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

TL;DR

This review explores topological superconductivity in 2D systems without spin-orbit coupling, focusing on magnetic textures like skyrmions and higher-order topology, highlighting Majorana modes and braiding prospects.

Contribution

It provides a comprehensive overview of topological superconductivity mechanisms involving magnetic textures and introduces higher-order topology in 2D systems.

Findings

Magnetic skyrmions can host Majorana modes.

Higher-order topology enables new Majorana defect states.

Magnetic textures influence effective triplet pairing.

Abstract

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.