General theory for geometry-dependent non-Hermitian bands

• URL: http://arxiv.org/abs/2506.22743v3
• Date: Thu, 06 Nov 2025 16:49:40 GMT
• Title: General theory for geometry-dependent non-Hermitian bands
• Authors: Chenyang Wang, Jinghui Pi, Qinxin Liu, Yaohua Li, Yong-Chun Liu,
• Abstract summary: In non-Hermitian lattices, the spectrum and eigenstates under open boundary conditions depend on the bulk geometry even in the thermodynamic limit.<n>We establish a higher-dimensional non-Bloch band theory based on the concept of "strip generalized Brillouin zones"<n>For the first time, we derive a general criterion for the geometry dependence of non-Hermitian bands.
• Score: 4.330177255999498
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In two- and higher-dimensional non-Hermitian lattices, systems can exhibit geometry-dependent bands, where the spectrum and eigenstates under open boundary conditions depend on the bulk geometry even in the thermodynamic limit. Although geometry-dependent bands are widely observed, the underlying mechanism for this phenomenon remains unclear. In this work, we address this problem by establishing a higher-dimensional non-Bloch band theory based on the concept of "strip generalized Brillouin zones" (SGBZs), which describe the asymptotic behavior of non-Hermitian bands when a lattice is extended sequentially along its linearly independent axes. Within this framework, we demonstrate that geometry-dependent bands arise from the incompatibility of SGBZs and, for the first time, derive a general criterion for the geometry dependence of non-Hermitian bands: non-zero area of the complex energy spectrum or the imaginary momentum spectrum. Our work opens an avenue for future studies on the interplay between geometric effects and non-Hermitian physics, such as non-Hermitian band topology.

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