Predicting topological materials: symmetry-based indicator theories and beyond

TL;DR

This paper develops an algorithm within symmetry-based indicator theories to diagnose topological band crossings in systems where traditional methods fail, extending the analysis to spinful systems with time-reversal symmetry.

Contribution

It introduces a simplified reinterpretation of the algorithm for diagnosing topological degeneracies beyond compatibility condition constraints, applicable to both spinless and spinful systems.

Findings

The algorithm successfully diagnoses topological band crossings in complex systems.

Application to material examples demonstrates the method's effectiveness.

Discussion of limitations guides future research in topological material diagnosis.

Abstract

Though symmetry-based indicators formulae are powerful in diagnosing topological states with a gapped band structure at/between any high-symmetry points, it fails in diagnosing topological degeneracies when the compatibility condition is violated. In such cases, we can only obtain information of whether there is a band degeneracy at some high-symmetry points or along some high-symmetry lines by the compatibility condition. Under the framework of symmetry-based indicator theories, we proposed an algorithm to diagnose the topological band crossings in the compatibility condition-violating systems to obtain the whole topological information, by using the symmetry-based indicator formulae of their subgroups. In this paper, we reinterpret the algorithm in a simpler way with two material examples preserving different topological states in spinless systems with time-reversal symmetry, discuss the limitation of the symmetry-based indicator theories, and make further discussions on the algorithm applying in spinful systems with time-reversal symmetry.