Hermitian chiral boundary states in non-Hermitian topological insulators

Eigenenergies of a non-Hermitian system without parity-time symmetry are complex in general. Here, we show that the chiral boundary states of higher-dimensional non-Hermitian topological insulators without parity time symmetry can be Hermitian with real eigenenergies under certain conditions. Our approach allows one to construct Hermitian chiral edge and hinge states from non-Hermitian two-dimensional Chern insulators and three-dimensional second-order topological insulators, respectively. Such Hermitian chiral boundary channels have perfect transmission coefficients (quantized values) and are robust against disorders. Furthermore, a non-Hermitian topological insulator can undergo the topological Anderson insulator transition from a topologically trivial non-Hermitian metal or insulator to a topological Anderson insulator with quantized transmission coefficients at finite disorders.

Automated summary

In this study, we have discovered that under certain conditions, the chiral boundary states of higher-dimensional non-Hermitian topological insulators can be Hermitian with real eigenenergies. By constructing Hermitian chiral edge and hinge states, these boundary channels exhibit perfect transmission coefficients and are robust against disorders. Furthermore, non-Hermitian topological insulators can undergo a unique topological Anderson insulator transition.