty, obuslovlennye konechnym perekrytiem volnovykh paketov. V sluchae rasseyaniya dvukh fermionov poluchena subbinominal'naya statistika dlya nezaputannykh vkhodyashchikh sostoyanii, v to vremya kak zaputannye sostoyaniya mogut porozhdat' superbinominal'nyi shum. Opisan sluchai s postoyannym napryazheniem, gde uchityvaetsya zavisimost' rasseyaniya ot energii i konechnykh vremen izmereniya. Predlozhena skhema, soderzhashchaya uslovnye izmereniya, v kotoroi neskol'ko kubitov sluzhat detektorom v zadache o polnoi statistike perenosa. Sformulirovana i reshena zadacha scheta v terminakh problemy razlichimosti kvantovykh sostoyanii pri odnokratnom izmerenii, dayushchaya konstruktivnuyu skhemu pribora dlya kvantovogo algoritma scheta. Issledovany razlichnye vozmozhnosti pribornoi realizatsii etogo algoritma. Rassmotreny vozmozhnosti sozdaniya zaputannykh sostoyanii putem chastichnogo opredeleniya chisla proshedshikh chastits. Predlozhen novyi sposob izmereniya napryazheniya pri pomoshchi odnogo ili neskol'kikh zaryadovykh kubitov.

Referativnyi doklad po rabote V. S. Denchev et al (Google Inc.), arxiv.org/1512.02206

Quantum annealing (QA) has been proposed as a quantum enhanced optimization heuristic exploiting tunneling. Here, we demonstrate how finite range tunneling can provide considerable computational advantage. For a crafted problem designed to have tall and narrow energy barriers separating local minima, the D-Wave 2X quantum annealer achieves significant runtime advantages relative to Simulated Annealing (SA). For instances with 945 variables, this results in a time-to-99%-success-probability that is ∼108 times faster than SA running on a single processor core. We also compared physical QA with Quantum Monte Carlo (QMC), an algorithm that emulates quantum tunneling on classical processors. We observe a substantial constant overhead against physical QA: D-Wave 2X again runs up to ∼108 times faster than an optimized implementation of QMC on a single core. We note that there exist heuristic classical algorithms that can solve most instances of Chimera structured problems in a timescale comparable to the D-Wave 2X. However, we believe that such solvers will become ineffective for the next generation of annealers currently being designed. To investigate whether finite range tunneling will also confer an advantage for problems of practical interest, we conduct numerical studies on binary optimization problems that cannot yet be represented on quantum hardware. For random instances of the number partitioning problem, we find numerically that QMC, as well as other algorithms designed to simulate QA, scale better than SA. We discuss the implications of these findings for the design of next generation quantum annealers.

In my talk I discuss the transport properties of disordered Weyl semimetals. In these systems, mechanisms of topological origin lead to the protection against Anderson localization, and at the same time to different types of transverse electromagnetic response -- the anomalous Hall effect (AQHE), and chiral magnetic effect (CME). I will demonstrate how an interplay of symmetry breaking and the chiral anomaly leads to the low-energy field theory containing two types of topological terms --- the Pruisken term describing AQHE and a variant of the non-Abelian Chern-Simons term responsible for CME. I will then discuss the signatures of CME in the magnetoconductance and shot noise assuming a quasi-one-dimensional geometry with a disordered Weyl semimetal nanowire being placed in the contact with two normal leads. An application of the magnetic field B along the nanowire creates the chiral 1d channels propagating parallel to B. They survive disorder averaging and the amount of them equals to the number of flux quanta piercing the nanowire. As the result, the magnetoconductance shows the crossover from quadratic to linear in B behavior while the Fano factor F is exponentially suppressed at high B as compared to F=1/3 at low B.
References: Dmitry Bagrets and Alexander Altland, PRL 114, 257201 (2015); PRB 93, 075113 (2016)

Superconducting quantum bits (qubits) are at the heart of quantum information processing schemes since they satisfy the requirements for being the building blocks of viable quantum computers. Here it is shown that quantum coherence, in the form of population inversion pulses, is induced by self-induced transparent pulses propagating in a quantum metamaterial comprising superconducting charge qubits. The experimental confirmation of that effect may open a new pathway to potentially powerful quantum computing.

Out-of-time-order correlators introduced recently in the context of quantum gravity describe the delocalization of information in quantum systems. In classical chaotic systems, these correlators are known to grow exponentially with the Lyupanov exponent. I discuss the behavior of these correlators in canonical examples of solid state quantum chaotic systems: disordered electrons with and without phonon interaction.

We explore a long Josephson contact transporting Cooper pairs between 1D charge-neutral chiral Majorana modes in the leads via charged Dirac chiral modes in the normal region. We investigate the regimes of transparent and tunnel junctions implemented in 3D topological insulator/superconductor/magnet hybrid structures. The setup acts as a SQUID controlled by the magnetic flux enclosed by the chiral loop of the normal region. This chirality leads to the fractional h/e-periodic pattern of critical current. The current-phase relation can have sawtooth-like shape with spikes at unusual even phases of 2\pi n.

Dynamical phase transitions can occur in isolated quantum systems that are brought out of equilibrium by either a sudden or a gradual change of their parameters. Theoretical examples rage from the behaviour of the O(N) model in the large N limit as well as spin-model with long range interactions, both showing dynamical criticality in their prethermal steady-states. In this talk I will start by discussing the characterization of such dynamical phase transitions based on the statistics of produced excitations. I will focus both on the role of fluctuations as well as on the difference between sudden and gradual changes of the parameters. Finally, I will discuss a second type type of dynamical criticality discussed in the literature, related to the emergence of zeroes in the Loschmidt amplitude, and show that this phenomenon is much less generic and robust than standard dynamical criticality.

Grafen predstavlyaet soboi znamenityi primer dvumernoi kristallicheskoi membrany. Teplovye fluktuatsii membrany stremyatsya razrushit' dal'nii poryadok v sisteme. Konkuriruyushchim effektom, blagodarya kotoromu membrana ostaetsya termodinamicheski stabil'noi, yavlyaetsya sil'noe angarmonicheskoe vzaimodeistvie mezhdu izgibnymi i prodol'nymi kolebatel'nymi modami. Angarmonicheskie effekty demonstriruyut kriticheskoe povedenie na masshtabakh bol'shikh, chem dlina Ginzburga. V chastnosti, izgibnaya zhestkost' chistoi izolirovannoi membrany vozrastaet stepennym obrazom po mere uvelicheniya razmera sistemy: $\varkappa \propto L^{\eta}.$ V rabote izuchaetsya vliyanie besporyadka na kriticheskoe povedenie membrany. Pokazano, chto sluchainye fluktuatsii krivizny membrany, vyzvannye staticheskim besporyadkom, radikal'no menyayut kharakter skeilinga izgibnoi zhestkosti. Vyvedeny uravneniya renormgruppy (RG), opisyvayushchie izmenenie $\varkappa$ i effektivnoi sily besporyadka $b$ po mere uvelicheniya razmera sistemy. Pokazano, chto obe velichiny nemonotonno zavisyat ot $L.$ Analiz uravnenii RG pozvolyaet postroit' kriticheskuyu krivuyu $b(\varkappa),$ razdelyayushchuyu ploskuyu i «skomkannuyu» (crumpled) fazy membrany. Geometriya membrany v okrestnosti kriticheskoi krivoi kharakterizuetsya (v opredelennom intervale masshtabov) fraktal'noi razmernost'yu. Takzhe podrobno izucheno povedenie $\varkappa$ i $b$ v ploskoi faze. Pokazano, chto gluboko v ploskoi faze besporyadok ubyvaet stepennym obrazom na masshtabakh bol'shikh, chem dlina Ginzburga, kotoraya, takim obrazom, zadaet kharakternyi masshtab ripplov (ripples) – staticheskikh izgibnykh deformatsii, eksperimental'no nablyudaemykh v izolirovannom grafene. V predele $L \to \infty $ ripply kharakterizuyutsya anomal'noi eksponentoi $2\eta$ po kontrastu s dinamicheskimi fluktuatsiyami, kotorye spadayut stepennym obrazom s pokazatelem $\eta$. Esli nachal'nyi besporyadok dostatochno velik, to sushchestvuet promezhutochnyi interval masshtabov, gde ripply ubyvayut sushchestvenno medlennee, s pokazatelem $\eta/4.$. Rezul'taty raschetov sravnivayutsya s imeyushchimisya eksperimental'nymi izmereniya parametrov ripplov v grafene. V rabote takzhe izuchaetsya povedenie membrany pod deistviem vneshnego natyazheniya. Pokazano, chto lineinyi zakon Guka narushaetsya, a imenno rastyazhenie lista grafena okazyvaetsya nelineinoi funktsiei prilozhennogo malogo natyazheniya: $\Delta L \propto \sigma^{\eta/(2-\eta)}$ i $\Delta L \propto \sigma^{\eta/(8-\eta)},$ sootvetstvenno, dlya chistoi i razuporyadochennoi membrany.

Issledovana plotnost' sostoyanii v diffuznykh sverkhprovodnikakh s magnitnymi primesyami, podchinyayushchimisya statistike Puassona. Takim obrazom mogut byt' opisany primesi proizvol'noi «sily», a izvestnyi sluchai bornovskikh magnitnykh primesei s gaussovoi statistikoi yavlyaetsya predel'nym sluchaem nashego rassmotreniya. Teoriya srednego polya predskazyvaet netrivial'nuyu strukturu plotnosti sostoyanii, soderzhashchuyu kontinuum kvazichastichnykh sostoyanii, a takzhe (v nekotorom diapazone parametrov) primesnuyu zonu. V priblizhenii srednego polya vse kraya spektra yavlyayutsya zhestkimi i oboznachayut chetkie granitsy mezhdu oblastyami konechnoi i nulevoi plotnosti sostoyanii. Rassmatrivaya instantony v tekhnike replichnoi sigma-modeli, my vychislyaem srednyuyu plotnost' sostoyanii za ramkami srednepolevogo priblizheniya. Takim obrazom, my nakhodim podshchelevye sostoyaniya («khvosty»), kotorye razmyvayut kraya spektra za schet fluktuatsii potentsial'nogo (obychnye primesi) i nepotentsial'nogo (magnitnye primesi) besporyadka. Neodnorodnost' kontsentratsii magnitnykh primesei privodit k poyavleniyu podshchelevykh sostoyanii za schet dvukh mekhanizmov: fluktuatsii para-razrushayushchego parametra (magnitnyi analog mezoskopicheskikh fluktuatsii) i fluktuatsii parametra poryadka (opredelyaemogo samosoglasovanno). V predel'nykh sluchayakh vosproizvodyatsya ranee poluchennye rezul'taty dlya podshchelevoi plotnosti sostoyanii v gryaznykh sverkhprovodnikakh s magnitnymi primesyami.

Controlled transformations of electronic states or even of whole phases are achievable today by impacts of very strong electric fields and/or the ultrafast optical pumping. The experimental success is coming from ferroelectrically and ionically enhanced field effect in high-Tc superconductors, induced metallization in oxides of transition metals and in organic materials, field-effect superconductivity in MBE monolayers. The techniques of the femto-second optical pumping span from the purely optical setups to the newer time-resolved photoemission spectroscopy and to the latest time-sliced diffraction. The tested electronic phases include: superconductivity, charge density waves, charge ordering, ferroelectricity, magnetic phases, Peierls and Mott insulators. A super goal is to attend “hidden” states which are inaccessible and even unknown under equilibrium conditions. Such a bistable switching has been achieved in a “polaronic Wigner-crystalline Mott insulator” 1T-TaS2. After the experimental review, some time will be devoted to a phenomenological theory (collaboration with N. Kirova). Thus, the modeling of the quasi-condensate of excitons interacting with the order parameter recovers the dynamical realization of the “excitonic insulator” state and spacio-temporal patterns with self-focusing, domains segregation, and local dynamical phase transitions.

This talk will be devoted to conducting systems with unhindered polar deformations: ferroelectric semiconductors near the critical temperature and charge density waves (CDW) subjected to pinning and junctions constraint. For ferroelectrics, epitomized by Mott insulators in organic stack materials, we shall find access to the critical dynamics, to the creep of domain walls, and to the polarization dumping by solitons. For CDWs, we shall model the reconstruction of their current carrying states in junctions channels via dynamical and static vortex structures. For completeness, we shall recall also old stories of frequency and temperature dependence of the permittivity of CDWs under pinning and Coulomb interactions.
The presented results are based on collaborations with P. Monceau and F. Nad in experiment and with N. Kirova and A. Larkin in theory.

V rabote issleduetsya myagkaya poperechnaya moda besshchelevykh vozbuzhdenii, svyazannaya s deformatsiei treugol'noi reshetki Abrikosova s odnim kvantom potoka v elementarnoi yacheike pri proizvol'nom znachenii parametra Ginzburga-Landau kappa. Pokazano. chto v uzkoi oblasti znachenii kappa, blizkikh k edinitse, reshetka Abrikosova s uglom F=\pi/3 mezhdu vektorami elementarnoi yacheiki neustoichiva. Spektr vozbuzhdenii rassmatrivaemoi mody pri malykh znacheniyakh impul'sa k (v k^2 priblizhenii) izotropen pri k, lezhashchem v ploskosti, perpendikulyarnoi magnitnomu polyu. Naiden interval neustoichivosti po velichine kappa.

We study Josephson junctions between superconductors connected by two parallel ferromagnetic arms. For fully polarised ferromagnets, supercurrent through such a SQUID only flows via Cooper pair splitting between the differently polarised arms. The average current is suppressed, but mesoscopic fluctuations lead to a significant typical current. We calculate this current for the SFS SQUID, as well as for a SQUID with metallic arms with magnetic impurities. The latter shows an h/e periodicity in flux. The current in both systems is of fluctuational origin and is stronger for materials with low conductivity and a low superconducting gap.

Anomalous Hall effect arises in systems with both spin-orbit coupling and magnetization. Generally, there are three mechanisms contributing to anomalous Hall conductivity: intrinsic, side jump, and skew scattering. The standard diagrammatic approach to the anomalous Hall effect is limited to computation of ladder diagrams. We demonstrate that this approach is insufficient. An important additional contribution comes from diagrams with a single pair of intersecting disorder lines. This contribution constitutes an inherent part of skew scattering on pairs of closely located defects and essentially modifies previously obtained results for anomalous Hall conductivity. We argue that this statement is general and applies to all models of anomalous Hall effect. We illustrate it by an explicit calculation for two-dimensional massive Dirac fermions with weak disorder. In this case, inclusion of the diagrams with crossed impurity lines reverses the sign of the skew scattering term and strongly suppresses the total Hall conductivity at high electron concentrations. The same mechanism for ordiary electrons with spin-orbit coupling (Bychkov-Rashba model) produces an opposite effect increasing the Hall conductivity. In the conduction band, skew scattering with crossed impurity lines is the only source of the anomalous Hall effect.

