Abstract
Spectra of bulk or edges in topological insulators are often made complex by non-Hermiticity. Here, we show that symmetry protection enables entirely real spectra for both bulk and edges even in non-Hermitian topological insulators. In particular, we demonstrate entirely real spectra without non-Hermitian skin effects due to a combination of pseudo-Hermiticity and Kramers degeneracy. This protection relies on nonspatial fundamental symmetry and has stability against disorder. As an illustrative example, we investigate a non-Hermitian extension of the Bernevig-Hughes-Zhang model. The helical edge states exhibit oscillatory dynamics due to their nonorthogonality as a unique non-Hermitian feature.
Highlights
Physics of non-Hermitian systems has generated considerable recent research interest [1,2]
Despite the significance of the reality of spectra, Ref. [32], which is one of the earliest works on non-Hermitian topological systems [30,31,32], showed that entirely real spectra of both bulk and edges are impossible in a large class of non-Hermitian topological insulators with parity-time symmetry
On the other hand, when we introduce asymmetric hopping to the Su-Schrieffer-Heeger model [84] without breaking sublattice symmetry, the entirely real spectrum for both bulk and edges can be realized under the open boundary conditions [35,44,46]; it relies on the non-Hermitian skin effect and the spectrum becomes complex under the periodic boundary conditions
Summary
Physics of non-Hermitian systems has generated considerable recent research interest [1,2]. [32], which is one of the earliest works on non-Hermitian topological systems [30,31,32], showed that entirely real spectra of both bulk and edges are impossible in a large class of non-Hermitian topological insulators with parity-time symmetry. We show that symmetry protection enables the entirely real spectra for both bulk and edges even in non-Hermitian topological insulators. This protection is due to nonspatial symmetry and stable against disorder. In the Appendix, we investigate another non-Hermitian extension of the BHZ model that is protected by time-reversal symmetry and possesses the complex edge spectrum
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