Abstract
Abstract
The synergy between non-Hermitian concepts and topological ideas have led to very fruitful activity in the recent years. Their interplay has resulted in a wide variety of new non-Hermitian topological phenomena being discovered. In this review, we present the key principles underpinning the topological features of non-Hermitian phases. Using paradigmatic models—Hatano–Nelson, non-Hermitian Su–Schrieffer–Heeger and non-Hermitian Chern insulator—we illustrate the central features of non-Hermitian topological systems, including exceptional points, complex energy gaps and non-Hermitian symmetry classification. We discuss the non-Hermitian skin effect and the notion of the generalized Brillouin zone, which allows restoring the bulk-boundary correspondence. Using concrete examples, we examine the role of disorder, describe the Floquet engineering, present the linear response framework, and analyze the Hall transport properties of non-Hermitian topological systems. We also survey the rapidly growing experimental advances in this field. Finally, we end by highlighting possible directions which, in our view, may be promising for explorations in the near future.
Funder
Science and Engineering Research Board
Subject
Condensed Matter Physics,General Materials Science
Reference375 articles.
1. Note that the definition for the adjoint of an operator O, denoted O∗ is, for a given notion of an inner product and vectors v,w,(Ov,w)=(v,O∗w) , which can be written as O∗=G−1O†G , where G denotes the Gram matrix of the corresponding inner product. An operator is said to be self-adjoint if O∗=O . In Hermitian quantum mechanics, G = 1, the identity matrix, and hence the notion of an operator being self-adjoint is equivalent to O=O† . In non-Hermitian quantum mechanics, G could be chosen differently, and the notion of self-adjointness changes [375]
2. Real Spectra in Non-Hermitian Hamiltonians HavingPTSymmetry
3. Making sense of non-Hermitian Hamiltonians
Cited by
30 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献