Abstract

The bulk-boundary correspondence (BBC), i.e. the direct relation between bulk topological invariants defined for infinite periodic systems and the occurrence of protected zero-energy surface states in finite samples, is a ubiquitous and widely observed phenomenon in topological matter. In non-Hermitian generalizations of topological systems, however, this fundamental correspondence has recently been found to be qualitatively altered, largely owing to the sensitivity of non-Hermitian eigenspectra to changing the boundary conditions. In this work, we report on two contributions towards comprehensively explaining this remarkable behavior unique to non-Hermitian systems with theory. First, we analytically solve paradigmatic non-Hermitian topological models for their zero-energy modes in the presence of generalized boundary conditions interpolating between open and periodic boundary conditions, thus explicitly following the breakdown of the conventional BBC. Second, addressing the aforementioned spectral fragility of non-Hermitian matrices, we investigate as to what extent the modified non-Hermitian BBC represents a robust and generically observable phenomenon.

Graphical abstract

中文翻译：

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非Hermitian系统中的体边界对应：广义边界条件的稳定性分析

摘要

体边界对应（BBC），即为无限周期系统定义的体拓扑不变量与有限样本中受保护的零能表面状态的发生之间的直接关系，是拓扑问题中普遍存在的现象。但是，在拓扑结构的非Hermitian概括中，最近发现这种基本对应关系发生了质的变化，这主要是由于非Hermitian特征谱对边界条件的更改敏感。在这项工作中，我们报告了两个方面的贡献，它们可以用理论全面地解释非厄米特系统所特有的非凡行为。第一，我们在存在开放边界和周期性边界条件之间插值的通用边界条件的情况下，通过解析方法求解非零范式拓扑结构的零能量模式，从而明确地遵循了常规BBC的细分方法。其次，针对上述非赫米特矩阵的频谱易碎性，我们研究了在多大程度上修改后的非赫米特BBC代表了一种健壮且普遍可观察的现象。

图形概要