Unified understanding of symmetry indicators for all internal symmetry classes

TL;DR

This paper provides a comprehensive framework for understanding symmetry indicators across all 10 Altland-Zirnbauer classes and 230 space groups, facilitating the identification of topological phases in electronic materials.

Contribution

It extends previous symmetry indicator studies to all symmetry classes and space groups, offering general principles for topological material discovery.

Findings

Derived general statements for symmetry indicators across all classes and groups

Facilitated identification of topological superconductors and semimetals

Enhanced tools for band topology analysis without Wilson loop calculations

Abstract

The interplay between symmetry and topology in electronic band structures has been one of the central subjects in condensed-matter physics. Recently, it has been getting clear that a wide variety of useful information about the band topology can be extracted by focusing the symmetry representations of valence bands without computing Wilson loops. In this work, we extend the previous studies on this subject to all 10 Altland-Zirnbauer symmetry classes in each of 230 space groups. We derive various general statements that should be useful in the search for topological superconductors and topological semimetals.