Kontekstual'nost' yavlyaetsya odnim iz fundamental'nykh svoistv, otlichayushchikh kvantovuyu mekhaniku ot klassicheskoi teorii. Predpolagalos', chto imenno blagodarya etomu "volshebnomu" parametru proiskhodit eksponentsial'noe uskorenie v kvantovykh komp'yuterakh. My predostavim pervye eksperimental'nye dokazatel'stva etogo resursa dlya trekhurovnevoi kvantovoi sistemy, postroennoi na sverkhprovodyashchikh konturakh - odnoi iz osnovnykh skhem dlya kvantovykh vychislenii. Svyazav dispersionnye sdvigi sverkhprovodyashchego kutrita s SVCh-rezonatorom, my poluchili sil'nye proektsionnye izmereniya s dvoinymi rezul'tatami. V sochetanii s vysokoi kontrastnost'yu schityvaniya, osushchestvlyaemoi blagodarya parametricheskomu usilitelyu, eto pozvolyaet nam ob'edinit' oba izmereniya i sovmestit' obkhody tsiklov, kotorye prisutstvovali v predydushchikh eksperimental'nykh ispytaniyakh.

We review a progress in experiments and theory, elucidating the role of microscopic solitons in quasi-1D electronic systems with a symmetry breaking. The new interest rises from studies of the «electronic ferroelectricity» in organic conductors, and from nano-scale tunneling experiments in Charge Density Wave (CDW) materials. Individual solitons have been visually captured in recent STM experiments. On this basis we extrapolate to a picture of combined topological excitations in general strongly correlated systems: from doped antiferromagnets to strong coupling and spin-polarized superconductors. At more macroscopic scales, we recover the electronic vortices generated in mesa-junctions, and domain walls evolving in femtosecond pump-probe experiments.

09 December 2015 the seminar "Coherent and self-organization phenomena in metamaterials" will take place in NUST «MISIS» (auditorium G-410, Leninsky pr., 6, The Mining College building, Metro station: Oktyabr`skaya kol`tsevaya)

The shedule:

11:00 «Chimeras in SQUID metamaterials», George P. Tsironis (NUST «MISIS»; University of Crete, Greese)

11:45 «Control of power in parity-time symmetric lattices», George P. Tsironis (NUST «MISIS»; University of Crete, Greese)

12:30 «Qubit lattice coherence induced by electromagnetic pulses in superconducting metamaterials», Zoran Ivic (Institute of Nuclear Sciences "Vinca", Serbia)

13:15 «Imaging coherent response of a superconducting metasurface», Alexander S. Averkin (NUST «MISIS»)

Everyone is welcome - especially young scientists interested in new experience in the field of micro- and nano-technology of superconductors.

Skip for seminar participants who are not students, graduate students or employees of NUST "MISIS", will be carried out upon presentation of passport subject to prior registration for the seminar

Contact: Andrew Maliszewski, tel. +7 916 135 03 25, vabanque@mail.ru

I shall report on several studies of phase transformations in cooperative electronic systems achieved by means of a femto-second optical pumping. 1. Experiments on charge density waves recovered coherent unharmonic undulations of the order parameter, critical slowing down of the collective mode, and evolution of the particle-hole gap. The numerical modeling reproduced the dynamical phase transition, and the waves emitted by “earthquakes” from in depth annihilation events of topological defects.*) 2. The bistable switching to a “hidden” state has been achieved in a “polaronic Wigner-crystalline Mott insulator” 1T-TaS2. The theory focuses upon evolution of electrons and holes as mobile charge carriers, and the crystallized electrons modifiable by intrinsic defects.*) 3. The special case of resonance optical pumping to excitons is realized in systems with a neutral-ionic ferroelectric transition. The modeling of the quantum-coherent quasi-condensate of excitons interacting with the order parameter recovers the dynamical realization of the “excitonic insulator” state and spacio-temporal patterns with self-focusing, domains segregation, and local dynamical phase transitions.**) ----------------------------------------------------------------------------------------------- *)After collaboration with D. Mihailovic group at the Jozef Stefan Institute, Ljubljana, Slovenia. **) After collaboration with N. Kirova, LPS, University Paris-Sud, Orsay, France.

Superconductivity is a phenomenon where the macroscopic quantum coherence appears due to the pairing of electrons. The symmetry properties of the pairing, i.e., the parity and spin-singlet/spin-triplet, determine the physical properties of the superconducting state. Odd-frequency pairing originally discussed by Berezinskii as a bulk state. Although the bulk odd-frequency superconductor has not discovered experimentally, the importance of odd-frequency pairing amplitude has been recognized in ferromagnet / superconductor junctions and non-uniform systems. We have clarified that odd-frequency pair amplitude arises in the spatially non-uniform situation quite ubiquitously where bulk superconductor has a conventional even-frequency symmetry. Especially, it has been revealed that when the Andreev bound state (ABS) appears at the surface/interface of the sample, odd-frequency pairing is enhanced. It has been revealed that there are many exotic properties relevant to odd-frequency pairing like anomalous proximity effect in spin-triplet superconductor junctions. This anomalous proximity effect becomes prominent if we consider disordered normal (N) nano wire attached to a topologically nontrivial superconducting (S) one. The transport properties in superconducting nano-wire junctions show universal behaviors irrespective of the degree of disorder: the quantized zero-bias differential conductance at in NS junctions. The odd-frequency pairs exist wherever the Majorana fermions stay. We further discuss a strong relationship between Majorana fermions and odd-frequency Cooper pairs in several topological superconducting systems.

Gibridnye struktury sverkhprovodnik/ferromagnetik/sverkhprovodnik (SFS) s effektom blizosti yavlyayutsya udobnym ob'ektom dlya izucheniya fazovykh perekhodov, vyzvannykh vzaimodeistviem dvukh konkuriruyushchikh parametrov poryadka: sverkhprovodyashchego i ferromagnitnogo. Neobychnoe povedenie sloistykh SF struktur, kak pravilo, svyazano s interesnym yavleniem π-sverkhprovodimosti pri kotorom v gibridnoi strukture formiruetsya ravnovesnoe sostoyanie s netrivial'noi raznost'yu faz π mezhdu sosednimi sverkhprovodnikami. Effekt blizosti na SF granitsakh privodit k chastichnomu ili polnomu podavleniyu sverkhprovodimosti v S sloyakh, a velichina effekta zavisit ot struktury parnoi volnovoi funktsii, t.e. ot tipa sostoyaniya (0 ili π), kotoroe ustanavlivaetsya v SFS strukture. V doklade obsuzhdayutsya prichiny rezkogo uvelicheniya effektivnoi glubiny proniknoveniya magnitnogo polya λ(T) pri ponizhenii temperatury T, kotoroe nablyudalos' v diffuznykh SFS strukturakh Nb/PdNi/Nb s tonkimi (poryadka sverkhprovodyashchei dliny kogerentnosti) S sloyami [1]. Predlozhena model', ob'yasnyayushchaya podobnuyu anomaliyu proyavleniem fazovogo perekhoda mezhdu 0 i π sverkhprovodyashchimi sostoyaniyami SFS struktury. Osnovyvayas' na mikroskopicheskikh uravneniyakh Uzadelya, polucheno razlozhenie Ginzburga—Landau, koeffitsienty kotorogo zavisyat ot raspredeleniya parnoi volnovoi funktsii v ferromagnetike i razlichny dlya 0 i π sostoyanii SFS struktury. Vypolneny raschety svobodnoi energii 0 i π sostoyanii, temperatury 0−π perekhoda, i privedena fazovaya diagramma SFS struktury na ploskosti parametrov (temperatura — tolshchina F sloya). Perekhod mezhdu 0 i π sostoyaniyami pri izmenenii temperatury proiskhodit po tipu fazovogo perekhoda pervogo roda, soprovozhdaetsya skachkoobraznym izmeneniem amplitudy volnovoi funktsii v S sloyakh i, kak sledstvie, rezkim izmeneniem ekraniruyushchikh svoistv SFS struktury. Priveden obobshchennyi funktsional Ginzburga—Landau, spravedlivyi dlya proizvol'noi raznosti faz sverkhprovodyashchikh parametrov poryadka S sloev, i vypolneny raschety tok-fazovoi zavisimosti SFS dzhozefsonovskogo perekhoda s tonkimi sverkhprovodyashchimi elektrodami v okrestnosti perekhoda mezhdu 0 i π sostoyaniyami [2]. Literatura: [1] N. Pompeo et al., Phys. Rev. B 90, 064510 (2014). [2] A. V. Samokhvalov and A. I. Buzdin, Phys. Rev. B 92, 054511 (2015).

We study the low frequency admittance of a small metallic island coupled to a gate electrode and to a massive reservoir via a multi channel tunnel junction. The ac current is caused by a slowly oscillating gate voltage. We focus on the regime of inelastic cotunneling in which the dissipation of energy (the real part of the admittance) is determined by two-electron tunneling with creation of electron-hole pairs on the island. We demonstrate that at finite temperatures but low frequencies the energy dissipation is ohmic whereas at zero temperature it is super-ohmic. We find that (i) the charge relaxation resistance (extracted from the real part of the admittance) is strongly temperature dependent, (ii) the imaginary and real parts of the admittance do not satisfy the Korringa-Shiba relation. At zero temperature the charge relaxation resistance vanishes in agreement with the recent zero temperature analysis [M. Filippone and C. Mora, Phys. Rev. B86, 125311 (2012) and P. Dutt, T. L. Schmidt, C. Mora, and K. Le Hur, Phys. Rev. B 87, 155134 (2013)].

In this talk, I will present a theoretical study of thermal transport in the disordered two-dimensional electron liquid. At temperatures smaller than the impurity scattering rate, in the diffusive regime, thermal conductivity acquires non-analytic quantum corrections. Our approach to this problem is based on an analysis of the heat density-heat density correlation function. To this end, Luttinger’s gravitational potentials are introduced in the action as sources that couple to the heat density. In a two-stage procedure, a renormalization group calculation based on the Keldysh non-linear sigma model in the presence of Luttinger’s gravitational potentials is supplemented with a perturbative study of scattering processes induced by the Coulomb interaction in the sub-temperature energy range. These scattering processes are at the origin of logarithmic corrections violating the Wiedemann-Franz law. As an application, I intend to discuss thermal transport on the metallic side of the metal-insulator transition in Si MOSFETs. References: G. Schwiete and A.M. Finkel’stein, PRB 90, 060201 (2014); PRB 90, 155441 (2014); arXiv:1509.02519; arXiv:1510.06529.

Referativnyi doklad po rabote Cecile Monthus, arxiv:1510.08322.

Interes k zadache ob odnochastichnoi lokalizatsii na sluchainom regulyarnom grafe (RRG) v poslednee vremya vozros v svyazi s problemoi mnogochastichnoi lokalizatsii (MBL). Kachestvenno, MBL mozhno ponimat' kak Andersonovskuyu lokalizatsiyu v prostranstve Sleterovskikh determinantov, kotorye igrayut rol' uzlov v neoporyadochennoi pryzhkovoi modeli. Tak kak struktura Fokovskogo prostranstva ierarkhichna, sootvetstvuyushchaya reshetka napominaet sluchainyi regulyarnyi graf. V etoi rabote my izuchaem Andersonovskii perekhod v ansamble RRG s besporyadkom s pomoshch'yu tochnoi chislennoi diagonalizatsii. My pokazyvaem, chto poluchennaya kartina perekhoda na RRG sovmestima s sushchestvuyushchei teoriei, s usloviem pravil'noi interpretatsii poluchennykh rezul'tatov i ucheta effektov konechnosti razmera grafa. Nash analiz snimaet protivorechie mezhdu imeyushchimisya teoreticheskimi rezul'tatami i chislennymi issledovaniyami drugikh avtorov.

Khorosho izvestno chto provodimost' Kholla kvantuetsya s vysokoi tochnost'yu. Sushchestvuyut li drugie transportnye koeffitsienty, kvantuyushchiesya s takoi zhe tochnost'yu? Okazyvaetsya, chto takikh koeffitsientov kak minimum dva. Oni svyazany s transportom, vyzvannym izmeneniem geometricheskoi formy elektronnoi zhidkosti.

Po rabote: S. Klevtsov, P. Wiegmann: Phys. Rev. Lett. 115: 086801 (2015)

V rabote teoreticheski pokazano, chto kriticheskii tok dzhozefsonovskogo kontakta, soderzhashchego nanoprovoloku s dvumya provodyashchimi kanalami, ispytyvaet mnogoperiodicheskie magnitnye ostsillyatsii. Mnogoperiodichnost' voznikaet iz-za kvantovomekhanicheskoi interferentsii mezhdu kanalami, na kotoruyu sushchestvennoe vliyanie okazyvayut sil'nye spin-orbital'noe i zeemanovskoe vzaimodeistviya. Rassmotrennaya minimal'naya dvukhkanal'naya model' pozvolyaet ob'yasnit' slozhnye interferentsionnye yavleniya, obnaruzhennye v eksperimentakh po izmereniyu dzhozefsonovskogo transporta cherez nanoprovoloki vismuta.

Khorosho izvestno, chto sverkhprovodimost' i magnetizm - antagonisticheskie yavleniya, kotorye ne mogut odnovremenno realizovyvat'sya v odnom materiale. Odnako, ikh sosushchestvovanie stanovitsya vozmozhnym v mnogosloinykh gibridnykh sistemakh, v kotorykh sverkhprovodyashchie i ferromagnitnye oblasti prostranstvenno razdeleny. Osnovnaya osobennost' takikh sistem - vozniknovenie neodnorodnykh sverkhprovodyashchikh sostoyanii s ekzoticheskimi magnitnymi i transportnymi svoistvami, kotorye mogut byt' polozheny v osnovu novogo klassa ustroistv vychislitel'noi mikroelektroniki. Seminar budet posvyashchen obzoru osnovnykh svoistv takikh neodnorodnykh sostoyanii i printsipov raboty ustroistv na ikh osnove.

My rassmatrivaem nestatsionarnuyu sistemu provodnikov, soprotivleniya mezhdu kotorymi ispytyvayut sil'nye fluktuatsii vo vremeni. Transport mezhdu paroi sosednikh provodnikov opredelyaetsya temi momentami, kogda sootvetstvuyushchee soprotivlenie anomal'no malo (provodniki “kasayutsya drug druga”). V takie momenty voznikaet “proboi” i zaryad legko peretekaet mezhdu paroi soprikosnuvshikhsya provodnikov. Protsess perenosa zaryada za schet proboev, voznikayushchikh v sluchainye momenty v sluchainykh mestakh, my nazvali polzuchei provodimost'yu. My rassmatrivaem kak trekhmernye, tak i nizkorazmernye massivy provodnikov i issleduem provodimost' sistemy, rastekanie zaryada, pervonachal'no sosredotochennogo na odnom provodnike, a takzhe fluktuatsii zaryadov i elektricheskikh polei i ikh prostranstvenno-vremennuyu korrelyatsiyu. Obsuzhdayutsya vozmozhnye realizatsii modeli v kolloidnykh rastvorakh i sistemakh metallicheskikh sharikov, soedinennykh deformiruemymi polimernymi molekulami.

