Bulk-boundary correspondence is the cornerstone of topological physics. In some non-Hermitian topological system this fundamental relation is broken in the sense that the topological number calculated for the Bloch energy band under the periodic boundary condition fails to reproduce the boundary properties under the open boundary. To restore the bulk-boundary correspondence in such non-Hermitian systems a framework beyond the Bloch band theory is needed. We develop a non-Hermitian Bloch band theory based on a modified periodic boundary condition that allows a proper description of the bulk of a non-Hermitian topological insulator in a manner consistent with its boundary properties. Taking a non-Hermitian version of the Su-Schrieffer-Heeger model as an example, we demonstrate our scenario, in which the concept of bulk-boundary correspondence is naturally generalized to non-Hermitian topological systems.

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非厄米体-边界对应的广义布洛赫带理论

体边界对应是拓扑物理的基石。在一些非厄米拓扑系统中，这种基本关系在周期性边界条件下为布洛赫能带计算的拓扑数无法再现开放边界下的边界特性的意义上被打破。为了恢复这种非厄米系统中的体边界对应，需要一个超越布洛赫带理论的框架。我们基于修改的周期性边界条件开发了非厄米布洛赫带理论，该理论允许以与其边界特性一致的方式正确描述非厄米拓扑绝缘体的体积。以 Su-Schrieffer-Heeger 模型的非 Hermitian 版本为例，我们演示我们的场景，