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.

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.

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.

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.

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.

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.

Referativnyi doklad po rabote Cecile Monthus, arxiv:1510.08322.

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.

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

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).

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.

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.

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 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.

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.

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.

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.

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.

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

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 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.

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.

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).

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.

V rabote byli issledovany sverkhprovodniki, obladayushchie tripletnym p_x+ip_y tipom sparivaniya, obladayushchie dvukratno vyrozhdennym osnovnym sostoyaniem. Bylo pokazano nalichie fazovogo perekhoda pod deistviem vneshnego magnitnogo polya ili transportnogo toka, snimayushchego dvukratnoe vyrozhdenie i vosstanavlivayushchego Z_2 simmetriyu. Takoi perekhod daet vozmozhnost' dlya upravlyaemoi generatsii domennykh stenok, svyazannykh s narushennoi Z_2 simmetriei osnovnogo sostoyaniya, po mekhanizmu Kibbla-Zureka. Predlozhennyi sposob generatsii domennykh stenok mozhet byt' realizovan v takikh ekzoticheskikh sverkhprovodnikakh kak Sr2RuO4 i v nekotorykh soedineniyakh s tyazhelymi fermionami.

po rabote V. Vadimov, M. Silaev, Phys. Rev. Lett. 111, 177001 (2013)

Budet rasskazano o nedavnikh izmereniyakh sverkhtoka v SNS-kontakte v geterostrukture HgTe/HgCdTe v rezhime kvantovogo spinovogo effekta Kholla [1]. Maksimal'nyi sverkhtok v sisteme izmeren kak funktsiya magnitnogo polya, napravlennogo perpendikulyarno dvumernomu obraztsu, a takzhe zavtornogo napryazheniya, reguliruyushchego plotnost' nositelei v ob'eme. V rezhime, kogda ob'emnye nositeli predpolozhitel'no otsutstvuyut, zavisimost' I(B) imeet priblizitel'no sinusoidal'nyi vid, chto sootvetstvuet sverkhtoku, tekushchemu tol'ko po krayam obraztsa. Period ostsillyatsii sootvetstvuet kvantu potoka Phi_0 cherez kontakt, a amplituda medlenno zatukhaet s rostom magnitnogo polya. Budut obsuzhdeny vozmozhnye prichiny zatukhaniya sverkhtoka, perenosimogo gelikoidal'nymi kraevymi modami.

[1] Molenkamp, Yacoby et al., http://arxiv.org/abs/1312.2559

Rassmatrivaetsya provodyashchee sostoyanie v 2D i 3D topologicheskom izolyatore (TI), tunnel'nym obrazom soedinennom s elektrodami iz normal'nogo metalla. Pokazano, chto kontakty, igraya rol' termostata, vyzyvayut zatukhanie i privodyat k relaksatsii elektronov v TI. Predlozhena prostaya struktura na osnove TI s tunnel'nymi kontaktami, sozdayushchaya chisto spinovyi tok vo vneshnei tsepi. Issleduetsya zavisimost' elektricheskogo i spinovogo toka vo vneshnei tsepi ot sootnosheniya mezhdu kharakternymi dlinami: dlinoi zatukhaniya iz-za tunnelirovaniya, dlinoi kontaktov i, v sluchae 3D TI, dlinoi svobodnogo probega i relaksatsii spina, vyzvannoi rasseyaniem impul'sa na primesyakh.

A number of physical problems may be formulated in terms of non-Hermitian quantum theories. A notable example is provided by mapping of 1D Coulomb gases onto an effective non-Hermitian Quantum Mechanics. Employing methods from algebraic topology we describe a non-perturbative method of instanton calculus for non-Hermitian Hamiltonians. Treating momentum and coordinate as complex variables yields Riemann surfaces of complex energy. The classical and instanton actions are given by the periods of this surface. We demonstrate the accuracy of this analytic procedure in comparison with numerical simulations for a class of periodic non-Hermitian Hamiltonians, as well as the validity of the Bohr-Sommerfeld quantization and Gamow’s formula in these cases.

Recently a new high-mobility Dirac material, trilayer graphene, was realized experimentally. The band structure of ABA-stacked trilayer graphene consists of a monolayer-like and a bilayer-like pair of bands. Here we study electronic properties of ABA-stacked trilayer graphene biased by a perpendicular electric field. We find that the combination of the bias and trigonal warping gives rise to a set of new Dirac points: In each valley, seven species of Dirac fermions with small masses of order of a few meV emerge. The positions and masses of the emergent Dirac fermions are tunable by bias, and one group of Dirac fermions becomes massless at a certain bias value.

Further, we analyze the evolution of the Landau level spectrum as a function of bias. We develop a theoretical model and argue that, in contrast to monolayer and bilayer graphene, the Landau level splittings and quantum Hall phase transitions observed in a recent experiment can be understood within a single-particle picture, but imply the presence of a charge density imbalance between the inner and outer layers of TLG, even at charge neutrality and zero transverse electric field. Our results indicate the importance of a previously unaccounted band structure parameter. We show that the pattern of Landau level crossings is very sensitive to certain band structure parameters, and can therefore provide a useful tool for determining their precise values.