We study one-dimensional anisotropic XY-Heisenberg spin-1/2 chain with weak random fields h^z_iS^z_i by means of Jordan-Wigner transformation to spinless Luttinger liquid with disorder and bosonization technique. First we investigate phase diagram of the system in terms of dimensionless disorder γ=⟨h²⟩/J²≪1 and anisotropy parameter Δ=J_z/J_xy and find the range of these parameters where disorder is irrelevant in the infrared limit and spin-spin correlations are described by power laws. Then we use the diagram technique in terms of plasmon excitations to study low-temperature behavior of heat conductivity κ and spin conductivity σ in this power-law phase. The obtained Lorentz number L≡κ/σT differs from the value derived earlier by means of memory function method. We argue also that in the studied region inelastic scattering is strong enough to suppress quantum interference in the low-temperature limit.

Referativnyi doklad po rabote Y.-C. He, S. Bhattacharjee, F. Pollmann, R. Moessner, arXiv:1509.03070

Doklad budet sostoyat' iz dvukh chastei. V pervoi iz nikh budet pokazano, na osnove sovmestnoi s L.B.Ioffe raboty [1], chto sverkhprovodniki s psevdoshchel'yu obladayut anomal'noi zavisimost'yu sverkhtekuchei plotnosti \rho_s ot velichiny sverkhprovodyashchei shcheli \Delta: \rho_s ~ \Delta^2. Pokhozhee povedenie bylo nedavno nablyudeno [2]. Vo vtoroi chasti doklada ya pokazhu, kak mozhno ob'yasnit' shiroko izvestnoe dlya sil'no gryaznykh sverkhprovodnikov anomal'noe povedenie verkhnego kriticheskogo polya H_c2(T) pri nizkikh temperaturakh, ispol'zuya nedavnii eksperimental'nyi rezul'tat [3] o nalichii perekhoda Berezinskogo-Kosterlitsa-Taulesa v sluchae sverkhprovodyashchei plenki v sil'nom magnitnom pole i rezul'taty izmereniya kriticheskogo toka kak funktsii magnitnogo polya v predele ochen' nizkikh temperaturakh [4].
[1] M. V. Feigel'man, L. B. Ioffe arXiv:1509.05138, Phys Rev B, accepted.
[2] D. Sherman et al, Nature Phys. (2015)
[3] S. Misra, L. Urban, M. Kim, G. Sambandamurthy, and A. Yazdani, Phys. Rev. Lett. 110, 037002 (2013)
[4] J.Seidemann et al, unpublished (Master diploma thesis, Grenoble 2013).

Referativnyi doklad pro vozmozhnuyu realizatsiyu topologicheskogo izolyatora v sil'nokorrelirovannoi elektronnoi sisteme. Teoreticheskoe predskazanie i eksperimental'nye svidetel'stva v materiale SmB_6.

[1] M. Dzero, K. Sun, V. Galitski, P. Coleman, PRL 104, 106408 (2010).
[2] M. Ye, J. W. Allen, K. Sun, http://arxiv.org/abs/1307.7191
[3] S. Wolgast, Ç. Kurdak, K. Sun, J. W. Allen, D.-J. Kim, Z. Fisk, PRB 88, 180405(R) (2013).

A nondissipative supercurrent state of a Josephson junction is metastable with respect to the formation of a finite-resistance state. This transition is driven by fluctuations, thermal at high temperatures and quantum at low temperatures. We evaluate the life time of such a state due to quantum fluctuations in the limit when the supercurrent is approaching the critical current. The decay probability is determined by the instanton action for the superconducting phase difference across the junction. At low temperatures, dynamics of the phase is massive and is determined by the effective capacitance, which is a sum of the geometric and intrinsic capacitance of the junction. We model the central part of the Josephson junction either by an arbitrary short mesoscopic conductor described by the set of its transmission coefficients, or by a diffusive wire of an arbitrary length. The intrinsic capacitance can generally be estimated as $C_* \sim G/E_g$, where $G$ is the normal-state conductance of the junction and $E_g$ is the proximity minigap in its normal part. The obtained capacitance is sufficiently large to qualitatively explain hysteretic behavior of the current-voltage characteristic even in the absence of overheating.

Recently in Kapitza Institute a new phase of the superfluid 3He was reported to exist in the aerogel-like nafen structure - the so-called polar phase. As distinct from the other phases - the chiral superfluid 3He-A with Weyl nodes and the fully gapped topological 3He-B with Dirac nodes on the surface - the polar phase has Dirac nodal line in bulk and dispersionless band of Andreev-Majorana fermions on the surface. Being the spin-triplet superfluid with equal-spin pairing the polar phase can support an exotic object - the half-quantum vortex (HQV). Originally the HQVs have been predicted to exist in the Weyl superfluid 3He-A in 1976, but still they have not been observed there: unfavorable combination of spin-orbit and magnetic anisotropy effects on the orientation of the order parameter did not allow to stabilize these vortices in bulk 3He-A under rotation. In nafen, the nearly parallel aerogel strands pin the orbital part of the order parameter of the polar phase. As a result, if the magnetic field is absent or is oriented parallel to nafen strands, the half-quantum vortices win over the conventional single-quantum vortices.
If HQVs are formed in rotation and then the field is tilted with respect to the strands, one expects that the spin-orbit interaction would induce the formation of the topological solitons between the neighboring HQVs providing the peculiar satellite peak in the NMR spectrum. We used this theoretical prediction to stabilize and identify the HQVs in the Helsinki rotated cryostat. For that we cool down a sample of nafen through transition temperature to the polar phase in rotation up to 2.75 rad/s without magnetic field. Then the field is switched on, and in the tilted field we observe a satellite peak in the NMR spectrum. The dependence of the satellite on the rotation velocity, temperature and the field orientation is in agreement with the predictions. If cool-down occurs with the field applied in the transverse direction, no satellite eak is observed. This demonstrates that the single-quantum vortices are formed instead, which have no NMR signatures. in such arrangement these vortices win over the HQVs as expected.

Dinamicheskii effekt Lemba yavlyaetsya odnim iz vozmozhnykh mekhanizmov parametricheskogo vozbuzhdeniya atoma v rezonatore [A.M. Fedotov, N.B. Narozhny, and Yu.E. Lozovik, PRA 64, 053807 (2001)]. Effekt voznikaet v rezul'tate modulyatsii lembovskogo sdviga atoma za schet, naprimer, neadiabaticheskogo izmeneniya chastoty fotonnoi mody. Tem ne menee, v sisteme s perestraivaemym rezonatorom etot mekhanizm vozbuzhdeniya slozhno izolirovat' ot drugikh kanalov, svyazannykh s generatsiei i pogloshcheniem kazimirovskikh fotonov. V doklade predlozhena al'ternativnaya realizatsiya dinamicheskogo effekta Lemba, kotoraya vozmozhna v sovremennykh sverkhprovodnikovykh sistemakh kubit-rezonator v rezhime perestraivaemoi energii svyazi. Pokazano, chto imenno za schet neadiabaticheskogo pereklyucheniya energii vzaimodeistviya mozhno modulirovat' lembovskii sdvig i vozbuzhdat' kubit v otsutstvie fotonnoi nakachki. Takoi podkhod pozvolyaet izbezhat' rozhdeniya kazimirovskikh fotonov, chto yavlyaetsya klyuchevym obstoyatel'stvom dlya realizatsii dinamicheskogo effekta Lemba. Dinamika sistemy opisyvaetsya v ramkakh nestatsionarnoi modeli Rabi dlya edinichnogo i periodicheskogo pereklyuchenii energii svyazi kubita i rezonatora. [D.S. Shapiro, A.A. Zhukov, W.V. Pogosov, Yu.E. Lozovik, "Dynamical Lamb effect in a tunable superconducting qubit-cavity system", Phys. Rev. A 91, 063814 (2015); arXiv:1503.01666]

Odnofotonnye detektory na osnove sverkhprovodyashchikh nanoprovolok (Superconducting Nanowire Single-Photon Detectors (SNSPD)) issleduyutsya nauchnym soobshchestvom uzhe v techenii nekotorogo vremeni, chto privelo k sushchestvennomu progressu v ponimanii ikh raznoobraznykh opticheskikh, elektricheskikh i drugikh fizicheskikh svoistv. Spektral'naya polosa propuskaniya SNSPD ogranichennaya dlinoi volny otsechki, kotoraya opredelyaetsya parametrami sverkhprovodyashchei plenki, ispol'zuemoi dlya detektora, i geometriei detektora. Na segodnyashnii den' sushchestvuet mnozhestvo razlichnykh prilozhenii, gde SNSPD detektory, integrirovannye v izmeritel'nye kriogennye sistemy, pozvolyayut provodit' eksperimenty v oblasti kvantovoi kriptografii, izlucheniya kvantovykh tochek ili spektroskopii. Prichinu shirokogo ispol'zovaniya SNSPD detektorov dlya takikh zadach mozhno legko ob'yasnit', esli prinyat' vo vnimanie nekotorye poleznye svoistva SNSPD detektorov, a imenno nizkuyu temnovuyu skorost' scheta, vysokuyu skorost' detektirovaniya i vysokuyu tochnost' sinkhronizatsii v pikosekundnom diapazone.

V nashi dni SNSPD sistemy osnovany, glavnym obrazom, na odnopiksel'nykh detektorakh. Mnogopiksel'nye sistemy dolzhny rasshirit' potentsial'nye oblasti primeneniya detektorov. Po etoi prichine, neobkhodimy novye kontseptsii dlya organizatsii schityvaniya dannykh s mnogopiksel'nykh SNSPD sistem. My daem obzor vozmozhnykh kontseptsii, uslovii raboty i sposobov optimizatsii SNSPD detektorov dlya konkretnykh prilozhenii, rabotayushchikh v odnofotonnom rezhime.

Osnovyvayas' na tekh zhe sverkhprovodyashchikh sverkhtonkikh plenkakh mogut byt' realizovany Bolometry na goryachikh elektronakh (Hot-Electron Bolometers (HEBs)) dlya neposredstvennogo detektirovaniya i ponizhayushchego preobrazovaniya teragertsovogo izlucheniya. My obsudim HEB-smesiteli na osnove ul'tratonkikh plenok NbN dlya geterodinnogo detektirovaniya TGts signalov. Krome togo, my razrabotali detektor neposredstvennogo TGts-detektirovaniya na osnove tonkoplenochnykh nanostruktur iz vysokotemperaturnogo sverkhprovodnika YBa2Cu3O7-kh. Eti detektory imeyut predel'noe vremennoe razreshenie okolo 10-20 ps, pozvolyaya provodit' izmereniya pikosekundnykh impul'sov, ispuskaemykh istochnikom sinkhrotronnogo izlucheniya.

Nekotoroe vremya nazad bylo rassmotreno povedenie edinichnogo atoma, pomeshchennogo v polost' s izmenyayushchimisya vo vremeni parametrami - [A. M. Fedotov, N. B. Narozhny, Yu. E. Lozovik, Phys. Rev. A 64, 053807 (2001)]. Bylo pokazano, chto v takoi sisteme realizuetsya neskol'ko mekhanizmov parametricheskogo vozbuzhdeniya atoma. Odin iz nikh svyazan s vozbuzhdeniem za schet neadiabaticheskoi modulyatsii lembovskogo sdviga v osnovnom sostoyanii atoma. Eto yavlenie bylo nazvano dinamicheskim effektom Lemba (po analogii s dinamicheskim effektom Kazimira). V sluchae real'nogo atoma, pomeshchennogo v polost' s izmenyayushchimisya vo vremeni parametrami, dinamicheskii effekt Lemba okazyvaetsya dovol'no slozhno izolirovat' ot inykh mekhanizmov vozbuzhdeniya atoma. V dannoi rabote pokazano, chto dlya realizatsii dinamicheskogo effekta Lemba perspektivno ispol'zovat' iskusstvennyi «atom»-kubit, svyazannyi s SVCh-rezonatorom. Kharakternuyu energiyu vzaimodeistviya mezhdu kubitom i rezonatorom mozhno menyat' vo vremeni, chto vpolne osushchestvimo s tochki zreniya sovremennogo eksperimenta. Za schet neadiabaticheskogo izmeneniya energii vzaimodeistviya mozhno dobit'sya vozbuzhdeniya kubita. Dannyi podkhod pozvolyaet izbezhat' rozhdeniya kazimirovskikh fotonov, chto yavlyaetsya klyuchevym obstoyatel'stvom dlya realizatsii dinamicheskogo effekta Lemba.

[D. S. Shapiro, A. A. Zhukov, W. V. Pogosov, Yu. E. Lozovik, "Dynamical Lamb effect in a tunable superconducting qubit-cavity system", Phys. Rev. A 91, 063814 (2015); arXiv:1503.01666]

S uvelicheniem vychislitel'nykh moshchnostei, ostro vstal vopros potreblyaemoi energii. Razrabotka sverkhprovodnikovogo komp'yutera vo mnogikh laboratoriyakh rassmatrivaetsya kak reshenie problemy nizkoenergeticheskikh vychislenii. Nekotorye vidy adiabaticheskikh vychislenii na sverkhprovodnikakh (naprimer QFP) priblizhayutsya k teoreticheskomu predelu energozatrat. Odnokvantovaya logika, khotya i ustupaet im v energovydelenii, yavlyaetsya naibolee perspektivnoi na segodnyashnii den'.

V doklade budet priveden obzor tekushchego sostoyaniya del v razrabotke SFQ protsessorov, a takzhe budut zatronuty nekotorye drugie perspektivnye napravleniya v vychislitel'noi elektronike.

Sverkhprovodyashchie kvantovye interferometry (SKVIDy) shiroko izvestny svoei sposobnost'yu prevrashchat' prilozhennyi magnitnyi signal v otklik napryazheniya. V dannom doklade my predstavlyaem obzor ryada eksperimental'nykh i teoreticheskikh rabot, napravlennykh na sozdanie na osnove SKVIDov struktur so spetsificheskim vidom vol't-potokovoi kharakteristiki (primerom mogut posluzhit' struktury s vysokoi lineinost'yu preobrazovaniya magnitnogo potoka v napryazhenie). Budut razobrany fizicheskie osnovy sozdaniya sverkhprovodyashchikh kvantovykh interferentsionnykh fil'trov (SKIFov), differentsial'nykh dzhozefsonovskikh struktur, bi-SKVIDov i bi-SKVID SKIFov.

