Observation of non-Abelian Anderson localization and transition in topolectrical circuits
Haiteng Wang, Weixuan Zhang, Houjun Sun, Xiangdong Zhang
Abstract
Anderson localization, which originates from the wave interference between multiple-scattering paths, has been widely explored in quantum and classical systems with disordered Abelian gauge potentials. Recently, the interplay between disorder and non-Abelian gauge fields has been theoretically investigated, revealing non-Abelian Anderson localization and transition without Abelian analogy. Due to the limitation on engineering non-Abelian gauge potentials with disorder, the experimental observation of non-Abelian Anderson phenomena is still lacking. Here, we report on the experimental realization of non-Abelian Anderson localization and transition based on engineered topolectrical circuits, which are directly mapped to the quasiperiodic Aubry-Andr\'e Harper model with non-Abelian gauge fields. Disorder can be suitably introduced into the effective non-Abelian coupling matrices by randomly setting the values of coupling and grounding circuit elements. In this case, different types of non-Abelian Anderson phases, including the delocalization phase, coexisting states with localized and delocalized spatial profiles, and the localization phase, can be clearly observed by measuring the site-resolved impedance spectra and voltage dynamics. Our proposal provides a flexible platform to investigate Anderson localization and transition driven by non-Abelian gauge potentials with disorder and could have potential applications in the electronic signal control.