Tailoring bound state geometry in high-dimensional non-hermitian systems
Ao Yang, Zixi Fang, Kai Zhang, Chen Fang
Abstract
It is generally believed that the non-Hermitian effect (NHSE), due to its non-reciprocal nature, creates barriers for the appearance of impurity bound states. In this paper, we find that in two and higher dimensions, the presence of geometry-dependent skin effect eliminates this barrier such that even an infinitesimal impurity potential can confine bound states in this type of non-Hermitian systems. By examining bound states around Bloch saddle points, we find that non-Hermiticity can disrupt the isotropy of bound states, resulting in concave dumbbell-shaped bound states. Our work reveals a geometry transition of bound state between concavity and convexity in high-dimensional non-Hermitian systems, offering theoretical insights for the experimental manipulation of bound states. In higher-dimensional systems, the non-Hermitian skin effect can manifest in highly geometry-dependent manners, depending on how non-Hermicity interplays with reciprocity. In this work, the authors provide a rigorous characterization of how impurity bound states are shaped by the non-Hermicity induced spatial inhomogeneity in a reciprocal system.