Tailoring Bound State Geometry in High-Dimensional Non-Hermitian Systems

TL;DR

This paper demonstrates that in high-dimensional non-Hermitian systems, geometry-dependent skin effects enable impurity bound states to form even with minimal impurity potential, revealing a geometry transition of bound states.

Contribution

It uncovers how geometry-dependent skin effects in high-dimensional non-Hermitian systems facilitate bound state formation and induce a transition in bound state geometry.

Findings

Impurity bound states can form with infinitesimal potential due to skin effects.

Bound states exhibit shape transitions from concave to convex geometries.

Non-Hermiticity disrupts isotropy, leading to novel bound state geometries.

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.