Strong impurities crucially affect the spectral and transport properties of graphene near the Dirac point creating the "mid-gap" states. We first consider the ultimate case of very strong on-site potential impurities that are equivalent to vacancies in the lattice. Vacancies in the honeycomb lattice possess two important properties: (i) they preserve the chiral symmetry of the model and (ii) they scatter resonantly at zero energy (Dirac point). We study the density of states in graphene with sublattice imbalance [1]: we assume that the concentration of vacancies is different in the two sublattices. The imbalance leads to a finite concentration of zero modes of the tight-binding Hamiltonian. We derive the non-linear sigma model for the chiral system with imbalance. Semiclassical density of states acquires a finite gap around the Dirac point with the delta-function peak exactly in the center of the gap. Finite density of zero modes results in the additional term in the sigma-model action. The perturbative renormalization group analysis of this theory yields corrections to the density of states above the gap. In order to obtain a finite density of states below the semiclassical gap, we include non- perturbative contributions to the partition function due to instanton configurations of the field.

Further, we explore the longitudinal conductivity of graphene at the Dirac point in strong magnetic field with two types of short-range scatterers of a finite strength: adatoms that mix the valleys and "scalar" impurities that do not mix them [2]. A scattering theory for the Dirac equation is employed to express the conductance of a graphene sample at charge neutrality as a function of impurity coordinates; an averaging over positions of impurities is then performed numerically. The conductivity is equal to the ballistic value for each disorder realization, provided the number of flux quanta considerably exceeds the number of impurities. For weaker fields, the conductivity in the presence of scalar impurities scales to the quantum-Hall critical point at half filling or to zero away from half filling due to the onset of Anderson localization. For adatoms, the localization behavior is obtained also at half filling due to splitting of the critical energy by intervalley scattering. Our results reveal a complex scaling flow governed by fixed points of different symmetry classes.

[1] E.J. Koenig, I.V. Protopopov, P.M. Ostrovsky, I.V. Gornyi, A.D. Mirlin, and M.A. Skvortsov, in preparation.

[2] S. Gattenloehner, W.-R. Hannes, P. M. Ostrovsky, I. V. Gornyi, A. D. Mirlin, and M. Titov, "Quantum Hall criticality and localization in graphene with short-range impurities at the Dirac point", arXiv:1306.5686.

My eksperimental'no issledovali transportnye svoistva odinochnogo planarnogo kontakta mezhdu niobievym sverkhprovodyashchim elektrodom i kraem dvumernoi elektronnoi sistemy s sil'nym spin-orbital'nym vzaimodeistviem, realizovannoi v uzkoi InGaAs kvantovoi yame. My prodemonstrirovali podavlenie Andreevskogo otrazheniya v oblasti malykh napryazhenii, prilozhennykh k kontaktu, pri sverkhnizkikh temperaturakh (30 mK). Iz analiza temperaturnoi (do 1 K) zavisimosti i zavisimosti ot magnitnogo polya, orientirovannogo v ploskosti dvumernoi sistemy, my interpretiruem obnaruzhennoe podavlenie kak rezul'tat spin-orbital'nogo vzaimodeistviya. Tak zhe, pri opredelennom nabore parametrov, issleduemaya sistema demonstriruet priznaki realizatsii rezhima topologicheskoi sverkhprovodimosti.

arXiv:1305.5685

We consider a bath of fermions in one dimension at zero temperature, and an impurity particle immersed in this bath with some initial momentum. The following questions are addressed: How does the impurity momentum evolve? Does it relax to zero in the long run?

V rabote izuchayutsya mezoskopicheskie fluktuatsii lokal'noi plotnosti sostoyanii okolo perekhoda metall-dielektrik v neuporyadochennoi vzaimodeistvuyushchei elektronnoi sisteme. Pokazano, chto mul'tifraktal'noe povedenie lokal'noi plotnosti sostoyanii vyzhivaet v prisutstvie kulonovskogo vzaimodeistviya. Dlya perekhoda metall-izolyator v prisutstvie kulonovskogo vzaimodeistviya v razmernosti 2+\epsilon vychislen spektr mul'tifraktal'nykh razmernostei, kotoryi okazyvaetsya drugim, chem v sluchae bez vzaimodeistviya.

Doklad po rabote: I.S. Burmistrov, I.V. Gornyi, A.D. Mirlin, "Multifractality at Anderson transitions with Coulomb interaction", arxiv:1305.2888

Teoreticheski izucheno vliyanie slabogo besporyadka na effekt Aaronova-Boma v odnokanal'nykh kvantovykh kol'tsakh s tunnel'nymi kontaktami. Temperatura predpolagaetsya mnogo bol'shei mezhurovnevogo rasstoyaniya v kol'tsakh. V otsutstvie besporyadka zavisimost' kondaktansa kolets ot magnitnogo potoka pri takikh temperaturakh imeet uzkie provaly (antirezonansy). Rassmotreno vliyanie razlichnykh tipov besporyadka na eti antirezonansy. Pokazano, chto korotkodeistvuyushchie primesi privodyat k ushireniyu antirezonansov, odnako ikh glubina ne menyaetsya v shirokom diapazone parametrov. Plavnyi besporyadok privodit k poyavleniyu novykh antirezonansov. Teoriya obobshchaetsya na sluchai, kogda v kol'tsakh pomimo primesei prisutstvuet spin-orbital'noe i zeemanovskoe vzaimodeistvie.

http://arxiv.org/abs/1303.3486

Planiruetsya (i) na dvukh primerakh iz stat. fiziki pokazat', kak mozhet vyglyadet' statistika minimumov gaussova sluchainogo protsessa; (ii) proyasnit' tekushchii matematicheskii status prostykh retseptov vychisleniya khvosta raspredeleniya minimuma; (iii) esli ostanetsya vremya, razobrat' vyvod polnoi statistiki dlya brounovskogo bluzhdaniya s kvadratichnym dreifom ("toy model") -- renormgruppu (Ma-Dasgupty) dlya sil'nogo besporyadka i ekvivalentnost' kvantovoi odnomernoi zadache Izinga v sluchainom poperechnom pole (chast' (iii) po Le Doussal, Monthus 2003).

