A Z$_2$ index of Dirac operator with time reversal symmetry

TL;DR

This paper introduces a Z$_2$ index for Dirac operators with time reversal symmetry, revealing a nontrivial topological invariant despite vanishing traditional indices, thus advancing understanding of topological phases.

Contribution

It defines a new Z$_2$ topological index for Dirac operators under time reversal symmetry, expanding the classification of topological phases.

Findings

Z$_2$ index is well-defined for Dirac operators with time reversal symmetry

The Z$_2$ index indicates nontrivial topological properties despite zero Chern number

A gauge field-dependent topological invariant is constructed

Abstract

With time reversal symmetry a Dirac operator has vanishing index and Chern number. We show that we can nevertheless define a nontrivial Z$_2$ index as well as a corresponding topological invariant given by gauge field, which implies that such a Dirac operator is topologically nontrivial.