Non-Hermitian impurity problem

TL;DR

This paper explores the effects of a single complex impurity in non-Hermitian lattices across multiple dimensions, revealing novel localization phenomena and exotic eigenstates relevant to experimental photonic systems.

Contribution

It introduces the first comprehensive study of a non-Hermitian impurity problem in various dimensions, uncovering counterintuitive localization behaviors and exotic localized states.

Findings

Localization vanishes and re-emerges with impurity strength

Discovery of scale-free localized states and exceptional points

Identification of cross-shaped localized eigenstates

Abstract

The problem of a single Hermitian impurity has long served as a cornerstone in condensed matter physics, offering fundamental insights into the mechanisms of Anderson localization. Yet, despite the increased interest in the spectral and localization properties of non-Hermitian lattices with defects, the non-Hermitian extension of the single impurity problem remains largely unexplored. In this work, we investigate the role of a single complex impurity in one-, two-, and three-dimensional infinite tight-binding lattices. Our study reveals a series of counterintuitive phenomena, including regions where localization vanishes and re-emerges as the impurity strength varies. Next, we study the corresponding finite-sized lattices, which are highly relevant to experimental realizations in readily accessible photonic platforms, revealing a variety of exotic features, such as scale-free localized states, exceptional points, and peculiar cross-shaped localized eigenstates, whose profiles deviate from the conventional exponential localization. This work paves the way for future studies on transport phenomena in non-Hermitian disordered lattices.