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arXiv · 2601.01524

Non-Hermitian second-order topological insulator with point gap

Xue-Min Yang·Hao Lin·Jian Li·Jia-Ji Zhu·Jun-Li Zhu·Hong Wu
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Abstract

The zero-mode corner states in the gap of two-dimensional non-Hermitian Su-Schrieffer-Heeger model are robust to infinitesimal perturbations that preserve chiral symmetry. However, we demonstrate that this general belief is no longer valid in large-sized systems. To reveal the higher-order topology of non-Hermitian systems, we establish a correspondence between the stable zero-mode singular states and the topologically protected corner states of energy spectrum in the thermodynamic limit. Within this framework, the number of zero-mode singular values is directly linked to the number of mid-gap corner states. The winding numbers in real space can be defined to count the number of stable zero-mode singular states. Our results formulate a bulk-boundary correspondence for both static and Floquet non-Hermitian systems, where topology arises intrinsically from the non-Hermiticity, even without symmetries.

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Xue-Min Yang, Hao Lin, Jian Li, Jia-Ji Zhu, Jun-Li Zhu, Hong Wu. 2026-01-04. Non-Hermitian second-order topological insulator with point gap. https://doi.org/10.1103/qy19-f9wm

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