An equivalent expression of Z2 Topological Invariant for band insulators using Non-Abelian Berry's connection

TL;DR

This paper presents a new gauge-invariant expression for the Z2 topological invariant in band insulators using non-Abelian Berry's connection, simplifying the identification of topological phases.

Contribution

It introduces an alternative formulation of the Z2 invariant that avoids gauge fixing issues and relates to Wannier function dynamics during time reversal pumping.

Findings

Provides a gauge-invariant expression for Z2 invariant

Links the invariant to Wannier center partner switching

Equivalent to Kane and Mele's Z2 invariant

Abstract

We introduce a new expression for the Z2 topological invariant of band insulators using non- Abelian Berry's connection. Our expression can identify the topological nature of a general band insulator without any of the gauge fixing problems that plague the concrete implementation of previous invariants. The new expression can be derived from the "partner switching" of the Wannier function center during time reversal pumping and is thus equivalent to the Z2 topological invariant proposed by Kane and Mele.