Seminar budet posvyashchen opisaniyu novykh nizkorazmernykh metamaterialov i transportnykh yavlenii, v kotorykh vazhnuyu rol' igraet interferentsiya fononov na atomarnykh defektakh reshetki kristalla. Budet pokazano, chto vozmozhno rezonansnoe polnoe otrazhenie ili polnoe pogloshchenie fonona dvumernym defektom reshetki, effektivnaya tolshchina kotorogo znachitel'no men'she dliny volny fonona. Chastoty takikh rezonansov opredelyayutsya dinamicheskimi svoistvami defektnoi ploskosti. Yavlenie polnogo otrazheniya (antirezonansa prokhozhdeniya) vozmozhno, v chastnosti, na monoatomnoi kristallicheskoi ploskosti, chastichno zapolnennoi atomarnymi defektami, i na dvumernom defekte reshetki, v kotorom sushchestvenny vzaimodeistviya kak blizhaishikh, tak i ne blizhaishikh sosedei. Analiz etikh yavlenii pokazyvaet, chto opredelyayushchuyu rol' v nikh, v otlichie ot rezonansa Fano, igraet destruktivnaya interferentsiya fononov, rasprostranyayushchikhsya cherez dvumernyi defekt po dvum putyam: po silovym svyazyam atomov matritsy i defektov, ili po svyazyam blizhaishikh i ne blizhaishikh sosedei. Pokazano, chto sluchainoe raspredelenie defektov v kristallicheskoi ploskosti i angarmonizm silovykh svyazei ne razrushayut interferentsionnyi antirezonans. Shirinu antirezonansnogo pika otrazheniya mozhno svyazat' s dlinoi kogerentnosti fononnogo volnovogo paketa, kak i v sluchae destruktivnoi interferentsii fotonnykh volnovykh paketov v effekte Khonga-U-Mandela. Pokazano, chto destruktivnaya interferentsiya fononov ponizhaet teplovoi kondaktans granitsy razdela kristallov, chastichno zapolnennoi rezonansnymi atomarnymi defektami. Na osnove atomarnykh metazerkal mozhet byt' postroen ul'tra kompaktnyi «fononnyi kondensator» dlya khraneniya i izlucheniya kogerentnykh teragertsovykh fononov. Vse osnovnye predstavlennye vyvody podtverzhdayutsya analiticheskimi raschetami ekvivalentnykh kvaziodnomernykh reshetok i molekulyarno-dinamicheskim modelirovaniem realistichnykh trekhmernykh reshetok. [Literatura: 1. Yu.A. Kosevich «Capillary phenomena and macroscopic dynamics of complex two-dimensional defects in crystals», Progr. Surf. Sci. 55, 1 (1997). 2. Yu.A. Kosevich «Mnogokanal'noe rasprostranenie i rasseyanie fononov i fotonov v nizkorazmernykh nanostrukturakh», UFN 178(8), 884 (2008). 3. H. Han, L. Potyomina, A.A. Darinskii, S. Volz, and Yu.A. Kosevich «Phonon interference and thermal conductance reduction in atomic-scale metamaterials», Phys. Rev. B 89(R), 180301 (2014). 4. H. Han, B. Li, S. Volz, and Yu.A. Kosevich «Ultracompact interference phonon nanocapacitor for storage and lasing of coherent terahertz lattice waves», Phys. Rev. Lett. 114, 145501 (2015).]

My izuchaem tokovyi shum v CdHgTe/HgTe/CdHgTe kvantovoi yame s invertirovannoi zonnoi strukturoi v rezhime neuporyadochennogo kraevogo transporta. V soglasii s predydushchimi eksperimentami soprotivlenie kraya sushchestvenno prevoskhodit h/e2 i slabo zavisit ot temperatury. Drobovoi shum v rezhime kraevogo transporta znachitel'no podavlen po sravneniyu s puassonovskim znacheniem i kharakterizuetsya faktorom Fano v diapazone 0.1 < F < 0.3 dlya razlichnykh obraztsov i znachenii zatvornogo napryazheniya. S uchetom togo, chto dlina kraya men'she ballisticheskoi dliny sboya fazy, eti nablyudeniya isklyuchayut vozmozhnost' odnomernogo gelikal'nogo kraevogo transporta v nashikh obraztsakh. Rezul'taty eksperimenta kachestvenno mozhno ob'yasnit' v modeli neuporyadochennogo mnogokanal'nogo kvazi-odnomernogo transporta vdol' kraya.

We consider the Z_2 topology of the Dirac lines - lines of band intersection - in graphite. Four lines (three with topological charge N_1=1 each and one with N_1=-1) merge near the H-point and annihilate due to summation law 1+1=0. The merging point is similar to the real-space nexus, the analog of Dirac monopole at which the Z_2 strings terminate.

Kvantovyi turniket predstavlyaet soboi nanoelektronnoe ustroistvo, kontroliruemym obrazom perenosyashchee elektrony po odnomu mezhdu dvumya sverkhprovodyashchimi elektrodami putem podachi peremennogo napryazheniya na metallicheskuyu nanochastitsu, raspolozhennuyu mezhdu dvumya elektrodami. Okazyvaetsya, chto kogerentnaya svyaz' mezhdu elektronnymi sostoyaniyami v nanochastitse i kvazichastichnymi sostoyaniyami v sverkhprovodnikakh nakladyvaet fundamental'nye ogranicheniya na rabotu ustroistva.

We study the thermoelectric transport of a small metallic island weakly coupled to two electrodes by tunnel junctions. In the Coulomb blockade regime, in the case when the ground state of the system corresponds to an even number of electrons on the island, the main mechanism of electron transport at the lowest temperatures is elastic cotunneling. In this regime, the transport coefficients strongly depend on the realization of the random impurity potential or the shape of the island. Using random-matrix theory, we calculate the thermopower and the thermoelectric kinetic coefficient and study the statistics of their mesoscopic fluctuations in the elastic cotunneling regime. The fluctuations of the thermopower turn out to be much larger than the average value.
[Phys. Rev. B 91, 085310 (2015)]

V vystuplenii budut rassmotreny voprosy razrabotki i sozdaniya osnovnykh elementov SKVID-sistem dlya biomagnitnykh issledovanii: SKVID-datchikov, stekloplastikovykh nemagnitnykh kriostatov, izmeritel'nykh zondov i elektroniki, v tom chisle dlya SKVID-sistem na osnove vysokotemperaturnykh sverkhprovodnikov. Rassmotreny voprosy razrabotki i sozdaniya magnitometricheskikh SKVID-sistem dlya primenenii v magnitokardiografii i magnitoentsefalografii. Privedeny rezul'taty ikh prakticheskogo ispol'zovaniya v klinicheskikh usloviyakh.

When single-particle excitations of a disordered quantum many-body system are all localized in the coordinate space, a sufficiently weak local interaction does not destroy localization at sufficiently low temperatures. Namely, all many-particle excitations remain localized in the Fock space, and there is no relaxation or transport in the system, which is known as many-body localization. It occurs because the local interaction effectively couples a finite number of discrete energy levels, corresponding to localized excitations. When the interaction is weak, these localized excitations are only weakly mixed.

In contrast to a quantum system, where a continuous energy spectrum can be obtained only in the limit of the infinite system size, and is thus subject to localization in the Fock space, in a classical system (e.g., in the disordered nonlinear Schroedinger chain, representing the classical limit of the Bose-Hubbard model), motion can have continuous spectrum already for a finite number of degrees of freedom, and this leads to chaotic dynamics. Because of this, in a disordered system with an extensive energy (with however small density), the probability to be on a chaotic trajectory tends to unity with increasing system size. This produces finite transport coefficients at arbitrarily weak nonlinearity.

Vychisleno transportnoe sechenie rasseyaniya elektronov v grafene na kruglom otverstii (ili defekte). Predpolagaetsya, chto na krayu otverstiya mogut sushchestvovat' kvazistatsionarnye kraevye (tammovskie) sostoyaniya, kotorye privodyat k pikam v sechenii rasseyaniya, kotorye mogli nablyudat'sya v transportnykh eksperimentakh [Yu.I. Latyshev i dr., Pis'ma v ZhETF 98, 242 (2013), Yu.I. Latyshev et al., Scientific Reports 4, 7578 (2014)]. Obsuzhdaetsya uchet neodnorodnosti kraya, a takzhe zaryazhennosti nanootverstiya (defekta), chto privodit k razmytiyu i smeshcheniyu pikov.

Dlya starshekursnikov i aspirantov, spetsializiruyushchikhsya v oblasti kvantovoi teorii kondensirovannogo sostoyaniya

Programma kursa: 1. Andersonovskaya lokalizatsiya v trekh izmereniyakh, lokatornoe razlozhenie. 2. Lokalizatsiya v odnomernoi tsepochke, uravnenie Fokkera-Planka dlya koeffitsienta prokhozhdeniya. 3. Lokalizatsiya v tolstykh kvaziodnomernykh provolokakh (kriterii Taulessa), dinamicheskaya lokalizatsiya v kvantovoi tochke pod nakachkoi i otobrazhenie na kvaziodnomernuyu provoloku. 4. Slabolokalizatsionnaya popravka k provodimosti v dvukh izmereniyakh. 5. Elektron-elektronnoe vzaimodeistvie v kvantovykh tochkakh, universal'nyi gamil'tonian, kulonovskaya blokada, skorostnye uravneniya. 6. Elektron-elektronnye stolknoveniya v nizkorazmernykh sistemakh, mnogochastichnaya lokalizatsiya. 7. Kotunnelirovanie cherez kvantovuyu tochku v rezhime kulonovskoi blokady. 8. Effekt Kondo v kvantovoi tochke v rezhime kulonovskoi blokady.

Vremya: po vtornikam (10-12) i chetvergam (16-18)

Pervaya lektsiya - vo vtornik 14 aprelya 2015 g.

Privedeny rezul'taty teoreticheskikh issledovanii elektronnoi struktury i osobennostei individual'nogo pinninga vikhrya Abrikosova, zakhvachennogo neprovodyashchim tsilindricheskim defektom (polost'yu) s kharakternym razmerom men'she ili poryadka sverkhprovodyashchei dliny kogerentnosti. Predlozhena mikroskopicheskaya model' depinninga (sryva) vikhrya Abrikosova pod vliyaniem vneshnego transportnogo toka, kotoraya uchityvaet izmenenie topologii kvaziklassicheskikh orbit s energiei Fermi i perestroiku spektra vozbuzhdenii v vikhre, zakhvachennom na protyazhennom defekte. Izucheno formirovanie neodnorodnykh i vikhrevykh sostoyanii v gibridnykh strukturakh sverkhprovodnik–ferromagnetik s neodnosvyaznoi geometriei (polyi sverkhprovodyashchii tsilindr s ferromagnitnoi serdtsevinoi), v kotorykh orbital'nyi i obmennyi mekhanizmy, podavlyayushchie sverkhprovodimost', konkuriruyut drug s drugom, a effekt blizosti mozhet stimulirovat' perekhody mezhdu sverkhprovodyashchimi sostoyaniyami s razlichnoi zavikhrennost'yu.

Sverkhprovodyashchie kvantovye metamaterialy - iskusstvenno sozdannye novye materialy, sostoyashchie iz bol'shogo chisla sil'no vzaimodeistvuyushchikh kubitov. Elektrodinamicheskie svoistva takikh materialov opredelyayutsya zakonami kvantovoi mekhaniki na makroskopicheskom urovne.

V doklade budet predstavlen obzor nedavnikh eksperimental'nykh i teoreticheskikh issledovanii prokhozhdeniya voln v sverkhprovodyashchikh kvantovykh metamaterialakh. Budut obsuzhdat'sya razlichnye kollektivnye kvantovye effekty v takikh sistemakh, osoboe vnimanie budet udeleno vozmozhnosti sinkhronizatsii kvantovykh dinamicheskikh ostsillyatsii otdel'nykh kubitov.

V sostoyanii s volnoi zaryadovoi ili spinovoi plotnosti v usloviyakh neideal'nogo nestinga chast' elektronnykh sostoyanii ostaetsya na urovne Fermi, chto sokhranyaet metallicheskuyu provodimost' obraztsa. Odnako poverkhnost' Fermi elektronov provodimosti v takom sostoyanii sil'no otlichaetsya ot iskhodnoi, potomu chto rasseyanie na vektor volny plotnosti privodit k perestroike poverkhnosti Fermi. Obychno eto soprovozhdaetsya vozniknoveniem novykh chastot magnitnykh kvantovykh ostsillyatsii, sootvetstvuyushchikh perestroennoi poverkhnosti Fermi. Odnako, v sil'nom magnitnom pole voznikaet magnitnyi proboi, kotoryi mozhet vosstanovit' dvizhenie elektronov po traektoriyam, sootvetstvuyushchim iskhodnoi poverkhnosti Fermi. Eto proiskhodit iz-za togo, chto rasstoyanie po energii mezhdu starymi i novymi elektronnymi traektoriyami okazyvaetsya malym, poryadka potentsiala rasseyaniya na volne plotnosti, to est' poryadka energeticheskoi shcheli volny plotnosti. Pri etom veroyatnost' elektronov dvigat'sya vdol' staroi ili novoi poverkhnosti Fermi eksponentsial'no zavisit ot velichiny etoi shcheli. Poetomu prostranstvennye fluktuatsii parametra poryadka volny plotnosti privodyat k prostranstvennym fluktuatsiyam veroyatnosti magnitnogo proboya, i v itoge k dopolnitel'nomu rasseyaniyu elektronov. Pri vysokoi kontsentratsii neodnorodnostei volny plotnosti etot novyi mekhanizm rasseyaniya elektronov provodimosti mozhet okazat'sya dostatochno sil'nym: sil'nee, chem rasseyanie na primesyakh. Etot mekhanizm mozhet privodit' k neobychnym effektam, takim kak sil'noe nemonotonnoe magnitosoprotivlenie, ili inversiya fazy magnitnykh kvantovykh ostsillyatsii. Imenno eto nablyudaetsya v razlichnykh organicheskikh metallakh, naprimer, v a-(BEDT-TTF)₂KHg(SCN)₄. Obsuzhdaetsya takzhe vozmozhnost' ispol'zovaniya etogo mekhanizma rasseyaniya dlya izmereniya fluktuatsii parametra poryadka volny plotnosti v vysokotemperaturnykh sverkhprovodnikakh.

Na model'nom uravnenii Shredingera s del'taobraznym potentsialom obsuzhdayutsya sushchestvennye otlichiya obratnoi zadachi rasseyaniya na vsei osi ot sluchaya poluosi. Ispol'zuetsya pri etom ekvivalentnost' rassmatrivaemoi model'noi zadachi diskretnoi tsepochke uravnenii s vzaimodeistviem blizhaishikh sosedei dostatochno obshchego vida. Ustanavlivayutsya takzhe yavnye formuly dlya funktsii Grina uravnenii Shredingera s del'taobraznymi potentsialami i issleduyutsya svoistva etikh funktsii Grina.

V doklade predstavlena istoriya sozdaniya sverkhprovodnikovogo integral'nogo priemnika i dan kratkii obzor ego primenenii. Odnim iz takikh prilozhenii stalo issledovanie spektrov izlucheniya Bi2Sr2CaCu2O8 meza-struktur v teragertsovom diapazone. Privedeny rezul'taty izmerenii, obsuzhdayutsya perspektivy sozdaniya kompaktnykh istochnikov teragertsovogo izlucheniya.

