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arXiv · 2204.11601

Non-Hermitian Topology and Exceptional-Point Geometries

Kun Ding·Chen Fang·Guancong Ma
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Abstract

Non-Hermitian theory is a theoretical framework that excels at describing open systems. It offers a powerful tool in the characterization of both the intrinsic degrees of freedom (DOFs) of a system and the interactions with the external environment. The non-Hermitian framework consists of mathematical structures that are fundamentally different from those of Hermitian theories. These structures not only underpin novel approaches for precisely tailoring non-Hermitian systems for applications but also give rise to topologies not found in Hermitian systems. In this paper, we comprehensively review non-Hermitian topology by establishing its relationship with the behaviors of complex eigenvalues and biorthogonal eigenvectors. Special attentions are given to exceptional points - branch-point singularities on the complex eigenvalue manifolds that exhibit non-trivial topological properties. We also discuss recent developments in non-Hermitian band topology, such as the non-Hermitian skin effect and non-Hermitian topological classifications

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Kun Ding, Chen Fang, Guancong Ma. 2022-04-19. Non-Hermitian Topology and Exceptional-Point Geometries. https://doi.org/10.1038/s42254-022-00516-5

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