Wavefunction topology of two-dimensional time-reversal symmetric superconductors

TL;DR

This paper explores the wavefunction topology of 2D time-reversal symmetric superconductors, analyzing how order parameter signs and spin-orbit interactions influence their topological classification.

Contribution

It provides a detailed analysis of the topological properties of various 2D superconducting states and clarifies the $Z_2$ classification in these systems.

Findings

Relative sign of order parameters affects topology

Explicit connection between wavefunction sign and $Z_2$ classification

Topological distinctions in systems with spin-orbit interaction

Abstract

We discuss the topology of the wavefunctions of two-dimensional time-reversal symmetric superconductors. We consider (a) the planar state, (b) a system with broken up-down reflection symmetry, and (c) a system with general spin-orbit interaction. We show explicitly how the relative sign of the order parameter on the two Fermi surfaces affects this topology, and clarify the meaning of the $Z_2$ classification for these topological states.