$\mathbb{Z}_2$-enriched symmetry indicators for topological superconductors in the 1651 magnetic space groups

TL;DR

This paper develops a comprehensive framework for diagnosing topological superconductors using $ ext{Z}_2$-enriched symmetry indicators across all magnetic space groups, enhancing detection capabilities and enabling analysis of real materials.

Contribution

It introduces the full computation of $ ext{Z}_2$-enriched symmetry indicators for superconductors in all symmetry settings, addressing a key challenge in topological superconductor diagnosis.

Findings

Increases diagnostic power in about 60% of symmetry settings.

Framework can be integrated with first-principles calculations.

Analyzes topological properties of CaPtAs and CaSb$_2$ superconductors.

Abstract

While the symmetry-based diagnosis of topological insulators and semimetals has enabled large-scale discovery of topological materials candidates, the extension of these approaches to the diagnosis of topological superconductors remains a major open question. One important new ingredient in the analysis of topological superconductivity is the presence of $\mathbb Z_2$-valued Pfaffian invariants associated with certain high-symmetry momenta. Such topological invariants lie beyond the conventional scope of symmetry representation theory for band structures, and as such they are nontrivial to incorporate into the systematic calculations of the symmetry indicators of band topology. Here, we overcome this challenge and report the full computation of the $\mathbb Z_2$-enriched symmetry indicators for superconductors in all symmetry settings. Our results indicate that incorporating the $\mathbb Z_2$ band labels enhance the diagnostic power of the scheme in roughly $60\%$ of the symmetry settings. Our framework can also be readily integrated with first-principles calculations to elucidate on the possible properties of unconventional superconductivity in a given compound. As a demonstration, we analyze explicitly the interplay between pairing symmetry and topological superconductivity in the recently discovered superconductors CaPtAs and CaSb$_2$.