Fermi-surface diagnosis for topological superconductivity with $s$-wave-like pairing symmetries

TL;DR

This paper develops a Fermi-surface based method to diagnose topological superconductivity with s-wave-like pairing in various materials, facilitating the discovery of new topological superconductors.

Contribution

It derives comprehensive Fermi-surface formulas for diagnosing topological phases in all layer and space groups, applicable to both thin-film and bulk materials.

Findings

Complete diagnosis for 159 space groups

Partial diagnosis for 40 space groups

Applicable to both gapped and gapless phases

Abstract

Theoretical prediction of topological superconductivity is key to their discovery. Recently, it is proved that in 199 out of 230 space groups, topological superconductivity coexists with an $s$-wave-like pairing symmetry, raising the hope of finding more candidates for this exotic phase. However, a comprehensive and efficient method for diagnosing topological superconductivity in realistic materials remains elusive. Here, we derive Fermi-surface formulas for gapped and gapless topological phases of time-reversal symmetric superconductors with $s$-wave-like pairing symmetries in all layer and space groups, applicable to thin-film and bulk materials. Our diagnosis uses only the sign of the pairing and the Fermi velocity at several Fermi points, and yields complete (partial) diagnosis for gapped topological superconductivity in 159 (40) out of the 199 space groups. This provides a fundamental basis for the first-principles prediction of new topological superconductors.