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.
@article{arxiv.2504.18926,
title = {Critical Non-Hermitian Edge Modes},
author = {Kunling Zhou and Zihe Yang and Bowen Zeng and Yong Hu},
journal= {arXiv preprint arXiv:2504.18926},
year = {2025}
}