Extension of symmetry-based indicators and its application*

The goal of the study of topological phases is to achieve the complete classification of phases for all spatial and internal symmetries. The topological periodic table, the classification table of topological insulators for each internal symmetry class, is a milestone in this line of research.
Recently, the method of “symmetry-based indicators (SI)” has been developed. It diagnoses the topology of band structures based on their symmetry representations. The prototypical example of SI is the Fu-Kane formula, which distinguishes topological insulators from normal insulators in terms of inversion parities.
So far, as an internal symmetry, only the time-reversal symmetry has been taken into account in the calculation of SI. In this talk, we discuss how to incorporate with the chiral symmetry and the particle-hole symmetry.

Ref: S. Ono and H. Watanabe, Phys. Rev. B 98, 115150 (2018)