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.

中文翻译：

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非厄米拓扑现象：回顾


在过去的几十年里，人们对拓扑材料的兴趣激增，凝聚态物理中引入了许多数学概念。其中，体边界对应是拓扑物理的中心课题，激发了研究人员对边界物理的关注。最近，拓扑相的概念已扩展到非厄米哈密顿量，其特征值可能很复杂。除了拓扑之外，非厄米性还会引起称为非厄米集肤效应的边界现象，这是光谱对边界条件的极端敏感性。在本文中，我们主要关注边界问题，回顾非厄米拓扑物理学的发展。除了非厄米性和拓扑边界现象之间的竞争之外，我们还讨论了非厄米性本身固有的拓扑性质。