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 noncollinear 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.

Automated summary

This review focuses on the topological superconductivity in two-dimensional systems without spin-orbit interaction, emphasizing on long-range noncollinear spin ordering or magnetic skyrmions. It also introduces the concept of higher-order topology, including the role of effective triplet pairings and odd fermion parity in ground state wave functions in different systems. Discussing the formation of Majorana modes due to magnetic textures and the peculiarities of magnetic skyrmions in relation to Majorana modes and defects. The problem of braiding in higher-order topological superconductors is also considered.