Во втором порядке операторной формы теории возмущений получены эффективные взаимодействия в сверхпроводящей нанопроволоке при сильных электронных корреляциях, когда параметр спин-орбитальной связи сравним с интегралом перескока. Методом точной диагонализации в коротких нанопроволоках с открытыми граничными условиями при большой величине кулоновского отталкивания показано наличие возбуждений, соответствующих краевым состояниям майорановского типа с энергией, лежащей ниже величины объемной сверхпроводящей щели. Ключевые слова: сверхпроводящая нанопроволока, спин-орбитальное взаимодействие, майорановские моды, сильные электронные корреляции.

It is shown that axially symmetric inhomogeneous magnetic fields can lead to stabilization of higher-order magnetic skyrmions with topological charge |Q| > 1 due to orbital effects. We describe the analytical theory on the energy, size, and domain wall width of the such skyrmions in a power-law inhomogeneous fields, with a parameters corresponding to strongly correlated electron systems. The results obtained may have applications in describing the formation of nontrivial magnetic structures in inhomogeneous fields of superconducting vortices in heterostructures superconductor - chiral magnet of the type [Ir1Fe0.5Co0.5Pt1]10 /MgO/Nb.

Majorana corner modes have a number of advantages over the classical Majorana states in terms of performing topologically protected quantum computations. However, the problem of the influence of Coulomb repulsion on higher-order phases, which inevitably arises when trying to implement such systems in practice, has been poorly studied. In this article, we analyze the features of a topological invariant describing the nontrivial phase with the corner modes for a two-dimensional two-orbital model of a hybrid structure in the regime of extremely strong electron correlations. For this purpose, approximate wave functions of the edge states with a linear dispersion law and the associated Dirac masses, which arise when superconducting pairing in the system is taken into account, are obtained.

For superconducting nanowire with the pairing of extended s-type symmetry, Rashba spin-orbit interaction in a magnetic field, the influence of strong intersite charge correlations on single-particle Majorana excitations is analyzed. This problem is investigated on the basis of the density matrix renormalization group numerical method. It is shown that with an increase in the repulsion intensity of electrons located at the neighboring sites, two subbands emerge in the lower Hubbard band of the open system. Based on calculations of the Majorana polarization and degeneracy of the entanglement spectrum, it was found that a topologically nontrivial phase with one edge state survives at the edge of each of the subbands where the concentration of electrons or holes is minimal.