A diagnosis scheme for topological degeneracies at high-symmetry momenta

TL;DR

This paper introduces a recursive protocol using subgroup indicators to diagnose topological degeneracies at high-symmetry points, extending existing methods to analyze band degeneracies in phonon spectra.

Contribution

The authors develop a new recursive diagnostic scheme that overcomes limitations of existing symmetry-based indicators for topological band degeneracies.

Findings

Predicted iso-energy Weyl points in In2Te phonon bands

Identified a node-line cage in ZrSiO phonon spectra

Demonstrated the method's effectiveness on real materials

Abstract

Theories of symmetry-based indicators and topological quantum chemistry, while powerful in diagnosing gapped topological materials, cannot be directly applied to diagnosing band degeneracies at high-symmetry momenta due to the violation of the compatibility conditions. Here we design a recursive protocol that utilizes indicators of maximal subgroups to infer the topological nature of band degeneracies at high-symmetry lines. For demonstration, the method is used to predict the existence of iso-energy Weyl points and a node-line cage, respectively, in the phonon bands of In2Te and ZrSiO.