Non-Hermitian band topology with generalized inversion symmetry

Abstract

Non-Hermitian skin effects and exceptional points are topological phenomena characterized by integer winding numbers. In this study, we give methods to theoretically detect skin effects and exceptional points by generalizing inversion symmetry. The generalization of inversion symmetry is unique to non-Hermitian systems. We show that parities of the winding numbers can be determined from energy eigenvalues on the inversion-invariant momenta when generalized inversion symmetry is present. The simple expressions for the winding numbers allow us to easily analyze skin effects and exceptional points in non-Hermitian bands. We also demonstrate the methods for (second-order) skin effects and exceptional points by using lattice models.

12 pages, 7 figures

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• Magnetic Flux Response of Non-Hermitian Topological Phases
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• Topological Invariant for Multi-Band Non-hermitian Systems with Chiral Symmetry
• Exceptional second-order topological insulators
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• Optical non-Hermitian skin effect in two-dimensional uniform media
• Phase Diagram of a Non-Hermitian Chern Insulator: Destabilization of Chiral Edge States and Bulk-Boundary Correspondence
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• Self-healing of non-Hermitian topological skin modes