Topological Superconductivity Induced by Magnetic Texture Crystals

Abstract

We present an in-depth classification of the topological phases and Majorana fermion (MF) excitations that arise from the bulk interplay between unconventional multiband spin-singlet superconductivity and various magnetic textures. We focus on magnetic texture crystals with a periodicallyrepeating primitive cell of the helix, whirl, and skyrmion types. Our analysis is relevant for a wide range of layered materials and hybrid devices, and accounts for both strong and weak, as well as crystalline topological phases. We identify a multitude of accessible topological phases which harbor flat, uni-or bi-directional, (quasi-)helical, or chiral MF edge modes. This rich variety of MFs originates from the interplay between topological phases with gapped and nodal bulk energy spectra, with the resulting types of spectra and MFs controlled by the size of the pairing and magnetic gaps.

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

“…For a more complex case (5) the magnetic BZ must be considered. The topological classification taking into account magnetic groups was made in [90].…”

“…It is supposed that the same electrons can be responsible for the coexistence state in this case. The chiral symmetry of superconductivity is supported by the symmetry of the triangular lattice [94]; -iron-based superconductors with the coexistence of the multi-band spin-singlet superconductivity and different magnetic textures (such as helix, spin whirl, skyrmion in an external magnetic field) [90]. In Ref.…”

“…This invariant can be calculated through the particle-hole invariant momenta (PHIMs) which are k = − k + G (G is a reciprocal lattice vector) for the transformed Hamiltonian. The details of this approach for topological superconductors with magnetic textures are presented in [90]. Nevertheless, for the 2D lattice, this topological invariant is calculated only for the fixed quasi-momentum k 2 in the second direction of the reciprocal space.…”

“…It is known that the effective time-reversal symmetry can be present in the exact 1D theoretical models similar to (11) even in the presence of the magnetic field (see for example [83,90,99,127,131,132]). Such an additional symmetry leads to the BDI class topological symmetry instead of the D class.…”