Majorana zero modes are central to the pursuit of fault-tolerant topological quantum computation. While traditionally sought in one-dimensional hybrid nanowires, a robust alternative platform involves heterostructures combining superconductors with noncollinear magnets. This work focuses on a particularly promising system: a chiral ferromagnet hosting a magnetic skyrmion coupled to a superconducting film containing a superconducting vortex. Such skyrmion-vortex pairs have recently been realized experimentally and are theorized to harbor localized Majorana states, offering a potential pathway for braiding operations. We present a comprehensive theoretical analysis of the low-energy quasiparticle bound states in these heterostructures. Extending previous studies [1], we develop an analytical framework for the Majorana wavefunctions as well as the wavefunctions and spectrum of other lowlying states within a Bogoliubov-de Gennes approach. Our analytical results explicitly demonstrate the critical role of spin-orbit coupling for the stabilization of Majorana modes and provides approximate analytical expressions for low-lying states localized at the vortex, both with and without an accompanying skyrmion. The derived analytical results show excellent agreement with numerical simulations. We further elucidate the role of realistic effects, including vector potentials and texture perturbations from stray magnetic fields, to assess their impact.

[1] S. Rex, I. V. Gornyi, and A. D. Mirlin, Majorana bound states in magnetic skyrmions imposed onto a superconductor, Phys. Rev. B 100, 064504 (2019).

V dlinnykh dzhozefsonovskikh S-TI-S kontaktakh v magnitnom pole predskazano sushchestvovanie maioranovskikh nulevykh mod, lokalizovannykh na dzhozefsonovskikh vikhryakh. V nedavnikh eksperimentakh nablyudalis' osobennosti sverkhtoka pri tselykh nechetnykh znacheniyakh magnitnogo potoka cherez kontakt. Eto yavlenie mozhet ob'yasnyat'sya protsessami vkhoda i vykhoda maioranovskikh nulevykh mod iz kontakta. Provedeno detal'noe rassmotrenie protsessa obrazovaniya maioranovskikh mod na vneshnei granitse pri roste polya i ego vliyaniya na kriticheskii tok v zavisimosti ot chetnosti potoka. Obsuzhdaetsya zavisimost' rassmatrivaemogo yavleniya ot ustroistva vneshnego kraya kontakta.