Metodom chislennogo analiza uravnenii na volnovye funktsii v priblizhenii Khatri-Foka pokazano, chto v standartnoi modeli Andersona na 3-kh mernoi reshetke s on-site disorder pri besporyadke W slegka men'she kriticheskogo znacheniya W_c=16.5, uchet kulonovskogo vzaimodeistviya privodit k fraktal'nomu povedeniyu volnovykh funktsii vblizi urovnya Fermi. Rezul'taty ukazyvayut na vozmozhnost' sushchestvovaniya tseloi promezhutochnoi "kriticheskoi fazy" v nekotoroi polose znachenii kulonovskoi konstanty vzaimodeistviya.

We experimentally demonstrate the simultaneous reconstruction of the bulk and the edge energy spectra caused by strong spin-orbit interaction, at the two lowest filling factors ν=1 and ν=2 for InxGa1−xAs two-dimensional electron system with x=0.75. The observed reconstruction is of different character at these filling factors: It is characterized by zeroing of the energy gap at the levels crossing point at ν=2, while the reconstruction at ν=1 goes through the coexistence of two ν=1 quantum Hall phases with different spin projections. An analysis indicates a strong influence of many-body interaction on the reconstruction at ν=1.

[A. Kononov, G. Biasiol, L. Sorba, and E. V. Deviatov, Phys. Rev. B 86, 125304 (2012)]

It has been recently predicted that Coulomb interaction drives a surface of a 3D topological insulator into a critical state (Ostrovsky et al., PRL 105, 036803 (2010)). We employ the sigma-model formalism to investigate the effect of electron-electron interaction on the transport by surface states in topological insulator thin films. We take into account the interaction of electrons on different surfaces and also the top-bottom asymmetry of the film (different densities of states and strength of disorder on top/bottom surface). This asymmetry is naturally present in experiments where the electronic densities on the surfaces are controlled independently by means of electrostatic gates. The lack of symmetry between top and bottom surfaces is shown to have strong effect on the film conductivity. The interplay of weak antilocalization, Coulomb interaction within and between surfaces and topological protection leads to a rich flow diagram representing the low temperature behavior of the system. In particular, the intersurface interaction is found to evoke a non-monotonic temperature dependence of the conductuctivity and eventually drives the film into a metallic state. The connection with recent experiments on Bi_2Se_3 films is discussed.

We address the problem of a Luttinger liquid with a scatterer that allows for both coherent and incoherent scattering channels. The asymptotic behavior at zero temperature is governed by a new stable fixed point: a Goldstone mode dominates the low energy dynamics, leading to a universal behavior. This limit is marked by equal probabilities for forward and backward scattering. Notwithstanding this non-trivial scattering pattern, we find that the shot noise as well as zero cross-current correlations vanish. We thus present a paradigmatic picture of an impurity in the Luttinger model, alternative to the Kane-Fisher picture.

Field-theoretical approach to Anderson localization in 2D disordered fermionic systems of chiral symmetry classes (BDI, AIII, CII) is developed. Important representatives of these symmetry classes are random hopping models on bipartite lattices at the band center. As was found by Gade and Wegner two decades ago within the sigma-model formalism, quantum interference effects in these classes are absent to all orders of perturbation theory. We demonstrate that the quantum localization effects emerge when the theory is treated non-perturbatively. Specifically, they are controlled by topological vortex-like excitations of the sigma models. We derive renormalization group equations including these non-perturbative contributions. Analyzing them, we find that the 2D disordered systems of chiral classes undergo a metal-insulator transition driven by topologically induced Anderson localization. We also show that the Wess-Zumino and Z_2 theta terms on surfaces of 3D topological insulators (in classes AIII and CII, respectively) overpower the vortex-induced localization.

po rabote E.J. König, P. M. Ostrovsky, I. V. Protopopov, A. D. Mirlin, "Metal-insulator transition in 2D random fermion systems of chiral symmetry classes", arXiv:1201.6288v1

Budet sdelan kratkii (minut na 30) kommentarii na temu, obsuzhdavshuyusya G. Lesovikom na ego doklade 15 dekabrya v IFP, s ispol'zovaniem resheniya (E. Cuevas, M. Feigel'man, L.Ioffe, M. Mezard) zadachi o reshetke spinov so sluchainym polem, rasskazannoi ranee (21.10.2011).

Budet predstavleno bolee podrobnoe izlozhenie rezul'tatov raboty E.Cuevas, M.Feigelman, L.Ioffe, M.Mezard "Level statistics of disordered spin-1/2 systems and its implications for materials with localized Cooper pairs", ob'yavlennykh v sentyabre na Uchenom Sovete ITF.

Obsuzhdaetsya obobshchenie fluktuatsionnogo deistviya Ginzburga-Landau v sigma-modeli Keldysha na sluchai proizvol'nykh temperatur i magnitnykh polei . Etot podkhod pozvolyaet vosproizvesti standartnye rezul'taty dlya fluktuatsionnykh popravok vo vsei oblasti vyshe perekhoda, a takzhe poluchit' novye rezul'taty dlya effekta Kholla, voznikayushchego za schet sverkhprovodyashchikh fluktuatsii.

