Non-Hermitian topology and exceptional-point geometries
By Kun Ding, Chen Fang, Guancong Ma. Nature Reviews Physics, 2022
591 citations recorded by the source corpus.
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. Non-Hermitian theory consists of mathematical structures that are used to describe open systems, which can give rise to non-Hermitian topology not found in Hermitian systems. This Review provides an overview of non-Hermitian band topology and discusses recent developments, such as the non-Hermitian skin effect and non-Hermitian topological classifications. A non-Hermitian Hamiltonian that describes an open system generically has complex eigenvalues, which must be studied on the complex plane, which leads to the emergence of eigenvalue topology, or spectral topology. This additional ‘layer’ of topology is a unique feature for non-Hermitian systems. Spectral topology fundamentally affects the parallel-transport behaviours of eigenvectors of a non-Hermitian Hamiltonian. Exceptional points are branch singularities on non-Hermitian eigenvalue manifolds and exhibit exotic topological phenomena associated with the winding of eigenvalues and eigenvectors. The confluence of non-Hermiticity and band topology generates new phenomena such as the non-Hermitian skin effect, which is characterized by non-Bloch band theory and the re-establishment of bulk–boundary correspondence. It also ramifies the possible symmetry classes, thereby expanding the classifications of topological bands. A non-Hermitian Hamiltonian that describes an open system generically has complex eigenvalues, which must be studied on the complex plane, which leads to the emergence of eigenvalue topology, or spectral topology. This additional ‘layer’ of topology is a unique feature for non-Hermitian systems. Spectral topology fundamentally affects the parallel-transport behaviours of eigenvectors of a non-Hermitian Hamiltonian. Exceptional points are branch singularities on non-Hermitian eigenvalue manifolds and exhibit exotic topological phenomena associated with the winding of eigenvalues and eigenvectors. The confluence of non-Hermiticity and band topology generates new phenomena such as the non-Hermitian skin effect, which is characterized by non-Bloch band theory and the re-establishment of bulk–boundary correspondence. It also ramifies the possible symmetry classes, thereby expanding the classifications of topological bands.
Subfields: Atomic and Molecular Physics, and Optics, Organic Chemistry, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/1f91fa2a89208b977829639abbe48d7cf149b7a3
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Citations in the corpus
- Applications of bound states in the continuum in photonics (2023, background): “However, when this balance between gain and loss is broken, the Hamiltonian undergoes a real-to-complex spectral phase transition at the exceptional points 213–215 , at which both the eigenvalues and eigenvectors coalesce.”