We consider a class of strongly correlated Fermi systems that possess interaction-induced flat bands, pinned to the Fermi surface. We demonstrate that in such systems, the fundamental Landau equation, connecting the single-particle spectrum to the quasiparticle momentum distribution, fails. We propose a method, allowing to rectify drawbacks of Landau theory and, with the aid of the Pitaevskii identity, generalize equations obtained to apply the method to electron systems of solids. The emergent non-Fermi-liquid behavior, derived from the theory constructed, is compared with relevant experimental data on two-dimensional liquid He-3, heavy-fermion metals and electron-doped high-T_c compounds.

Gapped 2D Dirac materials, in which inversion symmetry is broken by a gap-opening perturbation, feature a unique valley transport regime. The system ground state hosts dissipationless persistent valley currents existing even when topologically protected edge modes are absent or when they are localized due to edge roughness. Topological valley currents in such materials are dominated by bulk currents produced by electronic states just beneath the gap rather than by edge modes. Dissipationless currents induced by an external bias are characterized by a quantized half-integer valley Hall conductivity. The under-gap currents dominate magnetization and the charge Hall effect in a light-induced valley-polarized state.

Razvitie metodov polucheniya izobrazheniya na SVCh i v oblasti dal'nego IK izlucheniya yavlyaetsya bystro rastushchei oblast'yu, ogranicheniem kotoroi na segodnya yavlyaetsya effektivnost' ustroistv schityvaniya. Predlozheno usovershenstvovat' sistemu schityvaniya s razdeleniem chastot dlya sverkhprovodyashchikh TES detektorov, otkazavshis' ot nabora SKVID-usilitelei v pol'zu odnogo shirokopolosnogo okhlazhdaemogo usilitelei SVCh na poluprovodnikakh, kotoryi mozhet obsluzhit' do 10 tysyach i bolee pikselei. Predlozheno nagruzit' mostikom TES vysokodobrotnyi SVCh rezonator, slabo svyazannyi s liniei peredachi, i registrirovat' otklik na chastote rezonansa v vide izmeneniya urovnya prokhozhdeniya, vyzvannogo razogrevom takogo mostika, analogichno MKID detektoram. Dannaya kontseptsiya byla proverena na mostikakh-prototipakh iz niobiya v diapazone temperatur 1-5 K, i bylo polucheno NEP = 2×10^{‑14} Vt/Gts^{0.5} pri kriticheskoi temperature plenok Tc=5 K v diapazone 600-700 GGts. Byla skonstruirovana metapoverkhnost' (matritsa), pozvolyayushchaya registrirovat' slabye signaly, a takzhe razrabotan printsip uvelicheniya razmernosti takoi matritsy.

S tsel'yu dal'neishego integrirovaniya tsepei priema (matritsy detektorov) i tsepei obrabotki signala (generatora nakachki i usilitelya), razrabatyvayutsya dva novykh aktivnykh metamateriala: dlya generatsii i usileniya signalov gigagertsovogo diapazona. Oba pribora osnovany na dvumernykh reshetkakh dzhozefsonovskikh kontaktov s parallel'no-posledovatel'nym vklyucheniem po postoyannomu toku, podstraivaemykh s pomoshch'yu magnitnogo polya. Sverkhprovodyashchii generator predstavlyaet soboi skhemu iz neshuntirovannykh tunnel'nykh dzhozefsonovskikh perekhodov, a usilitel', naoborot, iz shuntirovannykh kontaktov, imeyushchikh bezgisterezisnuyu VAKh. Dvukhmernye reshetki dopuskayut neogranichennoe uvelichenie sistemy, chto pozvolyaet uvelichit' diapazon moshchnosti signala, a takzhe optimizirovat' impedans. Detal'noe elektromagnitnoe modelirovanie pokazyvaet, chto generator sposoben rabotat' na chastotakh do 0,7 TGts s perestroikoi chastoty magnitnym polem okolo 2%, a usilitel' - s shumami u kvantovogo predela v diapazone chastot 8-12 GGts s usileniem okolo 10 dB.

Rassmotreny osnovnye osobennosti effekta blizosti i effekta Dzhozefsona v strukturakh, sostoyashchikh iz sverkhprovodyashchikh, normal'nykh i ferromagnitnykh materialov. Dan kratkii obzor sovremennogo sostoyaniya issledovanii v oblasti razrabotki sverkhprovodnikovykh spinovykh ventilei. Obsuzhdeny vozmozhnye trudnosti prakticheskoi realizatsii takikh ustroistv.

Budut predstavleny rezul'taty nedavnego eksperimenta [1] po izucheniyu neravnovesnykh potokov energii mezhdu vstrechnymi kraevymi kanalami v rezhime kvantovogo effekta Kholla. Sistema iz dvukh takikh kanalov, razvyazannykh gal'vanicheski, no vzaimodeistvuyushchikh posredstvom kulonovskikh sil, yavlyaetsya pryamym analogom besspinovoi zhidkosti Lattinzhera [2] i ideal'no podkhodit dlya izucheniya energeticheskogo transporta. Original'nyi bolometricheskii podkhod k izmereniyu izbytochnogo potoka energii P v kraevom kanale pozvolil issledovat' zavisimosti P ot tyanushchego napryazheniya i protyazhennosti otrezka lattinzherovskoi zhidkosti. Pokazano, chto protsess peredachi energii kolichestvenno soglasuetsya s kontseptsiei uprugogo rasseyaniya kollektivnykh vozbuzhdenii plotnosti na granichnykh tochkakh lattinzherovskogo otrezka, pri etom imeetsya vozmozhnost' nepreryvnogo kontrolya parametra vzaimodeistviya i veroyatnosti rasseyaniya. Literatura: [1] M.G. Prokudina, S. Ludwig, V. Pellegrini, L. Sorba, G. Biasiol, V.S. Khrapai, Tunable non-equilibrium Luttinger liquid based on counter-propagating edge channels, Phys. Rev. Lett. 112, 216402 (2014). [2] Yuval Oreg and Alexander M. Finkel'stein, Interedge Interaction in the Quantum Hall Effect, Phys. Rev. Lett. 74, 3668 (1995).

The concept of the odd-frequency Cooper pairs was first proposed by Berezinskii in 1974 to describe superfluidity of 3He [1]. Although the odd-frequency superconductivity has never been confirmed in any materials, the odd-frequency pairs appear as the subdominant pairing correlation in various proximity structures such as superconductor / ferromagnet (SF) junctions [2] and normal-metal / superconductor (NS) junctions with unconventional pairing symmetry [3]. In the presentation, we explain what the odd-frequency pairs are, how they appear in such proximity structure, how to detect them, and how they are different from usual even-frequency pairs in the bulk. We first discuss the enhancement of the quasiparticle density of states at the zero-energy [2,4-5] and its influence on the low-energy electric transport [6]. Next we show the paramagnetic property of odd-frequency pairs [7-10] which can be confirmed in the surface impedance measurement at low temperature [11]. We also discuss a relation to the Majorana physics [12-13]. Finally we explain why such unusual pairs appear in inhomogeneous superconducting systems [14].

[1] V. L. Berezinskii, JETP Lett. 20, 287 (1974).
[2] F. S. Bergeret, A. F. Volkov, and K. B. Efetov, Phys. Rev. Lett. 86, 4096 (2001) [3] Y. Tanaka and A. A. Golubov, Phys. Rev. Lett. 98, 037003 (2007).
[4] Y. Asano, Y. Tanaka, and A. A. Golubov, Phys. Rev. Lett.98, 107002 (2007).
[5] T. Kontos, et. al. Phys. Rev. Let. 86, 304 (2001).
[6] Y. Asano, et. al., Phys. Rev. Lett. 99, 067005 (2007).
[7] H. Walter, et. al., Phys. Rev. Lett. 80, 3598 (1998).
[8] S. Higashitani, J. phys. soc. Jpn., 66, 2556 (1997).
[9] S.-I. Suzuki and Y. Asano, Phys. Rev. B 89, 184508 (2014).
[10] Y. Tanaka, et. al., Phys. Rev. B 72, 140503(R) (2005).
[11] Y. Asano, et. al,, Phys. Rev. Lett. 107, 087001 (2011).
[12] Y. Asano and Y. Tanaka, Phys. Rev. B 87, 104513 (2013).
[13] S. Ikegaya, Y. Asano, and Y. Tanaka, arXiv: 1411.3438
[14] Y. Asano, Y. V. Fominov, Y. Tanaka, Phys. Rev. B 90, 094512 (2014).

The concept of the odd-frequency Cooper pairs was first proposed by Berezinskii in 1974 to describe superfluidity of 3He [1]. Although the odd-frequency superconductivity has never been confirmed in any materials, the odd-frequency pairs appear as the subdominant pairing correlation in various proximity structures such as superconductor / ferromagnet (SF) junctions [2] and normal-metal / superconductor (NS) junctions with unconventional pairing symmetry [3]. In the presentation, we explain what the odd-frequency pairs are, how they appear in such proximity structure, how to detect them, and how they are different from usual even-frequency pairs in the bulk. We first discuss the enhancement of the quasiparticle density of states at the zero-energy [2,4-5] and its influence on the low-energy electric transport [6]. Next we show the paramagnetic property of odd-frequency pairs [7-10] which can be confirmed in the surface impedance measurement at low temperature [11]. We also discuss a relation to the Majorana physics [12-13]. Finally we explain why such unusual pairs appear in inhomogeneous superconducting systems [14].

[1] V. L. Berezinskii, JETP Lett. 20, 287 (1974). [2] F. S. Bergeret, A. F. Volkov, and K. B. Efetov, Phys. Rev. Lett. 86, 4096 (2001) [3] Y. Tanaka and A. A. Golubov, Phys. Rev. Lett. 98, 037003 (2007). [4] Y. Asano, Y. Tanaka, and A. A. Golubov, Phys. Rev. Lett.98, 107002 (2007). [5] T. Kontos, et. al. Phys. Rev. Let. 86, 304 (2001). [6] Y. Asano, et. al., Phys. Rev. Lett. 99, 067005 (2007). [7] H. Walter, et. al., Phys. Rev. Lett. 80, 3598 (1998). [8] S. Higashitani, J. phys. soc. Jpn., 66, 2556 (1997). [9] S.-I. Suzuki and Y. Asano, Phys. Rev. B 89, 184508 (2014). [10] Y. Tanaka, et. al., Phys. Rev. B 72, 140503(R) (2005). [11] Y. Asano, et. al,, Phys. Rev. Lett. 107, 087001 (2011). [12] Y. Asano and Y. Tanaka, Phys. Rev. B 87, 104513 (2013). [13] S. Ikegaya, Y. Asano, and Y. Tanaka, arXiv: 1411.3438 [14] Y. Asano, Y. V. Fominov, Y. Tanaka, Phys. Rev. B 90, 094512 (2014).

Izvestno, chto klassicheskii ob'ekt, nakhodyashchiisya v metastabil'noi potentsial'noi yame, ne mozhet pokinut' ee pri nulevoi temperature. Kvantovyi zhe ob'ekt mozhet tunnelirovat' iz takoi yamy dazhe pri nulevoi temperature. Voznikaet vopros, chto zhe proizoidet, esli kvantovaya stepen' svobody mozhet sochetat'sya s klassicheskoi stepen'yu svobody? Dannyi vopros byl teoreticheski rassmotren v rabote [1] dlya sluchaya slaboi svyazi mezhdu dvumya stepenyami svobody. Avtory obnaruzhili, chto tunnelirovanie kvantovomekhanicheskoi stepeni svobody menyaet potentsial klassicheskoi peremennoi, chto pozvolyaet takomu ob'ektu pokinut' metastabil'nuyu yamu. Etot effekt napominaet istoriyu o Barone Myunkhgauzene, kotoryi utverzhdal, chto vytashchil sebya i svoyu loshad' iz tryasiny, poetomu takoe teoreticheskoe predskazanie povedeniya bylo nazvano «effektom Myunkhgauzena» [1]. My popytalis' realizovat' predlozhennuyu sistemu shuntirovaniem odnogo iz dvukh perekhodov PT-SKVIDa dopolnitel'noi emkost'yu. V nashikh opytakh byla obnaruzhena svyaz' mezhdu kvantovymi i klassicheskimi protsessami pokidaniya yamy, chto svyazano s napravleniem dvizheniya v prostranstve energii. Bylo obnaruzheno, chto pri izmenenii vneshnego magnitnogo potoka makroskopicheskoe kvantovoe tunnelirovanie periodicheski smenyaetsya termoaktivirovannym vykhodom [2], chto yavlyaetsya priznakom «effekta Myunkhgauzena».

[1] A. U. Thomann, V. B. Geshkenbein and G. Blatter, Phys. Rev. B 79, 184515 (2009). [2] S. Butz, A.K. Feofanov, K.G. Fedorov, H. Rotzinger, A.U. Thomann, B. Mackrodt, R. Dolata, V.B. Geshkenbein, G. Blatter, and A.V. Ustinov, arXiv: 1404.3602 (2014), to appear in Phys. Rev. Lett. in December 2014.

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Na seminar priglashayutsya vse zhelayushchie. Propusk slushatelei seminara, ne yavlyayushchikhsya studentami, aspirantami ili sotrudnikami NITU «MISiS», budet osushchestvlyat'sya pri pred'yavlenii pasporta pri uslovii predvaritel'noi zapisi na seminar po ssylke http://smm.misis.ru/events/seminars/ (do 14:00 dnya seminara).

Seminar 25 dekabrya 2014 g. (15:00) sostoitsya v Auditorii – B-636 (glavnyi korpus) NITU «MISiS», 6 etazh.

The unconventional (half-integer) quantum Hall effect for a single species of Dirac fermions is analyzed. In the introduction I will discuss experimental measurements of the half-integer Hall conductance g_{xy} of topological insulator surface states and unveil its field theoretical origin. For the calculation of the conductivity tensor, the following two step procedure is applied. In the first step, semiclassical transport coefficients are derived in the case of both orbital and Zeeman coupling to an external magnetic field. In this context, I plan to give a pedagogic review of the modified Boltzmann transport theory for the anomalous Hall effect. The semiclassical conductivity tensor serves as input parameters for the second step: It consists in the renormalization group treatment of the appropriately modified non-linear sigma model and thus accounts for localization effects. The resulting phase diagram (levitation scenario) will also be discussed in this context. If time permits, I will further explain how to reconcile Laughlin's flux insertion argument with half-integer Hall conductance and/or present the calculation of the current density beyond linear response in the limit of smooth scalar potential.