Obzornyi doklad po rabotam o Spin Seebeck Effect (otklik spinovogo toka na gradient temperatury):
Theory of magnon-driven spin Seebeck effect, arxiv:1009.0318
Gigantic enhancement of spin Seebeck effect by phonon drag, arxiv:1010.4600
Acoustic spin pumping as the origin of the long-range spin Seebeck effect, arxiv:1103.6120

Izucheny admittans i dissipatsiya energii v odno-elektronnoi korobke (malen'kii metallicheskii ostrovok, soedinennyi s rezervuarom tunnel'nym kontaktom; potentsial elektronov na ostrovke kontroliruetsya dopolnitel'nym zatvornym elektrodom) v neravnovesnom rezhime pri prilozhenii peremennogo zatvornogo napryazheniya v rezhime sil'noi kulonovskoi blokady. Vychislen admittans pri ne slishkom nizkoi effektivnoi temperature (energii) elektronov na ostrovke, kogda mozhno prenebrech' elektronnoi kogerentnost'yu, no neobkhodimo polnost'yu uchityvat' kvantovye fluktuatsii zaryada iz-za sil'nogo kulonovskogo vzaimodeistviya. Kak okazalos', dissipatsiya energii mozhet byt' vyrazhena cherez soprotivlenie zaryadovoi relaksatsii i perenormirovannuyu zaryadovuyu emkost' dazhe v neravnovesnykh usloviyakh. Povedenie admittansa kak funktsii vneshnei chastoty opredelyaetsya funktsiei raspredeleniya, otvechayushchei bozonnym kollektivnym vozbuzhdeniyam na ostrovke. Poetomu, mozhno ispol'zovat' admittans odno-elektronnoi korobki dlya izmereniya etoi bozonnoi funktsii raspredeleniya.

Vychislen tok v rezhime ko-tunnelirovaniya cherez dvukhurovnevuyu kvantovuyu tochku slabo svyazannuyu s ferromagnitnymi kontaktami. Pokazano, chto zavisimost' differentsial'nogo kondaktansa ot prilozhennogo napryazheniya imeet vid stupenek, kotorye razlichny v sluchayakh parallel'noi i antiparallel'noi orientatsii magnitnykh momentov v kontaktakh. Vklady v tok ot uprugikh i neuprugikh protsessov rassmotreny otdel'no. Naideno, chto v neuprugoi chasti toka ko-tunnelirovaniya est' interferentsionnaya chast' (zavisimost' ot faz tunnel'nykh amplitud).

Izuchaetsya perekhod ot dvukhchastichnoi zadachi Kupera k mnogochastichnoi modeli Bardina-Kupera-Shriffera (BKSh). Dlya opisaniya osnovnogo sostoyaniya sistemy predlozhen analiticheskii sposob resheniya uravnenii Richardsona, matematicheski ogranichennyi razrezhennym predelom kuperovskikh par. Nesmotrya na eto ogranichenie, sopostavlenie s rezul'tatami teorii BKSh ukazyvaet na to, chto poluchennye rezul'taty ostayutsya tochnymi i v plotnom rezhime par. Predlagaetsya al'ternativnaya interpretatsiya rezul'tatov teorii BKSh dlya energii osnovnogo sostoyaniya v terminakh "energii svyazi kuperovskoi pary", evolyutsioniruyushchei prostym obrazom pri perekhode ot razrezhennogo k plotnomu rezhimu par. V etom podkhode shchel' tipa BKSh v spektre vozbuzhdenii yavlyaetsya pryamym sledstviem mnogochastichnykh effektov, vyzvannykh blokirovkoi otdel'nykh odnoelektronnykh sostoyanii.

Temperaturnaya zavisimost' provodimosti na perekhode mezhdu plato v rezhime tselochislennogo kvantovogo effekta Kholla opredelyaetsya kriticheskim indeksom κ, kotoryi est' otnoshenie indeksa korrelyatsionnoi dliny (ν) i indeksa dliny razfazirovki (p), κ=p/(2ν). V otlichie ot indeksa korrelyatsionnoi dliny, kotoryi mnogo raz vychislyalsya, indeks p izuchalsya tol'ko v rabotakh [1,2]. V etikh rabotakh indeks p dliny razfazirovki byl vychislen v predpolozhenii, chto on opredelyaetsya anomal'noi razmernost'yu irrelevantnogo operatora, vkhodyashchego v `inverse participation ratio'. V rabote my analiticheski pokazyvaem, chto dlya sluchaya ekranirovannogo kulonovskogo vzaimodeistviya v singletnom kanale eto predpolozhenie vypolnyaetsya dlya Andersonovskogo perekhoda v unitarnom klasse v razmernosti 2+ε. Provedennye chislennye raschety ukazyvayut na to, chto eto predpolozhenie vypolnyaetsya i dlya perekhoda mezhdu plato.

My issleduem relaksatsionnuyu dinamiku elektronov v odnoelektronnom tranzistore. Imenno, my otvechaem na sleduyushchii vopros. Predpolozhim, chto neravnovesnoe elektronnoe raspredelenie obrazovalos' v protsesse eksperimenta. Po kakomu zakonu ono budet relaksirovat' k ravnovesiyu? Issledovanie relaksatsii provedeno v rezhimakh slaboi i sil'noi kulonovskoi blokady. Vyvedeny i resheny osnovnye kvantovye kineticheskie uravneniya, upravlyayushchie dinamikoi funktsii raspredeleniya v protsesse ustanovleniya teplovogo ravnovesiya. Ustanovleny universal'nye formuly dlya transportnykh koeffitsientov, prigodnye dlya tranzistora s tunnel'noi svyaz'yu lyuboi prozrachnosti. Krome togo, osushchestvlena odnopetlevaya perenormirovka osnovnykh fizicheskikh velichin, opredelyayushchikh transportnye nablyudaemye, chto pozvolyaet nam poluchit' naibolee tochnye rezul'taty.

