A scenario of non-Hermitian bulk–boundary correspondence proposed for one-dimensional topological insulators is adapted to a non-Hermitian Chern insulator to examine its applicability to two-dimensional systems. This scenario employs bulk geometry under a modified periodic boundary condition and boundary geometry under an open boundary condition. The bulk geometry is used to define a topological number, whereas the boundary geometry is used to observe the presence or absence of a topological boundary state. It is demonstrated that the bulk–boundary correspondence holds in a two-dimensional Chern insulator with gain/loss-type non-Hermiticity; a nontrivial Chern number calculated in the bulk geometry is in one-to-one correspondence with the presence of a topological boundary state in the boundary geometry. This approach enables us to determine a phase diagram in the boundary geometry.

中文翻译：

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非埃尔米特式陈氏绝缘子的体-边界对应

为一维拓扑绝缘子提出的非赫米特体-边界对应方案适用于非赫米特尔·陈恩绝缘子，以检验其在二维系统中的适用性。此方案在修改的周期性边界条件下采用块几何，在开放边界条件下采用边界几何。体几何用于定义拓扑数，而边界几何用于观察拓扑边界状态的存在或不存在。证明了体-边界对应关系在具有增益/损耗型非赫米特性的二维Chern绝缘子中成立。在体几何中计算的非平凡切恩数与边界几何中存在拓扑边界状态一一对应。