Non-Hermitian topological phase transitions for quantum spin Hall insulators

TL;DR

This paper explores how non-Hermitian effects can induce topological phase transitions in quantum spin Hall insulators, introducing new invariants to characterize these phases and revealing exceptional edge phenomena.

Contribution

It introduces two biorthogonal topological invariants for non-Hermitian QSH phases and demonstrates phase transitions driven solely by non-Hermitian terms.

Findings

Non-Hermitian terms can induce trivial to QSH phase transitions.

Existence of exceptional edge arcs in non-Hermitian QSH phases.

Development of biorthogonal $ ext{Z}_2$ invariant and spin Chern number for characterization.

Abstract

The interplay between non-Hermiticity and topology opens an exciting avenue for engineering novel topological matter with unprecedented properties. While previous studies have mainly focused on one-dimensional systems or Chern insulators, here we investigate topological phase transitions to/from quantum spin Hall (QSH) insulators driven by non-Hermiticity. We show that a trivial to QSH insulator phase transition can be induced by solely varying non-Hermitian terms, and there exists exceptional edge arcs in QSH phases. We establish two topological invariants for characterizing the non-Hermitian phase transitions: i) with time-reversal symmetry, the biorthogonal $\mathbb{Z}_2$ invariant based on non-Hermitian Wilson loops, and ii) without time-reversal symmetry, a biorthogonal spin Chern number through biorthogonal decompositions of the Bloch bundle of the occupied bands. These topological invariants can be applied to a wide class of non-Hermitian topological phases beyond Chern classes, and provides a powerful tool for exploring novel non-Hermitian topological matter and their device applications.