Implementing non-Abelian Hatano-Nelson model in electric circuits

TL;DR

This paper introduces a non-Abelian Hatano-Nelson model implemented in electric circuits, revealing complex spectral braiding and bipolar skin effects, thus expanding experimental non-Hermitian physics and device design.

Contribution

It presents the first experimental realization of a non-Abelian gauge field in a non-Hermitian system using electric circuits, demonstrating novel spectral phenomena.

Findings

Observation of Hopf-link-shaped complex energy braiding

Detection of bipolar skin effect in electric circuits

Implementation of non-Abelian gauge fields in non-Hermitian systems

Abstract

Non-Hermitian systems generally host complex spectra that bring unique spectral topologies, leading to the spectral braiding and non-Hermitian skin effect. The experimental exploration of non-Hermitian physics is mainly concentrated in artificial systems due to the flexibility in the introduction of the non-Hermiticity, but to date has focused only on the systems without gauge fields or with Abelian gauge fields. Here, we propose a non-Abelian Hatano-Nelson model with a nonreciprocal U(2) gauge field. The gauge field induces two non-Hermitian phenomena: the first is the Hopf-link-shaped complex energy braiding, and the second is the bipolar skin effect arising under the non-Abelian condition. The non-Abelian Hatano-Nelson model is implemented in electric circuits, and the Hopf-link-shaped admittance spectra and bipolar skin admittance modes are observed. Our work enriches the experimental non-Hermitian physics, and provides an approach to designing multifunctional non-Hermitian devices.