arXiv subjects

A. D. Fedoseev

Publications and source records attributed to A. D. Fedoseev.

4 recordsLinked to original sources

arXiv2025

Coexistence of gapless and gapped vortex modes with Majorana corner states in a 2D second-order topological superconductor

Although the appearance of vortex-localized states with zero energy in first-order topological superconductors is well known, their possibility to form in the higher-order topological phase of 2D systems has not been completely uncovered yet. Here we demonstrate the coexistence of zero-energy vortex modes and Majorana corner modes in the model of a 2D second-order topological superconductor. The model describes an interface between a normal layer supporting the topological insulating phase and a superconducting layer, for which different symmetries of the spin-singlet superconducting order parameter are considered. We show that the gapless vortex modes can appear under certain conditions in the superconducting state with a vortex if the bulk energy spectrum of the normal (non-superconducting) state is gapless and has Dirac cones. The number of pairs of such vortex modes corresponds to the number of Dirac cones. It is essential that if the normal bulk spectrum becomes gapped and the system is in the state of a topological insulator, then the zero-energy vortex modes can not be realized, while Majorana corner modes hold in the superconducting state. The interaction of the vortex modes with the edge and topological corner modes is studied when the vortex appears near the boundaries.

cond-mat.supr-con↗

arXiv2022

Effect of local Coulomb interaction on Majorana corner modes: weak and strong correlation limits

Here we present an analysis of the evolution of Majorana corner modes realizing in a higher-order topological superconductor (HOTSC) on a square lattice under the influence of local Coulomb repulsion. The HOTSC spectral properties were considered in two regimes: when the intensities of many-body interactions are either weak or strong. The weak regime was studied using the mean-field approximation with self-consistent solutions carried out both in the uniform case and taking into account of the boundary of the finite square-shaped system. It is shown that in the uniform case the topologically nontrivial phase on the phase diagram is widened by the Coulomb repulsion. The boundary effect, resulting in an inhomogeneous spatial distribution of the correlators, leads to the appearance of the crossover from the symmetric spin-independent solution to the spin-dependent one characterized by a spontaneously broken symmetry. In the former the corner states have energies that are determined by the overlap of the excitation wave functions localized at the different corners. In the latter the corner excitation energy is defined by the Coulomb repulsion intensity with a quadratic law. The crossover is a finite size effect, i.e. the larger the system the lesser the critical value of the Coulomb repulsion. In the strong repulsion regime we derive the effective HOTSC Hamiltonian in the atomic representation and found a rich variety of interactions induced by virtual processes between the lower and upper Hubbard subbands. It is shown that Majorana corner modes still can be realized in the limit of the infinite repulsion. Although the boundaries of the topologically nontrivial phase are strongly renormalized by Hubbard corrections.

cond-mat.mes-hall↗

arXiv2022

Topological superconductivity and Majorana states in low-dimensional systems

We discuss the properties of topologically nontrivial superconducting phases and the conditions for their realization in condensed matter, and the principles for identifying Majorana bound states (MBSs). Along with the well-known Kitaev chain and superconducting nanowire (SW) models with spin-orbit coupling in an external magnetic field, we discuss models of quasi-2D materials in which MBSs are realized in the presence of noncollinear spin ordering. For finite-length SWs, we demonstrate a cascade of quantum transitions occurring with a change in the magnetic field, accompanied by a change in the fermion parity of the ground state. The corresponding anomalous behavior of the magnetocaloric effect can be used as a tool for identifying MBSs. We devote considerable attention to the analysis of the transport characteristics of devices that contain topologically nontrivial materials. The results of studying the conductance of an Aharonov-Bohm ring whose arms are connected by an SW are discussed in detail. An important feature of this device is the appearance of Fano resonances in the dependence of conductance on the magnetic field when the SW is in a topologically nontrivial phase. We establish a relation between the characteristics of such resonances and the spatial structure of the lowest-energy SW state. The conditions for the occurrence of an MBS in the phase of the coexistence of chiral $d+id$ superconductivity and 120-degree spin ordering are determined in the framework of the $t-J-V$ model on a triangular lattice. We take electron-electron interactions into account in discussing the topological invariants of low-dimensional superconducting materials with noncollinear spin ordering. The formation of Majorana modes in regions with an odd value of a topological $\mathbb{Z}$ invariant is demonstrated. The spatial structure of these excitations in the Hubbard fermion ensemble is determined.

cond-mat.mes-hall↗

arXiv2021

Aspects of topological superconductivity in 2D systems: noncollinear magnetism, skyrmions, and higher-order topology

The review is aimed at highlighting the aspects of topological superconductivity in the absence of spin-orbit interaction in two-dimensional systems with long-range non-collinear spin ordering or magnetic skyrmions. Another purpose is to give a brief introduction to the new concept of topological superconductivity, i.e. higher-order topology in two-dimensional systems including spin-orbit coupled structures. The formation of Majorana modes due to magnetic textures is discussed. The role of effective triplet pairings and odd fermion parity of the ground state wave function in different systems is emphasized. We describe the peculiarities of the magnetic skyrmions, leading to the formation of the Majorana modes and defects on which the modes are localized. The problem of braiding in the two-dimensional systems, especially in higher-order topological superconductors, is considered.

cond-mat.supr-con↗