Non-Hermitian topology and exceptional-point geometries

Kun Ding*, Chen Fang*, Guancong Ma*

*Corresponding author for this work

Research output: Contribution to journalReview articlepeer-review

80 Citations (Scopus)


Non-Hermitian theory is a theoretical framework used to describe open systems. It offers a powerful tool in the characterization of both the intrinsic degrees of freedom 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 Review, we provide an overview of non-Hermitian topology by establishing its relationship with the behaviours of complex eigenvalues and biorthogonal eigenvectors. Special attention is given to exceptional points — branch-point singularities on the complex eigenvalue manifolds that exhibit nontrivial topological properties. We also discuss recent developments in non-Hermitian band topology, such as the non-Hermitian skin effect and non-Hermitian topological classifications.

Original languageEnglish
Pages (from-to)745-760
Number of pages16
JournalNature Reviews Physics
Issue number12
Publication statusPublished - Dec 2022

Scopus Subject Areas

  • Physics and Astronomy(all)


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