Budet predstavleny predvaritel'nye rezul'taty chislennogo issledovaniya spektra i korrelyatsionnykh funktsii v spetsial'noi modeli 2-mernoi Boze-zhidkosti (s nerelyativistskoi supersimmetriei), dopuskayushchei modelirovanie kvantovykh svoistv pri pomoshchi klassicheskoi molekulyarnoi dinamiki.

Dlya sistem s sil'nymi korrelyatsiyami, pri otsutstvii yavnogo malogo parametra, prakticheski edinstvennym effektivnym metodom opisaniya yavlyayutsya interpolirushchie teorii, osnovannye na priblizheniyakh effektivnoi sredy. V chastnosti, dlya opisaniya sistem sil'nokorrelirovannykh elektronov rasprostranenie poluchil dinamicheskii metod srednego polya (DMFT), polnost'yu opisyvayushchii fiziku lokal'nykh (na uzle reshetki) elektronnykh fluktuatsii, no prenebregayushchii prostranstvennoi dispersiei korrelyatsii. Predlagaemyi metod, startuya s rezul'tata DMFT, pozvolyaet uchest' effekty prostranstvennoi dispersii posredstvom regulyarnogo diagrammnogo razlozheniya. Metod osnovan na tochnom perekhode k ansamblyu dual'nykh peremennykh, gaussovo priblizhenie dlya kotorogo vosproizvodit DMFT, a diagrammnoe razlozhenie po nelineinosti pozvolyaet utochnit' etot rezul'tat. Dlya poluzapolnennoi modeli Khabbarda na kvadratnoi reshetke uchet prosteishei diagrammnoi popravki v rezhime sil'nykh korrelyatsii (U=8..16 t) pozvolyaet izbavit'sya ot nefizichnogo tsentral'nogo pika plotnosti odnoelektronnykh sostoyanii, a summirovanie lestnichnogo ryada - poluchit' antiferromagnitnuyu psevdoshchel'. Dlya modeli s dopirovaniem, opisano anizotropnoe razrushenie poverkhnosti Fermi v rezhime psevdoshcheli i effekty perenormirovki zakona dispersii vblizi osobennostei van Khova.

Doklad posvyashchen neravnovesnoi kinetike dvumernogo elektronnogo gaza na vysokikh urovnyakh Landau v usloviyakh mikrovolnovogo oblucheniya i/ili sil'nogo (v tom chisle neodnorodnogo) elektricheskogo polya. Budet predstavlena teoriya (osnovannaya na reshenii kvantovogo kineticheskogo uravneniya v prisutstvii plavnogo i korotkodeistvuyushchego potentsiala primesei, a takzhe elektron-elektronnogo i elektron-fononnogo vzaimodeistviya), pozvolyayushchaya v ramkakh edinogo podkhoda opisat' razlichnye tipy ravnovesnykh i neravnovesnykh magnetoostsillyatsii, nablyudaemykh v eksperimente. Pomimo Shubnikovskikh ostsillyatsii, syuda otnosyatsya ostsillyatsii magnetosoprotivleniya, indutsirovannye sil'nym postoyannym tokom, mikrovolnovym oblucheniem, i rezonansnym vzaimodeistviem s teplovymi fononami, a takzhe kvantovye ostsillyatsii koeffitsienta pogloshcheniya mikrovoln i szhimaemosti elektronnogo gaza. Takzhe budet predstavlena teoriya fotogal'vanicheskikh yavlenii v neodnorodnom elektronnom gaze. Budet pokazano, chto fotoeds v takikh neravnovesnykh sistemakh voznikaet vsledstvie narusheniya sootnosheniya Enshteina mezhdu provodimost'yu i koeffitsientom diffuzii.

Vychislyaetsya popravka k provodimosti Sharvina dvumernogo ballisticheskogo mikrokontakta s bol'shim chislom kvantovykh kanalov. Ona voznikaet iz-za elektron-elektronnogo vzaimodeistviya, i mozhet byt' poluchena uzhe v kvaziklassicheskom predele. Popravka polozhitel'na, vozrastaet s temperaturoi i rezko umen'shaetsya s rostom magnitnogo polya. Poluchennye rezul'taty kachestvenno i kolichestvenno ob'yasnyayut anomal'noe polozhitel'noe magnetosoprotivlenie v malykh polyakh, nedavno nablyudavsheesya na eksperimente.

We report thermodynamic magnetization measurements of a 2-dimensional electron gas for several high mobility Si-MOSFETs. The low-temperature magnetization is shown to be strongly sub-linear function of the magnetic field. The susceptibility determined from the zero-field slope grows with cooling as 1/T^α, with α=2.4±0.2 even at high electron densities, in apparent contradiction with the Fermi-liquid picture.

izlozhenie rezul'tatov preprintov:
arxiv: 0904.0690 Topological insulators in three dimensions from spontaneous symmetry breaking, Yi Zhang, Ying Ran, Ashvin Vishwanath
arxiv: 0907.2962 Mott physics and band topology in materials with strong spin-orbit interaction, D. A. Pesin, and Leon Balents

Izuchaetsya kulonovskaya blokada v odno-elektronnom tranzistore v neravnovesnom rezhime (naprimer, kogda temperatura ostrovka bol'she temperatury rezervuarov). V sluchae tunnel'nykh kontaktov mezhdu ostrovkom i rezervuarami polucheno kvantovoe kineticheskie uravnenie na funktsiyu raspredeleniya elektronov na ostrovke. S pomoshch'yu nego reshena zadacha o relaksatsii temperatury ostrovka za schet mekhanizma tunnelirovaniya elektronov s ostrovka v rezervuary i obratno.

