Implementing Non-Abelian Hatano-Nelson Model in Electric Circuits

Non-Hermitian systems generally host complex spectra that bring unique spectral topologies, leading to spectral braiding and the 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 Letter enriches the experimental non-Hermitian physics and provides an approach to designing multifunctional non-Hermitian devices.