Impurity induced scale-free localization

TL;DR

This paper presents a comprehensive framework for understanding impurity effects in non-Hermitian, non-reciprocal lattices, revealing complex localization phenomena including scale-free accumulation and their experimental detection.

Contribution

It introduces a full theoretical framework for impurity physics in non-Hermitian non-reciprocal systems, highlighting novel localization behaviors and proposing experimental setups.

Findings

Localization behaviors vary with impurity strength, including skin effect and scale-free states.

Coexistence of skin effect and scale-free localization observed.

Spectral properties are highly sensitive to impurity strength.

Abstract

This work develops a full framework for non-Hermitian impurity physics in a non-reciprocal lattice, with PBCs, OBCs and even their interpolations being special cases across a whole range of boundary impurity strengths. As the impurity strength is tuned, the localization of steady states can assume very rich behavior, including the expected non-Hermitian skin effect, Bloch-like states albeit broken translational invariance, and surprisingly, scale-free accumulation along or even against the direction of non-reciprocity. We further uncover the possibility of the co-existence of non-Hermitian skin effect and scale-free localization, where qualitative aspects of the system's spectrum can be extremely sensitive to impurity strength. We have also proposed specific circuit setups for experimental detection of the scale-free accumulation, with simulation results confirming our main findings.