V rabote izuchaetsya zaryad v kvantovoi tochke, prisoedinennoi k sverkhprovodyashchim beregam pri nalichii kulonovskogo i elektron-fononnogo vzaimodeistvii v predele beskonechnoi sverkhprovodyashchei shcheli. Rassmotreno vliyanie fononov na chuvstvitel'nost' zaryada k raznitse sverkhprovodyashchikh faz. Pokazano, chto, v nekotorom smysle, elektron-fononnoe vzaimodeistvie deistvuet kak "otritsatel'noe" kulonovskoe vzaimodeistvie.

I will review old and recent results for eigenfunction and eigenvalue statisitics of certain random matrix ensembles and show the correspondence between them and statistics in the 3D Anderson model at criticality. From the conventional viewpoint of RMT the two ensembles belong to distinctly different universality classes, being invariant and non-invariant with respect to rotation of basis, respectively.

Yet we show the similarity of their level statistics and a possibility of unifying them using the Luttinger liquid formalism. We also show that the level correlations in the invariant RMT show properties similar to expected density correlations in the sonic analogue of black holes.

Planiruetsya rasskazat' o topologicheskikh izolyatorakh s T-simmetriei so "standartnoi" tochki zreniya (polyarizatsiya otnositel'no obrashcheniya vremeni pervichna, poverkhnostnye urovni vtorichny) po stat'yam Fu i Kane "Time reversal polarization and adiabatic spin pump" (2006) i "Topological insulators with inversion symmetry" (2007). Esli poluchitsya, to mozhno budet zadet' i obshchuyu klassifikatsiyu po Kitaevu.

v kotoroi izuchaetsya RKKY vzaimodeistvie na poverkhnosti topologicheskogo izolyatora, a takzhe o ryade rabot svyazannykh s etim voprosom.

V programme zasedaniya:
11.30-12.15 G.E. Volovik «Sila Iordanskogo i kvantovaya turbulentnost'»
12.15-13.00 A.M. Finkel'shtein «Effektivnaya teoriya rasprostraneniya impul'sov v nelineinykh i neuporyadochennykh sredakh»
13.00-13.15 Pereryv
13.15-14.00 S.E. Korshunov «Fazovye perekhody v dvumernykh reshetkakh SFS kontaktov»
14.00-14.45 E.A. Brener «Asimptoticheskie nelineinosti v smektikakh»
15.00-17.00 Furshet

Spin and Charge Correlations in Quantum Dots: An Exact Solution (for the Tunneling Density of States)

I.Burmistrov, Y. Gefen, M. Kiselev

Abstract: The inclusion of charging and spin-exchange interactions within the Universal Hamiltonian description of quantum dots is challenging as it leads to a non-Abelian action. Here we present an exact analytical solution of the probem, in particular, in the vicinity of the Stoner instabilty point. We specifically calculate the tunneling density of states (TDOS) and the spin susceptibility. Near the instability point the TDOS exhibits a non-monotonous behavior as function of the tunneling energy, even at temperatures higher than the exchange energy. Our approach is generalizable to a broad set of observables, including the a.c. susceptibility and the absorption spectrum for anisotrpic spin interaction. Our results could be tested in nearly ferromagnetic materials.

Eksperimental'no obnaruzheny znakoperemennye ostsillyatsii fototoka i foto-EDS, voznikayushchie pri mikrovolnovom obluchenii neodnorodnykh obraztsov s dvumernymi elektronnymi sistemami. Polozhenie ostsillyatsii sootvetstvuet polozheniyu garmonik tsiklotronnogo rezonansa. Pokazano, chto vozniknovenie fotosignalov svyazano so vstroennym v obraztse elektricheskim polem. V etom sluchae ostsillyatsii fototoka sootvetstvuyut ego protekaniyu vdol' i protiv elektricheskogo polya, a ostsillyatsii foto-EDS otrazhayut libo ekranirovanie, libo usilenie elektricheskogo polya foto-vozbuzhdennymi elektronami.

V teoreticheskoi chasti raboty pokazano, chto vozniknovenie foto-gal'vanicheskikh signalov svyazano s narusheniem v neravnovesnom sostoyanii sootnosheniya Einshteina mezhdu provodimost'yu i koeffitsientom diffuzii. Vychislennye provodimost' i koeffitsient diffuzii dvumernoi elektronnoi sistemy pod oblucheniem, a takzhe vol't-ampernaya kharakteristika obraztsa s omicheskimi kontaktami pozvolyayut ob'yasnit' eksperimental'nye nablyudeniya.

[1] S.I. Dorozhkin, I.V. Pechenezhskii, L.N. Pfeiffer, K.W. West, V. Umansky, K. von Klitzing, J.H. Smet, Photocurrent and photovoltage oscillations in the two-dimensional electron system: enhancement and suppression of built-in electric fields, Phys. Rev. Lett. 102, 036602 (2009).

[2] I.A. Dmitriev, S.I. Dorozhkin, and A.D. Mirlin, Theory of the microwave-induced photocurrent and photovoltage magneto-oscillations in a spatially non-uniform 2D electron gas.

