Momentum-Space Spin Texture in a Topological Superconductor

TL;DR

This paper investigates how the spin texture in momentum space signals the transition to a topological superconductor, characterized by a change in skyrmion number, influenced by spin-orbit coupling and Zeeman energy.

Contribution

It introduces a method to identify topological superconductivity through momentum-space spin textures and analyzes the role of singular points in this topological transition.

Findings

Skyrmion counting number switches from 0 to 1/2 at the transition

Spin texture change signals topological phase transition

Finite temperature effects on spin-map complexity analyzed

Abstract

A conventional superconductor with spin-orbit coupling turns into a topological superconductor beyond a critical strength of the Zeeman energy. The spin-expectation values $\mathbf{S}(\mathbf{k})$ in momentum space trace this transition via a characteristic change in the topological character of the spin texture within the Brillouin zone. At the transition the skyrmion counting number switches from 0 to 1/2 identifying the topological superconductor via its meron-like spin texture. The change in the skyrmion counting number is crucially controlled by singular points of the map $\mathbf{S}(\mathbf{k})/|\mathbf{S}(\mathbf{k})|$ from the Brillouin zone, i.e. a torus, to the unit sphere. The complexity of this spin-map is discussed at zero temperature as well as for the extension to finite temperatures.