Non-Hermitian topological phases: principles and prospects

Author:

Banerjee Ayan,Sarkar Ronika,Dey Soumi,Narayan AwadheshORCID

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

Publisher

IOP Publishing

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

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