The simulation of non-Hermitian disordered system in linear circuits

TL;DR

This paper reports the experimental observation of the non-Hermitian skin effect in a linear circuit system, demonstrating how voltage responses reveal eigenstate localization and the transition from skin effect to Anderson localization with increasing disorder.

Contribution

It introduces a novel linear circuit implementation to simulate non-Hermitian phenomena without using logic components, and explores the interplay between skin effect and localization.

Findings

Voltage response indicates non-Hermitian skin effect

Transition from skin effect to Anderson localization with disorder

Eigenstates localized at edges or affected by voltage input

Abstract

Non-Hermitian skin effect (NHSE) is a novel phenomenon appearing in non-Hermitian systems. Here, we report the experimental observation of NHSE. Different from the previous non-reciprocal circuit implementation scheme using logic components, we construct our one-dimensional (1D) circuits using linear components only. Besides, we achieve the non-reciprocity by proportionally varying the parameter value of the components. By measuring the voltage response of each site, the information of eigenstates can be mapped out. The results show that the voltage response is always larger on one end of the circuit no matter on which end voltage driving is applied, indicating clearly the presence of the NHSE. Furthermore, we also simulate the interplay of NHSE and Anderson localization (AL) when additional disorder is introduced. Upon increasing the disorder strength, we observe the transformation from the skin effect phase to the localized phase. In the regime of skin effect phase, the eigenstates are all localized at one edge while eigenstates are affected by the voltage supply input in localized phase. Our findings unveil a possible new route for simulation of topological phenomena in non-Hermitian systems.