Momentum-space spin texture in a topological superconductor

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 S(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 S(k)/|S(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.