Detal'no issledovany staticheskie prodol'nye i dinamicheskie poperechnye spinovye vospriimchivosti v kvantovykh tochek i nanochastitsakh v ramkakh gamil'toniana, kotoryi yavlyaetsya rasshireniem universal'nogo gamil'toniana na sluchai odnoosnogo anizotropnogo obmena. Dlya predel'nykh sluchaev obmennogo vzaimodeistviya tipa Izinga i Geizenberga, izucheno kak fluktuatsii odnochastichnykh urovnei energii vliyayut na stounerovskuyu neustoichivost' v kvantovykh tochkakh. Okazyvaetsya, chto v rezhime sil'nykh fluktuatsii zadacha svoditsya k zadache o statistike ekstremumov nekotorogo gaussovskogo protsessa. Dokazano, chto, nesmotrya na sil'nye fluktuatsii odnochastichnykh urovnei energii, spinovaya vospriimchivost' i vse ee momenty raskhodyatsya odnovremenno v tochke, kotoraya opredelyaetsya s pomoshch'yu standartnogo kriteriya neustoichivosti Stounera s uchastiem tol'ko srednego rasstoyanie mezhdu odnochastichnymi urovnyami energii. Takzhe issledovano povedenie tunnel'noi plotnosti sostoyanii v sluchae anizotropnogo obmena. Pokazano, chto predskazannoe v rabote Y. Gefen, M. Kiselev, PRL96, 066805 (2006) nemonotonnoe (s dvumya maksimumami i minimumom) povedenie tunnel'noi plotnosti sostoyanii, kak funktsii energii, na samom dele ne sushchestvuet. Podrobno, nashi rezul'taty predstavleny v sleduyushchikh rabotakh: 1. D.S. Lyubshin, A.U. Sharafutdinov, I.S. Burmistrov, «Statistics of spin fluctuations in quantum dots with Ising exchange», Phys. Rev. B 89, 201304(R ) (2014). 2. A.U. Sharafutdinov, D.S. Lyubshin, I.S. Burmistrov, «Spin fluctuations in quantum dots», Phys. Rev. B 90, 195308 (2014). 3. A.U. Sharafutdinov, I.S. Burmistrov, «Tunneling density of states in quantum dots with anisotropic exchange», gotovitsya k otpravke v pechat'.

V pervoi chasti doklada budet sdelan nebol'shoi obzor teoreticheskikh rabot po shumam i statistike perenosa v tselom. Zatem obsudim teoreticheskie raboty, v kotorykh byli opisany vozmozhnosti sozdaniya odnochastichnykh izolirovannykh vozbuzhdenii (govorya bolee tochno, vozbuzhdeniya neobychnoi pary elektron-dyrka pri pomoshchi impul'sa vektornogo potentsiala lorentsevskoi formy), ne zaputannykh za fermi more. Vo vtoroi chasti budet obsuzhdat'sya eksperiment gruppy Glattli (opublikovano v 2013 g., Nature), v kotorom anonsirovano nablyudenie sootvetstvuyushchikh vozbuzhdenii. Budut izlozheny argumenty v pol'zu togo, chto v etom eksperimente usloviya dlya sozdaniya sootvetstvuyushchikh vozbuzhdenii (i ikh registratsii) ne vypolnyayutsya. Tem ne menee v eksperimente opredelenno nablyudalos' drugoe yavlenie, svyazannoe s katastrofoi ortogonal'nosti dlya fermi morya, pri opredelennykh formakh impul'sa.

Obychno schitaetsya, chto v topologicheskikh izolyatorakh (TI) spektr poverkhnostnykh sostoyanii imeet besshchelevoi lineinyi (ul'trarelyativistskii) spektr v tsentre zony Brillyuena. Takoi spektr deistvitel'no poluchaetsya v prosteishikh modelyakh pri ispol'zovanii “otkrytykh granichnykh uslovii” (open boundary conditions) [X.-L. Qi, S.-C. Zhang, Rev. Mod. Phys. 83, 1057 (2011)], t.e. granichnykh uslovii zanulyayushchikh volnovuyu funktsiyu na granitse. Odnako, izvestno, chto effektivnaya volnovaya funktsiya, opisyvayushchaya elektrony v kristalle, ne obyazana zanulyat'sya na granitse [E.L. Ivchenko “Optical Spectrosopy of Semiconductor Nanostructires”, Alpha Science, Harrow, UK (2005) i ssylki v nei]. Teoriya TI, a tochnee “printsip sootvetstviya granitsa-ob'em” (bulk boundary correspondence) predskazyvaet nalichie kraevykh sostoyanii v ob'emnoi shcheli, no ne sam spektr, kotoryi dolzhen zaviset' ot svoistv i mikrostruktury poverkhnosti, chto ne uchityvaetsya otkrytymi granichnymi usloviyami. V nashei rabote arXiv:1407.0945 byli proanalizirovany vozmozhnye granichnye usloviya v 2D TI na osnove kvantovykh yam CdHgTe i v 3D TI Bi2Se3. Pokazano, chto poverkhnostnye sostoyaniya mogut imet' sushchestvenno ne lineinyi spektr ili vovse otsutstvovat' v tsentre zony Brillyuena.

Printsip Pauli privodit k antisimmetrii anomal'noi funktsii Grina, opisyvayushchei sverkhprovodimost', pri perestanovke koordinat elektronov. Polnyi nabor koordinat vklyuchaet v sebya, pomimo prostranstvennykh koordinat i proektsii spinov, takzhe i vremya. V matsubarovskom predstavlenii funktsiya Grina, v printsipe, mozhet byt' nechetnoi po chastote, chto bylo otmecheno Berezinskim. Zatem teoreticheski bylo pokazano, chto nechetnye po chastote sverkhprovodyashchie korrelyatsii mogut voznikat' v neodnorodnykh kontaktakh sverkhprovodnikov i ferromagnetikov kak subdominantnye komponenty vblizi granitsy. Neobychnoi osobennost'yu takogo sostoyaniya yavlyaetsya "paramagnitnyi" (protivopolozhnyi obychnomu) znak svyazi mezhdu vektornym potentsialom i sverkhtokom (anomal'nyi effekt Meissnera). V ob'emnom sverkhprovodnike takoe sostoyanie bylo by neustoichivym. Nedavno neskol'kimi gruppami byla predlozhena vozmozhnost' realizatsii ob'emnogo nechetnogo po chastote sverkhprovodyashchego sostoyaniya s obychnym diamagnitnym meissnerovskim otklikom. V doklade budut obsuzhdeny fizicheskie sledstviya takogo predpolozheniya.

Predlozhena novaya kontseptsiya Bolometra na Kholodnykh Elektronakh (BKhE) dlya sverkhchuvstvitel'nogo priema radioastronomicheskikh signalov. V etom bolometre realizovan effekt pryamogo elektronnogo okhlazhdeniya absorbera, chto pozvolyaet uluchshit' shumovye svoistva i rasshirit' dinamicheskii diapazon bolometra po sravneniyu s bolometrami na krayu sverkhprovodyashchego perekhoda. BKhE okazalsya nechuvstvitel'nym k kosmicheskim lucham iz-za malosti ob'ema nanoabsorbera i printsipial'noi razvyazki elektronnoi i fononnoi sistem. V rezul'tate interes k BKhE rezko vozros dlya primenenii v kosmicheskikh i ballonnykh proektakh.

Vtoroi original'noi kontseptsiei, predlozhennoi dlya realizatsii v evropeiskikh kosmicheskikh proektakh, yavlyaetsya Rezonansnyi Bolometr na Kholodnykh Elektronakh (RBKhE), ispol'zuyushchii vnutrennii nanofil'tr iz kineticheskoi induktivnosti sverkhprovodyashchei poloski i emkosti tunnel'nogo perekhoda. Stimuliruyushchei prichinoi dlya izobreteniya RBKhE yavilsya zapros Evropeiskogo Kosmicheskogo Agenstva na sovmeshchenie v odnom piksele dvukh i bolee chastot dlya umen'sheniya razmera fokal'noi ploskosti i sravneniya signalov raznykh chastot.

Budet obsuzhdeno primenenie etikh kontseptsii v ballonnykh i kosmicheskikh proektakh.

Na seminar priglashayutsya vse zhelayushchie. Propusk slushatelei seminara, ne yavlyayushchikhsya studentami, aspirantami ili sotrudnikami NITU «MISiS», budet osushchestvlyat'sya pri pred'yavlenii pasporta pri uslovii predvaritel'noi zapisi na seminar po ssylke http://smm.misis.ru/events/seminars/ (do 14:00 dnya seminara).

Seminar 11 dekabrya 2014 g. (15:00) sostoitsya v Auditorii – B-636 (glavnyi korpus) NITU «MISiS», 6 etazh.

Budet rassmotreno odno iz interesnykh yavlenii - atomnyi kollaps, predstavlyayushchii soboi spontannoe rozhdenie elektron-pozitronnykh par v sil'nykh elektricheskikh polyakh vblizi sverkhtyazhelykh atomnykh yader. Dokladchik podrobno rasskazhet o simmetriinykh aspektakh kollapsa, svyazannykh s anomal'nym narusheniem masshtabnoi invariantnosti, a takzhe o pervom nablyudenie etogo yavleniya v 2013 godu.

Podrobnaya informatsiya

Ob'yavlenie o doklade na saite FOPF

My rassmatrivaem sistemu provodnikov, pomeshchennykh v dielektricheskuyu matritsu. Matritsa ne predpolagaetsya sovershenno zhestkoi (naprimer, eto mozhet byt' zhidkost'), poetomu tolshchiny dielektricheskikh zazorov mezhdu provodnikami fluktuiruyut vo vremeni i inogda provodniki mogut soprikasat'sya. V takie momenty voznikaet "proboi" i zaryad legko peretekaet mezhdu paroi soprikosnuvshikhsya provodnikov. Protsess perenosa zaryada za schet proboev, voznikayushchikh v sluchainye momenty v sluchainykh mestakh, my nazvali polzuchei provodimost'yu. My rassmatrivaem kak trekhmernye, tak i nizkorazmernye massivy provodnikov i issleduem rastekanie zaryada, pervonachal'no sosredotochennogo na odnom provodnike, provodimost' na postoyannom toke, fluktuatsii zaryadov na provodnikakh i ikh prostranstvenno-vremennuyu korrelyatsiyu.

Ponyatie "khaos" chasto upominaetsya v kontekste osnov statisticheskoi fiziki. V to zhe vremya, do sikh por ne do kontsa yasno, chto nazyvat' khaosom v mnogochastichnykh kvantovykh sistemakh. Sushchestvuet rasprostranennoe mnenie, chto povedenie kvantovykh sistem yavlyaetsya klassicheski khaotichnym v makroskopicheskom predele na fizicheski nablyudaemykh (t.e. ne slishkom dlinnykh) vremenakh. V etom doklade budet pokazano, chto, dazhe v makroskopicheskom predele i na fizicheski nablyudaemykh vremenakh, tipichnye neintegriruemye sistemy vzaimodeistvushchikh kvantovykh spinov ne obladayut opredelyayushchim svoistvom klassicheskogo khaosa, a imenno, eksponentsial'moi chuvstvitel'nost'yu k malym vozmushcheniyam. Etot rezul'tat poluchen putem sravneniya povedeniya sistem klassicheskikh i kvantovykh spinov v otvet na nepolnoe obrashchenie spinovoi dinamiki vo vremeni. Takoe obrashchenie vo vremeni izvestno v statisticheskoi fizike kak "Loshmidtovskoe ekho" i realizuemo metodami yadernogo magnitnogo rezonansa kak "magicheskoe ekho". V poslednem sluchae, otsutstvie eksponentsial'noi chuvstvitel'nosti k malym vozmushcheniyam dolzhno byt' eksperimental'no nablyudaemo. [B. V. Fine, T. A. Elsayed, C. M. Kropf, and A. S. de Wijn, Phys. Rev. E 89, 012923 (2014)]

Issledovany dinamicheskie svoistva SNS perekhoda s zadannoi raznost'yu faz sverkhprovodnikov na dvukh beregakh pod deistviem slabogo vysokochastotnogo vneshnego napryazheniya. Ispol'zovan glavnym obrazom analiticheskii metod, osnovannyi na reshenii nestatsionarnogo uravneniya Uzadelya, okonchatel'nye vychisleniya provedeny chislenno. Vychislena veshchestvennaya i mnimaya chasti lineinoi vysokochastotnoi provodimosti Y(ω) kak funktsii staticheskoi raznosti faz φ pri proizvol'nom sootnoshenii mezhdu chastotoi ω, temperaturoi T, energiei Taulesa E_Th, no predpolagaya, chto vse eti velichiny maly po sravneniyu so shchel'yu Δ v spektre sverkhprovodnika. Poluchennye rezul'taty nakhodyatsya v khoroshem soglasii s eksperimentom.
[Napravleno v Phys. Rev. B., oktyabr' (2014)]

Sformulirovana teoreticheskaya model' dlya opisaniya kontaktov mezhdu obychnymi nizkotemperaturnymi sverkhprovodnikami i sverkhprovodyashchimi materialami na osnove ferropniktidov, v kotorykh predskazana vozmozhnaya realizatsiya nefononnogo mekhanizma sverkhprovodyashchego sparivaniya. Obsuzhdaetsya rol' primesnogo rasseyaniya, v chastnosti, vozmozhnost' fazovogo perekhoda mezhdu razlichnymi simmetriinymi sostoyaniyami parametra poryadka v zavisimosti ot sily rasseyaniya. Obsuzhdayutsya vozmozhnye fazo-chuvstvitel'nye eksperimenty po opredeleniyu simmetrii parametra poryadka, kotorye pozvolyat opredelit' mekhanizm sverkhprovodyashchego sparivaniya s dannykh materialakh. Eksperimenty osnovany na ispol'zovanii Dzhozefsonovskikh kontaktov mezhdu obychnymi sverkhprovodnikami i sverkhprovodyashchimi materialami na osnove ferropniktidov. Sformulirovany usloviya na parametry , kotorye pozvolyat proizvesti takie eksperimenty.

----------------------- Na seminar priglashayutsya vse zhelayushchie. Propusk slushatelei seminara, ne yavlyayushchikhsya studentami, aspirantami ili sotrudnikami NITU «MISiS», budet osushchestvlyat'sya pri pred'yavlenii pasporta pri uslovii predvaritel'noi zapisi na seminar po ssylke http://smm.misis.ru/events/seminars/ (do 14:00 dnya seminara).

Seminar 27 noyabrya 2014 g. (15:00) sostoitsya v Auditorii – B-636 (glavnyi korpus) NITU «MISiS», 6 etazh.

Obzor rabot

Nature 505, 528 (2014) Tunable symmetry breaking and helical edge transport in a graphene quantum spin Hall state, A F Young, J D Sanchez-Yamagishi, B Hunt, S H Choi, K Watanabe, T Taniguchi, R C Ashoori and P Jarlillo-Herrero,

Nat Phys 8, 550 (2012) Spin and valley quantum Hall ferromagnetism in graphene, A F Young, C R Dean, L Wang, H Ren, P Cadden-Zimansky, K Watanabe, T Taniguchi, J Hone, K L Shepard and P Kim

We study transport via edge modes of a 2D topological insulator. Topological protection prevents complete localization of the edge states; however, quantum interference effects are still relevant for the transport properties at finite length scales. We mainly focus on the two most experimentally relevant cases: (i) a junction between two quantum Hall insulators with different filling factors and hence an imbalance in the number of right- and left-propagating modes (symmetry class A) and (ii) a relatively thick HgTe quantum well in the insulating state with an arbitrary number of edge modes (symmetry class AII). We derive the distribution of transmission probabilities as a function of the distance between leads. This allows us to demonstrate topological effects in the average conductance and the shot noise of the setup. We also consider mesoscopic fluctuations and compute the variance of conductance. This quantity is strongly influenced by topology in the quantum Hall case. All the calculations are carried out assuming localization effects are weak, i.e., in the short length limit. Technically, this amounts to studying 1D non-linear sigma model with a proper topological term and source fields on the semiclassical level. Remarkably, the semiclassical limit of the 1D sigma model can be exactly mapped onto a fully quantum 0D sigma model of a different symmetry class. This allows us to identify the distribution of transmission probabilities with the spectrum of a certain random matrix.

