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arXiv · 2504.18926

Critical Non-Hermitian Edge Modes

Kunling Zhou·Zihe Yang·Bowen Zeng·Yong Hu
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Abstract

We unveil a unique critical phenomenon of topological edge modes in non-Hermitian systems, dubbed the critical non-Hermitian edge modes (CNHEM). Specifically, in the thermodynamic limit, the eigenvectors of edge modes jump discontinuously under infinitesimal on-site staggered perturbations. The CNHEM arises from the competition between the introduced on-site staggered potentials and size-dependent non-reciprocal coupling between edge modes, and are closely connected to the exceptional point (EP). As the system size increases, the coupling between edge modes decreases while the non-reciprocity is enhanced, causing the eigenvectors to gradually collapse toward the EP. However, when the on-site potentials dominate, this weakened coupling assists the eigenvectors to stay away from the EP. Such a critical phenomenon is absent in Hermitian systems, where the coupling between edge modes is reciprocal.

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Kunling Zhou, Zihe Yang, Bowen Zeng, Yong Hu. 2025-04-26. Critical Non-Hermitian Edge Modes. https://arxiv.org/abs/2504.18926

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