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Annual Review of Condensed Matter Physics

Volume 14, 2023

Non-Hermitian Topological Phenomena: A Review

Abstract

The past decades have witnessed an explosion of interest in topological materials, and a lot of mathematical concepts have been introduced in condensed matter physics. Among them, the bulk-boundary correspondence is the central topic in topological physics, which has inspired researchers to focus on boundary physics. Recently, the concepts of topological phases have been extended to non-Hermitian Hamiltonians, whose eigenvalues can be complex. Besides the topology, non-Hermiticity can also cause a boundary phenomenon called the non-Hermitian skin effect, which is an extreme sensitivity of the spectrum to the boundary condition. In this article, we review developments in non-Hermitian topological physics by focusing mainly on the boundary problem. As well as the competition between non-Hermitian and topological boundary phenomena, we discuss the topological nature inherent in non-Hermiticity itself.

Keyword(s): bulk-boundary correspondence, Non-Hermitian physics, spectral theory, topological phase
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2023-03-10
2024-05-13
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Non-Hermitian Topological Phenomena: A Review
Annual Review of Condensed Matter Physics 14, 83 (2023); https://doi.org/10.1146/annurev-conmatphys-040521-033133
/content/journals/10.1146/annurev-conmatphys-040521-033133
/content/journals/10.1146/annurev-conmatphys-040521-033133
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