We study quantum interference effects in a two-dimensional chiral metal (bipartite lattice) with vacancies. We demonstrate that randomly distributed vacancies constitute a peculiar type of chiral disorder leading to strong modifications of critical properties at zero energy as compared to conventional chiral metals. In particular, the average density of states diverges as ρ ~ E^-1 |lnE|^-3/2 and the correlation length L_c ~ |lnE| in the limit E→0. When the average density of vacancies is different in the two sublattices, a finite concentration of zero modes emerges and a gap in the quasiclassical density of states opens around zero energy. Interference effects smear this gap resulting in exponentially small tails at low energies.

V pervoi chasti doklada budut predstavleny printsipy raboty i osnovnye kharakteristiki sverkhprovodyashchikh detektorov, takikh kak bolometry i SKVIDy. Budut obsuzhdat'sya nekotorye napravleniya, v kotorykh sverkhprovodyashchie datchiki nashli shirokoe primenenie.

Vtoraya chast' doklada budet posvyashchena original'nym rezul'tatam, poluchennym gruppoi, kotoroi rukovodit avtor. Oni osnovany na uzkom raspredelenii pereklyuchenii neshuntirovannogo dzhozefsonovskogo tunnel'nogo kontakta iz sostoyaniya s nulevym napryazheniem v sostoyanie s konechnym napryazheniem pri temperaturakh nizhe 1 K. Takoe povedenie kontakta mozhet byt' ispol'zovano dlya realizatsii sverkhchuvstvitel'nykh detektorov v gigagertsovom diapazone. Budut predstavleny teoreticheskie otsenki i pervye eksperimental'nye dannye.

We will review Manchester experiments on quantum turbulence in superfluid 4He generated by various means. The main focus is on the limit of zero temperatures, in which the turbulence is fully represented by tangled quantized vortex lines. In this regime, the dynamics of the vortex lines span length scales from the size of container to nearly atomic scale, at which energy is transmitted to phonons. A quantum cascade of energy, involving individual quantized vortex lines (and hence, having no analogs in classical turbulence), is necessary for the energy of large-scale flow to be transferred to the dissipative short scales. The processes maintaining the cascade are believed to be: hydrodynamic interactions of vortex lines, reconnections of vortex lines, interaction of excitations such as small vortex loops and Kelvin waves on vortex lines. The dissipative length scale can be increased (i.e. the quantum cascade curtailed) by increasing temperature above 0.4 K due to the scattering of thermal excitations by vortex lines. Three different means of generating turbulence will be discussed (each having an analog in classical turbulence, thus allowing comparison with classical results): (a) With the towed grid, we produce turbulence that is nearly homogeneous and isotropic. Studying the free decay allows the rate of dissipation to be quantified [6]. (b) An unsteady rotation of a square-shaped container allows to create anisotropic turbulence — that decays more slowly [1,5,6]. In the presence of the steady background rotation, the following phenomena are observed: steady polarization of vortex lines, non-zero threshold for turbulence onset, resonances of inertial waves [4]. (c) With an immersed jet of variable duration and intensity (created by a current of injected electrons), a cross-over from ultraquantum («non-structured» or «Vinen») turbulence to quasiclassical («structured» or «Kolmogorov») turbulence is observed [2,3]. (References: [1] P. M. Walmsley, A. I. Golov, H. E. Hall, A. A. Levchenko and W. F. Vinen, Dissipation of quantum turbulence in the zero-temperature limit, Phys. Rev. Lett. 99, 265302 (2007). [2] P. M. Walmsley and A. I. Golov, Quantum and quasiclassical types of superfluid turbulence, Phys. Rev. Lett. 100, 245301 (2008). [3] A. I. Golov, P. M. Walmsley, P. Tompsett, Charged Tangles of Quantized Vortices in Superfluid 4He, J. Low Temp. Phys. 161, 509-525 (2010). [4] P. M. Walmsley and A. I. Golov, Rotating quantum turbulence in superfluid 4He in the T=0 limit, Phys. Rev. B 86, 060518(RC) (2012). [5] Paul Walmsley, Dmitry Zmeev, Fatemeh Pakpour, and Andrei Golov, Dynamics of quantum turbulence of different spectra, PNAS 111 (Supplement 1) 4691-4698 (2014). [6] D. E. Zmeev, P. M. Walmsley, A. I. Golov, P. V. E. McClintock, S. N. Fisher, and W. F. Vinen, Turbulence in superfluid 4He generated by various means (in preparation).)

Rabota posvyashchena izgotovleniyu submikronnykh planarnykh S-N-S dzhozefsonovskikh kontaktov, planarnykh gibridnykh struktur na osnove sverkhprovodnika, normal'nogo metalla i ferromagnetika, eksperimental'nomu issledovaniyu osobennostei effekta blizosti i sverkhprovodyashchego transporta cherez takie struktury, realizatsii S-(N/F)-S - dzhozefsonovskogo kontakta s ferromagnitnym monodomennym podsloem (F), issledovaniyu vliyaniya ferromagnitnogo podsloya na parnyi i kvazichastichnyi transport cherez dzhozefsonovskii S-(N/F)-S kontakt, izucheniyu nelokal'nykh neravnovesnykh effektov v mnogoterminal'nykh SNS strukturakh, svyazannykh s inzhektsiei kvazichastits v odin iz beregov dzhozefsonovskogo S-N-S kontakta.

Studying the oscillatory magnetorestance in crossed fields, we found that the product (m^*T_D) that determines damping of quantum oscillations, to the first approximation is equal in the majority and minority subbands even though the spin polarization degree amounts to about 66%. This result confirms theory predictions that the interaction takes place at high energies > E_F rather than within narrow strip of energies E_F ± T. To the next approximation, we revealed a difference in the damping factor of the two spin subbands, which causes skewness of the oscillation lineshape. The difference, quantified with the skew factor can be as high as 20%. The skew factor decreases as B_∥ or temperature grow, or B_⊥ decreases; for low electron densities and high in-plane field the skew factor even changes sign. In contrast to the conventional theory, the product (m^*T_D) varies with perpendicular field and (nonmonotonically) with temperature. These dependencies explain notable scattering of the m^*(n) values experimentally obtained under assumption of the T-independent (m^*T_D).

The monotonic magnetoconductance in the in-plane field δσ(B,T) was found to scales in a sharp contrast to the theory predictions: whereas below a density dependent temperature T<T^* it scales as theory predicted, (B²/T), at higher temperatures T>T^*, it scales as (B²/T²). The latter dependence, hence, mimics the behavior anticipated for the low-temperature diffusive regime of interaction. These functional dependencies are at odd with interaction quantum corrections. The crossover temperature T^*(n) correlates well with the inflection point at the strong σ(T) dependence in zero field, inherent for high mobility samples. Our data thus point at the existence of an energy scale T^* beyond the E_F. The results also call in question the previous attempts to exploit the parallel field MR as a tool to determine Fermi liquid coupling constants, F₀^a and γ₂, and to plot the two-parameter phase diagrams for interacting and disordered 2D electron systems.

We consider small ferromagnetic particles or quantum dots close to Stoner instability, and investigate the dynamics of the total magnetization in the presence of tunneling coupling to the metallic leads. We generalize the Ambegaokar-Eckern-Sch\"on effective action and the corresponding semiclassical equations of motion from the U(1) case of the charge degree of freedom to the SU(2) case of the magnetization. The Langevin forces (torques) in these equations are strongly influenced by the geometric phase. As a first but nontrivial application we predict low temperature quantum diffusion of the magnetization on the Bloch sphere, which is governed by the geometric phase. We propose a protocol for experimental observation of this phenomenon.

Lokal'nost' — odin iz osnovopolagayushchikh printsipov postroeniya fizicheskikh modelei. Tak, v modeli Izinga, kazhdyi chlen v gamil'toniane mozhet sootvetstvovat' svyazi mezhdu blizhaishimi sosedyami na zadannoi reshetke. Chto poluchitsya esli uslovie lokal'nosti opustit'? Ya otvechu na etot vopros na primere neuporyadochennykh spinovykh modelei opisyvayushchikh protseduru dekodirovaniya kvantovykh nizkoplotnostnykh kodov. Takim obrazom mogut byt' polucheny kak traditsionnye lokal'nye spinovye modeli (model' Izinga, kalibrovochnaya model' Z2), tak i netrivial'nye nelokal'nye modeli kotorye ne byli izucheny ranee. Uporyadochennaya faza v takikh modelyakh sootvetstvuet nalichiyu glubokogo minimuma svobodnoi energii; “post-topologicheskimi” vozbuzhdeniyami yavlyayutsya protyazhennye defekty obobshchayushchie ponyatie domennoi stenki. Izvestno neskol'ko konstruktsii kvantovykh nizkoplotnostnykh kodov s konechnoi skorost'yu. V sootvetstvuyushchikh spinovykh modelyakh chislo razlichnykh tipov defektov eksponentsial'no veliko. V takikh modelyakh vozmozhen chisto entropiinyi fazovyi perekhod, kogda analog poverkhnostnogo natyazheniya dlya defektov kazhdogo tipa ostaetsya konechnym.

[A. A. Kovalev and L. P. Pryadko, “Spin glass reflection of the decoding transition for quantum error correcting codes”, arXiv:1311.7688]

V doklade budet predstavlen obzor sovremennogo sostoyaniya issledovanii v oblasti andersonovskoi lokalizatsii v neuporyadochennykh sistemakh. V chastnosti, budut obsuzhdeny: mul'tifraktal'nost' volnovykh funktsii v okrestnosti perekhodov Andersona ili mezhdu razlichnymi fazami topologicheskikh izolyatorov, klassy simmetrii neuporyadochennykh sistem i rol' simmetrii v lokalizatsii, effekty topologii, topologicheskie izolyatory i sverkhprovodniki, rol' mezhelektronnogo vzaimodeistviya.

Predstavleny rezul'taty issledovaniya atomno-chistoi poverkhnosti topologicheskogo izolyatora Bi2Se3 metodami sverkhvysokovakuumnoi nizkotemperaturnoi skaniruyushchei tunnel'noi mikroskopii (STM) i spektroskopii (STS). Obnaruzheny defekty glubina zaleganiya i ozhidaemyi zaryad kotorykh sootvetstvuet r-tipu provodimosti ob'ema kristalla. Znak termo-eds takzhe sootvetstvuet r-tipu provodimosti. Rezul'taty issledovanii metodami tunnel'noi spektroskopii pokazyvayut, chto uroven' khimicheskogo potentsiala nakhoditsya vnutri zapreshchennoi zony ob'ema. Obnaruzheno izmenenie lokal'noi plotnosti sostoyanii vblizi kraya pyatisloinoi stupeni, kotoroe sootvetstvuet sdvigu polozheniya vershiny dirakovskogo konusa otnositel'no ob'emnoi zony ili zhe takzhe sdvigu khimicheskogo potentsiala vblizi kraya stupeni.

po rabote A.Yu. Dmitriev et al., http://arxiv.org/abs/1408.4991

Many-body localized (MBL) systems are characterized by the absence of transport and thermalization, and therefore cannot be described by conventional statistical mechanics. In this talk I will discuss the behaviour of local observables in an isolated MBL system following a quantum quench. For the case of a global quench, the local observables reach stationary, highly non-thermal values at long times as a result of slow dephasing characteristic of the MBL phase. These stationary values retain the local memory of the initial state due to the existence of local integrals of motion in the MBL phase. The temporal fluctuations around stationary values exhibit universal power-law decay in time, with an exponent set by the localization length and the diagonal entropy of the initial state. Such a power-law decay holds for any local observable and is related to the logarithmic in time growth of entanglement in the MBL phase. This behaviour distinguishes the MBL phase from both the Anderson insulator (where no stationary state is reached), and from the ergodic phase (where relaxation is expected to be exponential). Quench protocols considered in this talk can be naturally implemented in systems of ultra cold atoms in disordered optical lattices, and the behaviour of local observables provides a direct experimental signature of many-body localization. [arXiv:1408.4105; arXiv:1403.0693]

In this talk I am going to discuss the experimental technique to measure entropy-per-electron in gated 2D systems, the we recently developed. We applied this technique to study magnetooscillations in Si and GaAs-based 2D systems and zero-perpendicular field effects. The latter originate from: (i) non-degeneracy of the Fermi system and (ii) electron-electron correlations. In particular, we explore enhanced effective mass in non-degenerate strongly correlated plasma regime E_F < T < U (where U is the Coulomb energy e² / ‹ r ›).

We study electronic properties of AA-stacked bilayer graphene. In the single-particle approximation such a system has one electron band and one hole band crossing the Fermi level. If the bilayer is undoped, the Fermi surfaces of these bands coincide. Such a band structure is unstable with respect to a set of spontaneous symmetry violations. Specifically, strong on-site Coulomb repulsion stabilizes antiferromagnetic order. At small doping and low temperatures, the homogeneous phase is unstable and experiences phase separation into an undoped antiferromagnetic insulator and a metal. The metallic phase can be either antiferromagnetic (commensurate or incommensurate) or paramagnetic depending on the system parameters. We derive the phase diagram of the system on the doping-temperature plane and find that under certain conditions, the transition from the paramagnetic to the antiferromagnetic phase may demonstrate reentrance. The application of the transverse voltage induces the exciton order parameter coexisting with antiferromagnetism. The value of this second order parameter is proportional to the biased voltage and the value of the nearest- neighbor inter-plane Coulomb repulsion.

We consider a Coulomb blockade effects for tunnelling through a piece of wire with large resistance $R\gg 1$. This system can not be treated as a zero-dimensional one, as the dynamics of internal inhomogeneous degrees of freedom is crucial. At moderately high temperatures the linear conductance $G$ of the system is suppressed due to the one-dimensional Coulomb zero bias anomaly effect. At low $T$, besides the standard activational factor, there is an additional $T$-independent (though also exponentially strong!) suppression of $G$. It arises due to the tunnelling evolution of the charge in the wire to the equivipotential distribution. In the intermediate range of $T$ the $G(T)$ dependence is a power law, as in the phenomenological environmental theory. The effective ``environmental resistance'', entering the power exponent, is found explicitly. It depends on the length of the wire and on the positions of the contacts.

