Non-Hermitian topological phase transitions for quantum spin Hall insulators

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.

10 pages, 9 figures

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Cited by in corpus (8)

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• Comparative study of Hermitian and non-Hermitian topological dielectric photonic crystals
• Wannier-type photonic higher-order topological corner states induced solely by gain and loss
• Gain/loss effects on spin-orbit coupled ultracold atoms in two-dimensional optical lattices
• Non-Hermitian Haldane-Hubbard model: Effective description of one- and two-body dissipation
• Competing topological phases in a non-Hermitian time-reversal symmetry-broken Bernevig-Hughes-Zhang model
• Berry curvature inside parity-time-symmetry protected exceptional surface
• Band topology of pseudo-Hermitian phases through tensor Berry connections and quantum metric