Symmetry and topology of two-dimensional noncentrosymmetric superconductors

TL;DR

This paper investigates the gap symmetry and topological properties of two-dimensional noncentrosymmetric superconductors, emphasizing the role of spin-orbit coupling and developing a topological classification framework.

Contribution

It introduces a topological classification of superconducting states in noncentrosymmetric materials using Maurer-Cartan invariants and Bogoliubov Wilson loops.

Findings

Classification of superconducting states based on topological invariants

Calculation of fermionic boundary mode spectra

Insights into the role of spin-orbit coupling in noncentrosymmetric superconductors

Abstract

We present a detailed study of the gap symmetry and the quasiparticle wave function topology in two-dimensional superconductors without inversion center. The strong spin-orbit coupling of electrons with the crystal lattice makes it necessary to describe superconductivity in terms of one or more nondegenerate bands characterized by helicity. We develop a topological classification of the superconducting states using the integer-valued Maurer-Cartan invariants and the Bogoliubov Wilson loops, and also calculate the spectrum of fermionic boundary modes.