We study the effects of strong coupling of a localized state charge to one-dimensional electronic channels out of equilibrium. While the state of this charge and the coupling strength determine the scattering phase shifts in the channels, the non-equilibrium partitioning noise induces the tunneling transitions to the localized state. The strong coupling leads to a non-perturbative backaction effect which is manifested in the orthogonality catastrophe and the Fermi edge singularity in the transition rates. The non-Gaussian component of noise brakes the charge symmetry, shifting the position of the tunneling resonance depending on the sign of the dissipative current and the transparency of the noise emitting partitioning quantum point contact.

We show that nonequilibrium phenomena in dispersive Luttinger liquids posses remarkable weak-strong coupling duality between bosonic and fermionic descriptions. The duality manifests itself both in the collisionless dynamics of a density pulse (via crossover from essentially free-fermion evolution to hydrodynamics) and in the relaxation of fermionic and bosonic excitations.

My issleduem defazirovku elektronov v grafene za schet vzaimodeistviya s izgibnymi fononami. Okazyvaetsya, chto sootvetstvuyushchii vklad mozhet byt' poryadka elektron-elektronnogo vklada dazhe pri nizkikh temperaturakh. Vychislenie provoditsya v shirokom diapazone temperatur, prodemonstrirovano, chto obsuzhdaemyi vklad menyaet temperaturnoe povedenie s T² na T c rostom temperatury i rastet s elektronnoi plotnost'yu, v otlichie ot vklada elektron-elektronnykh vzaimodeistvii, chto delaet printsipial'no vozmozhnym ego obnaruzhenie v eksperimentakh po slaboi lokalizatsii v grafene.

Izuchaetsya relaksatsiya odnogo vozbuzhdennogo elektrona v zone provodimosti grafena pri nulevoi temperature i urovne Fermi v dirakovskoi tochke posredstvom ispuskaniya elektronno-dyrochnykh par za schet kulonovskogo vzaimodeistviya. Vazhnuyu rol' v etom protsesse igraet otklonenie spektra ot konicheskoi formy (trigonal'naya gofrirovka). V rezul'tate, relaksatsiya okazyvaetsya zapreshchennoi dlya nekotorykh napravlenii nachal'nogo impul'sa elektrona i razreshennoi dlya drugikh (dlya etogo sluchaya soschitano vremya relaksatsii).

Rech' poidet o kvaziodnomernykh provodnikakh, v kotorykh nizhe temperatury paierlsovskogo perekhoda voznikaet volna zaryadovoi plotnosti (VZP). Bol'shinstvo takikh soedinenii predstavlyayut soboi nitevidnye kristally. Budet rasskazano o sleduyushchikh effektakh: snizhenii uprugikh modulei pri sryve VZP s primesei, izmenenii dliny obraztsov pod deistviem elektricheskogo polya ili termotsiklirovaniya, neodnorodnoi deformatsii obraztsov v elektricheskom pole. Naibolee podrobno budet rasskazano o deformatsii krucheniya, v chastnosti, o krutil'nykh kolebaniyakh. Vse perechislennye effekty mozhno kachestvenno opisat' na yazyke uprugogo vzaimodeistviya VZP s reshetkoi kristalla. Odnako est' osnovaniya polagat', chto takoe opisanie — chrezmerno uproshchennoe. [Literatura: V.Ya. Pokrovskii, S.G. Zybtsev, M.V. Nikitin, I.G. Gorlova, V.F. Nasretdinova, S.V. Zaitsev-Zotov. «Vysokochastotnye, „kvantovye“ i elektromekhanicheskie effekty v kvaziodnomernykh kristallakh s volnoi zaryadovoi plotnosti», UFN, 183, 33 (2013).]

Predlozhen novyi pokhod k resheniyu uravnenii Richardsona-Godena, kotorye opredelyayut sobstvennye sostoyaniya gamil'toniana teorii Bardina-Kupera-Shriffera (BKSh). Vmesto neposredstvennogo resheniya etikh uravnenii mozhno pereiti k veroyatnostnomu predstavleniyu i zatem rekonstruirovat' polozheniya kornei etikh uravnenii na kompleksnoi ploskosti, ispol'zuya metody integrirovaniya. Pri etom voznikayut integraly sel'bergovskogo tipa, figuriruyushchie v konformnoi teorii polya i teorii sluchainykh matrits. V rabote provedeny analiticheskie raschety dlya nizkoenergeticheskoi chasti spektra sistemy v termodinamicheskom predele, dlya kotorogo podtverzhdeno soglasie so srednepolevymi predskazaniyami BKSh. Takzhe predstavleny nekotorye rezul'taty dlya sistem proizvol'nogo razmera, dlya chego byla privlechena ideya o simmetrii mezhdu parami elektronov i parami dyrok. Veroyatnostnyi podkhod mozhet byt' polezen i dlya resheniya drugikh tipov uravnenii Bete.

Rassmotreny nedavnie eksperimenty po effektu Aaronova-Boma na provodyashchikh kraevykh sostoyaniyakh, lokalizovannykh vokrug nanootverstii v nanoperforirovannovannykh grafenovykh strukturakh [1], a takzhe eksperimenty po nablyudeniyu orbital'nogo kvantovaniya kraevykh dirakovskikh fermionov pri ikh dvizhenii vokrug nanootverstiya v nulevom magnitnom pole [2]. Rezul'taty eksperimentov oboikh tipov soglasuyutsya s teoriei kraevykh sostoyanii tammovskogo tipa v grafene. Literatura: [1] Yu.I. Latyshev et al., cond-mat arXiv : 1310.0991. [2] Yu.I. Latyshev, A.P. Orlov, A.V. Frolov et al., JETP Lett., 98, 214 (2013).

My eksperimental'no issledovali transport cherez interfeis mezhdu ferromagnetikom (permalloi) i kraem dvumernoi elektronnoi sistemy s sil'nym spin-orbital'nym vzaimodeistviem tipa Rashby. My obnaruzhili sil'no nelineinye transportnye kharakteristiki v oblasti malykh tokov pri millikel'vinovykh temperaturakh. Obnaruzhennaya nelineinost' polnost'yu podavlyaetsya pri dostizhenii nekotorykh znachenii temperatury, magnitnogo polya ili toka cherez interfeis. My interpretiruem dannoe povedenie kak rezul'tat spinovoi akkumulyatsii vblizi interfeisa i ee absorbtsii, vyzvannoi protekayushchim tokom (magnetization torque).

Using the combination of analytical and numerical techniques we develop the theory of quantum criticality in disordered topological multi-channel nanowires of symmetry classes AIII and BDI [1]. The minimal representative phase portrait is characterized by two parameters $(\mu, w)$, where $\mu$ is the external control parameter (e.g. the chemical potential) and $w$ is the disorder strength. With the increase of $w$ at a fixed value of $\mu$ the wires generically undergo a sequence of topological phase transitions before the asymptotic state of a trivial Anderson insulator is reached. The universal description of the systems is given in terms of two parameters $(g,\chi)$, where $g$ is conductance and $\chi$ is a topological angle. Contour lines of half-integer valued $\chi$ in $(\mu, w)$-parameter space define phase boundaries between distinct topological sectors. Upon increasing the length of the wire, the pair $(g, \chi)$ exhibits flow similar to the celebrated two parameter flow describing the class A quantum Hall insulator. However, unlike the quantum Hall system, an exact analytical description of the entire phase diagram can be given. We corroborate the quantitative validity of our theory by comparison to numerical transfer matrix computations.

[1] A. Altland, D. Bagrets, L. Fritz, A. Kamenev, H. Schmiedt, arXiv:1402.1738

Budet dana klassifikatsiya razlichnykh predel'nykh sluchaev, svyazannykh s sootnosheniyami mezhdu integralom mezhsloevogo pereskoka, rasstoyaniem, i shirinoi urovnei Landau. V kazhdom predel'nom sluchae budut ukazany metod vychisleniya mezhsloevoi provodimosti v sil'no anizotropnykh kvazidvumernykh metallakh, oblast' primenimosti etogo metoda, i glavnye rezul'taty etikh raschetov.

[*] P. D. Grigoriev, "Longitudinal interlayer magnetoresistance in quasi-two-dimensional metals", Phys. Rev. B 88, 054415 (2013).

a takzhe
[1] P. D. Grigoriev, «Theory of the Shubnikov-de Haas effect in quasi-two-dimensional metals», Phys. Rev. B 67, 144401 (2003).
[2] P. D. Grigoriev, “Monotonic growth of interlayer magnetoresistance in strong magnetic field in very anisotropic layered metals”, JETP Lett. 94, 47 (2011).
[3] P. D. Grigoriev, “Weakly incoherent regime of interlayer conductivity in magnetic field”, Phys. Rev. B 83, 245129 (2011).
[4] P. D. Grigoriev, M. V. Kartsovnik, W. Biberacher, «Magnetic-field-induced dimensional crossover in the organic metal α-(BEDT-TTF)2KHg(SCN)4», Phys. Rev. B 86, 165125 (2012).
[5] A. D. Grigoriev and P.D. Grigoriev, Crossover from the weak to strong-field behavior of the longitudinal interlayer magnetoresistance in quasi-two-dimensional conductors, Fizika nizkikh temperatur 40(4), 472 (2014).

V edinom eksperimente proiskhodit perestroika sistemy mezhdu bozonnym i fermionnym sostoyaniem. Eksperiment vypolnen s gazom fermi-atomov litiya-6 s s-vzaimodeistviem pri temperature ~ 10 nK. Pri roste vzaimodeistviya atomy ob'edinyayutsya v 2-atomnye molekuly bozony. 2-mernost' dostignuta plotnym uderzhaniem vdol' odnogo iz napravlenii. Chistota ul'trakholodnoi atomnoi sistemy daet vozmozhnost' sravnivat' dannye s teoreticheskimi modelyami, postroennymi iz pervykh printsipov, bez svobodnykh parametrov. V chastnosti, naidennoe nami otlichie davleniya slabo vzaimodeistvuyushchego fermi-gaza ot predskazaniya dlya odnorodnoi fermi-zhidkosti mozhet stat' stimulom dlya razvitiya teorii 2-mernykh mezoskopicheskikh sistem. Izmereniya v sil'no vzaimodeistvuyushchem gaze, mezhdu fermi- i boze-rezhimami, pokazyvayut neobkhodimost' ucheta 3-mernogo kharaktera vzaimodeistvii pri modelirovanii gaza s 2-mernoi kinematikoi.

We study the effect of external potential on transport properties of the fermionic two-leg ladder model. The response of the system to a local perturbation is strongly dependent on the ground state properties of the system and especially on the dominant correlations. We categorize all phases and transitions in the model (for incommensurate filling) and introduce ’’hopping-driven transitions’’ that the system undergoes as the inter-chain hopping is increased from zero. We also describe the response of the system to an ionic potential. The physics of this effect is similar to that of the single impurity, except that the ionic potential can affect the bulk properties of the system and in particular induce true long range order.

Over the last decade, magneto transport in very high Landau levels of high-mobility 2D electron systems (2DES) hosted in GaAs/AlGaAs quantum wells revealed a variety of new intriguing phenomena. Two prime examples of these phenomena are microwave-induced resistance oscillations (MIRO) and associated zero-resistance states which emerge when a high-mobility 2DES is irradiated by microwave radiation. Another prominent effect is Hall field-induced resistance oscillations (HIRO) which appear in differential resistivity when a system is driven by a dc field. Both MIRO and HIRO originate from inter-Landau level transitions owing to photon absorption and/or impurity scattering. In this talk I will discuss our recent experimental studies on i) Shubnikov-de Haas oscillations in conventional high-mobility 2D electron gas in GaAs/Al_0.24Ga_0.76As quantum wells irradiated by sub-terahertz (up to 0.4 THz) radiation, ii) MIRO and HIRO in Al_xGa_1-xAs/Al_0.24Ga_0.76As quantum wells with x up to 0.0078, and, finally, iii) observation of MIRO in a moderate-mobility 2D hole gas hosted in a pure Ga/Si_0.2Ge_0.8 quantum well.

Recent progress in realizing topological superconductors has paved the road to study new physical phenomena resulting from the non-abelian statistics of the Majorana modes they host. A particularly interesting situation arises when Majorana bound states in a closed topological superconducting dot are coupled to external normal leads. In this talk , we will show that interactions with the quantum dot drive the lead electrons into a non-Fermi liquid phase, which can be understood by mapping the problem to a variant of a Kondo system. Interestingly, the non-Fermi liquid states in these systems are more robust than in the conventional two channel Kondo problem. This is because realizations with different numbers of metallic leads are connected to each other by a line of fixed points. We will conclude with a discussion of the experimental consequences of our theory.

Thermal and thermoelectric conductivities are ideal probes of interaction effects in correlated electron systems. This is because, in contrast to an electric current, a heat current can be transmitted also by neutral quasiparticles. For instance, energy can be carried by excitations that mediate interactions between other quasiparticles. In my talk I will present two examples of the dramatic effect of interactions on thermal and thermoelectric transport phenomena. The first is the Nernst effect in the vicinity of the superconducting phase transition. I will discuss the anomalous behavior of the Nernst effect near the magnetic-field-induced quantum critical phase transition. The second example is thermal conductivity in spin liquids. Spin liquids can form in the vicinity of the Mott metal-insulator transition when the charge is gapped while the spin degrees of freedom strongly fluctuate. These low energy excitations, dubbed spinons, can conduct heat. The spinons also exhibit a magnetic interaction that leads to non-Fermi liquid behavior. I will show that even in the absence of disorder this strong interaction provides an efficient relaxation mechanism for the heat current.

We present new results on the bistability effect recently observed [Dorozhkin et al., Nature Physics 7, 336 (2011)] in two-dimensional electron systems subjected to the microwave radiation. The effect appears as switching between two states with different electric potential distribution across a sample. Our results here imply that the main difference between these two states is an opposite direction of a long lengthscale electric field which arises spontaneously under conditions when the observable magnetoresistance tends to zero. Although a possibility of the field reversal is an inherent property of states with spontaneously broken symmetry, so far such effect was never observed under stationary external conditions.

Developing of novel technologies of functionalization of nano-size ferroelectric samples emerged the growing interest in exploration of such naturally-formed structures as polarization domains. I will present two recent results concerning the dynamic and static properties of domain self-organization.
The first part of my talk will concern the possible application of the domain structures in emerging technologies of Terahertz-detecting devices. We have studied the dynamical permittivity in ferroelectric nanometricaly-thin films with periodic domain structure, sandwiched between two paraelectric layers. The resulting frequency-dependent permittivity demonstrates collective resonance mode in sub-Terahertz frequency region and Debye-like relaxation behavior at low frequencies.
In the second part of my talk I will consider the study of domain-shape instabilities, recently observed in the ferroelectric polymer PVDF-TrFE films having the lower orthorhombic crystallographic symmetry and demonstrating the hexagonal domain faceting. This effect can arise from purely electrostatic depolarizing forces. We show that in contrast to magnetic bubble shape domains where such type of deformation instability has a predominantly elliptical character, the emergence of more symmetrical circular harmonics is favored in ferroelectrics with high dielectric constant.