Quantum mechanics offers novel algorithms speeding up the solution of specific computational tasks. While applications in quantum cryptography are close to commercial realization, building a universal quantum computer with thousands of quantum bits lies in the distant future, if ever realized. In this situation, it is interesting to consider special tasks, less demanding in their requirements regarding the number of qubits and the network complexity. Here, we discuss an algorithm and its application where a few qubits serve as active or passive detectors. The core algorithmic element is a setup with K qubits allowing to count the elements in a stream of particles flowing in a quantum wire and represent it in a binary form. Applications include a divisibility-check to experimentally determine the size of a finite train of particles in a quantum wire and a scheme allowing to entangle multi-particle wave functions in a Mach-Zehnder interferometer, generating Bell-, Greenberger-Horne-Zeilinger-, or Dicke states.

referativnyi doklad po eksperimental'noi rabote V.Deshpandei, D.Novikov, M.Bockgrath et al, Science, v.323, p.106 (2009)

referativnyi doklad po rabote L. Glazman, A. Imambekov, arXiv:0812.1046

Issleduetsya zadacha o dissipatsii energii v zadache o metallicheskom ostrovke, soedinennym tunnel'nym kontaktom s rezervuarom, i emkost'yu s zatvorom, na kotoroe podaetsya peremennoe napryazhenie. Formuly dlya dissipatsii energii s uchetom kulonovskoi energii na ostrovke polucheny v dvukh predel'nykh sluchayakh: malykh i bol'shikh kondaktansov tunnel'nogo kontakta. Poluchennye rezul'taty pozvolyayut sdelat' predpolozhenie ob universal'nosti poluchennykh formul pri lyubykh kondaktansakh tunnel'nogo perekhoda.

po rabote:

arXiV:0802.0379 Creation and manipulation of anyons in the Kitaev model S. Dusuel, K. P. Schmidt, J. Vidal

We analyze the effect of local spin operators in the Kitaev model on the honeycomb lattice. We show, in perturbation around the isolated-dimer limit, that they create Abelian anyons together with fermionic excitations which are likely to play a role in experiments. We derive the explicit form of the operators creating and moving Abelian anyons without creating fermions and show that it involves multi-spin operations. Finally, the important experimental constraints stemming from our results are discussed.

Violation of Kirchhoff's Laws for a Coherent RC Circuit, J.Gabelli, et al, Science 313, 499 (2006)

i obzor lezhashchei v ee osnove teoreticheskoi raboty:

Buttiker, Thomas, Pretre, Phys. Lett. A 180, 364 (1993)

(doklad o zadache, nakhodyashcheisya v rabote)

Budet rasskazano o poluchennykh k nastoyashchemu vremeni analiticheskikh rezul'tatakh dlya SINIS perekhoda v rezhime zadannogo napryazheniya: vychislenie zavisyashchego ot vremeni toka v dissipativnom rezhime.

1) M. Dolev, M. Heiblum, V. Umansky, A. Stern, D. Mahalu, "Observation of a quarter of an electron charge at the \nu=5/2 quantum Hall state", Nature 452, 829 (2008) [arXiV:0802.0930]

2) 2) I.P. Radu, J.B. Miller, C.M. Marcus, M.A. Kastner, L.N. Pfeiffer, K.W. West, "Quasi-particle properties from tunneling in the \nu=5/2 fractional quantum Hall state", Science 320, 899 (2008) [arXiV:0803.3530]

Bergeret, Volkov, Efetov, "Induced ferromagnetism due to superconductivity in superconductor- ferromagnet structures", PRB 69, 174504 (2004); "Spin screening of magnetic moments in superconductors", Europhys. Lett. 66, 111 (2004).

Rassmotren kondaktans kvantovoi tochki s kulonovskim vzaimodeistviem v situatsii, kogda na tochku posylaetsya konechnoe chislo odnoelektronnykh volnovykh paketov. Iskhodya iz znaniya tochnoi N chastichnoi matritsy rasseyaniya sistemy pokazano, chto v sluchae nesimmetrichnoi kvantovoi tochki (otnositel'no zameny levo/pravo) pri nalichii vzaimodeistviya kondaktans sistemy okazyvaetsya takzhe asimmetrichnym otnositel'no napravleniya perenosa zaryada.

V rabote issleduetsya vliyanie spinovogo i dolinnogo rasshcheplenii na soprotivlenie, spinovuyu i dolinnuyu vospriimchivost' dvumernoi neuporyadochennoi elektronnoi zhidkosti. Kak vyyasnilos', v rabote na etu zhe temu, rasskazannoi god nazad, nami byla dopushchena oshibka. V doklade budet rasskazano o novykh odnopetlevykh uravneniyakh renorm-gruppy, kotorye opisyvayut sistemu v dvukh oblastyakh Δ_s << T << Δ_v i T << Δ_s << Δ_v, gde T - temperatura, Δ_s -spinovoe rasshcheplenie, i Δ_v - dolinnoe rasshcheplenie. S pomoshch'yu poluchennykh uravnenii renorm-gruppy nam udalos' kachestvenno ob'yasnit' proiskhozhdenie nemonotonnoi zavisimosti soprotivleniya ot temperatury, kotoraya nablyudaetsya eksperimental'no v parallel'nom magnitnom pole, a takzhe predskazat' vozmozhnost' nablyudeniya novogo tipa nemonotonnogo povedeniya, pri kotorom soprotivlenie kak funktsiya temperatury imeet dva maksimuma.

V priblizhenii tunnel'nogo gamil'toniana rassmatrivaetsya model' kvantovoi tochki, pomeshchennoi mezhdu dvumya sverkhprovodyashchimi provodnikami, k kotorym prilozhena raznost' potentsialov. Dopolnitel'no ryadom s tochkoi pomeshchen normal'nyi provodnik, po kotoromu ne techet tok: on igraet rol' rezervuara, sbivayushchego fazu tunneliruyushchikh v nego elektronov. Pri pomoshchi neravnovesnoi Keldyshevskoi tekhniki vychislyaetsya podshchelevoi elektricheskii tok, kotoryi, kak izvestno, voznikaet v protsesse perenosa zaryada pri mnozhestvennykh Andreevskikh otrazheniyakh. Pokazano, chto svyaz' s normal'nym provodnikom privodit k sglazhivaniyu osobennostei v postoyannom toke, voznikayushchikh pri mnozhestvennykh Andreevskikh otrazheniyakh. S drugoi storony, pervaya garmonika toka na Dzhozefsonovskoi chastote bolee ustoichiva k sboyu fazy, dazhe dlya napryazhenii, men'shikh sverkhprovodyashchei shcheli. Faza etoi pervoi garmoniki pozvolyaet provodit' izuchenie effektov, vyzvannykh normal'nym provodnikom.

Na primere billiarda Sinaya izucheno vliyanie difraktsii na spektral'nye kharakteristiki khaoticheskikh billiardov, granitsa kotorykh imeet vognutye vovnutr' uchastki. Difraktsiya privodit k poyavleniyu tselogo mnozhestva dopolnitel'nykh traektorii pomimo klassicheskikh. Vychislen "nediagonal'nyi" vklad ot nikh v korrelyatsionnuyu funktsiyu dvukh urovnei energii, proiskhodyashchii ot interferentsii mezhdu nimi. Pokazano, chto on yavlyaetsya ostsilirruyushchei funktsiei chastoty s periodom, ravnym t.n. vremeni Erenfesta.

Issleduyutsya instantonnye popravki k soprotivleniyu v neodnorodnom granulirovannom metalle. Obsuzhdaetsya kachestvennaya fizicheskaya kartina fiziki sistemy v sluchae prosteishei neodnorodnosti.

Zaryad podshchelevogo sostoyaniya v andreevskoi kvantovoi tochke (AKT), pomeshchennoi v sverkhprovodyashchuyu petlyu, ochen' chuvstvitelen k magnitnomu potoku, pronikayushchemu v petlyu. My obsuzhdaem vozmozhnost' ispol'zovaniya etoi ustanovki kak pribora dlya izmereniya slabykh magnitnykh potokov. My detal'no izuchili chuvstvitel'nost' kak funktsiyu parametrov AKT v predele Δ → ∞. Takzhe my izuchili slaboe kulonovskoe vzaimodeistvie v AKT.

My predlagaem novuyu model'nuyu sistemu dlya izucheniya perekhoda sverkhprovodnik-izolyator. Eta sitema predstavlyaet soboi regulyarnuyu reshetku, kazhdoe rebro kotoroi sostoit iz N>>1 dzhozefsonovskikh kontaktov, soedinennykh posledovatel'no. Dlya sluchaya, kogda dzhozefsonovskaya energiya kontaktov velika po sravneniyu s zaryadovoi, razvita teoriya, opisyvayushchaya takuyu setku. Vyvedeno tochnoe dual'noe preobrazovanie, perevodyashchee gamil'tonian iskhodnoi sistemy v standartnyi gamil'tonian dzhozefsonovskoi setki na kvadratnoi reshetke. Dlya magnitnykh frustratsii f=0, 1/2, 1/4 naideno kriticheskoe otnoshenie E_J/E_C, pri kotorom v rassmatrivaemoi sisteme proiskhodit nul'temperaturnyi perekhod sverkhprovodnik-izolyator, i opredelena zavisimot' temperatury sverkhprovodyashchego perekhoda ot E_J/E_C. Analogichnye velichiny otseneny dlya sluchaya nulevoi magnitnoi frustratsii, no v prisutstvii sil'noi sluchainoi zaryadovoi frustratsii.

V rabote rassmatrivaetsya vopros ob izmerimosti fluktuatsii toka vysshikh poryadkov lineinym detektorom. Rassmotreny dva razlichnykh tipa izmerenii: izmerenie spektral'noi moshchnosti fluktuatsii i izmerenie raznovremennykh korrelyatorov toka pri fiksirovannykh vremenakh. Dlya kazhdogo sluchaya polucheny formal'no tochnye vyrazheniya dlya pokazanii detektora, soderzhashchie uporyadochennye vdol' Keldyshevskogo kontura operatory elektronnogo toka. Naiden yavnyi vid vremennogo uporyadocheniya operatorov toka pod znakom srednego pri izmerenii raznovremennykh korrelyatorov toka vysshikh poryadkov. Rassmotrena situatsiya, kogda detektor izmeryaet korrelyatsii toka v razlichnykh tochkakh provodnika.

My rassmotrim zadachu o rasseyanii ploskoi volny na prepyatstvii ili neodnorodnostyakh. Transportnoe sechenie rasseyaniya sigma_T malo izucheno dazhe dlya potentsialov obladayushchikh tsentral'noi simmetriei. V sluchae zhe prepyatstviya proizvol'noi formy amplituda rasseyaniya prakticheski ne poddaetsya informativnomu analiticheskomu opisaniyu. Tem ne menee, v nekotorykh sluchayakh nam udalos' poluchit' nekotoruyu informatsiyu, vychislyaya i sravnivaya polnoe i transportnoe secheniya rasseyaniya, a takzhe reshaya zadachu o minimizatsii (maksimizatsii) sigma_T.

Pri nizkoi plotnosti, elektrony v kvantovoi provoloke mogut obrazovat' vignerovskii kristall. V etom sluchae geizenbergovskii obmen mezhdu paroi blizhaishikh elektronov voznikaet v rezul'tate tunnelirovaniya pod razdelyayushchim ikh kulonovskim bar'erom. Pri etom kulonovskoe vzaimodeistvie vovlekaet v protsess tunnelirovaniya i vse ostal'nye elektrony, ch'e vliyanie na velichinu konstanty geizenbergovskogo obmena my i izuchaem - kak analiticheski, tak i chislenno.

po rabote R.S. Keizer, M.G. Flokstra, J. Aarts i T. M. Klapwijk