Controlled probing of localization effects in the non-Hermitian Aubry-Andr\'e model via topolectrical circuits

Abstract

Anderson localization and the non-Hermitian skin effect are two distinct confinement phenomena of the eigenfunctions that are driven, respectively, by disorder and nonreciprocity. Understanding their interplay within a unified framework offers valuable insights into the localization properties of low-dimensional systems. To this end, we investigate a non-Hermitian version of the celebrated Aubry-Andr\'e model, which serves as an ideal platform due to its unique self-dual properties and ability to demonstrate a delocalization-localization transition in one dimension. Interestingly, in our setting, the competition between Anderson localization and the skin effect can be precisely controlled via the complex phase of the quasiperiodic disorder. Additionally, by analyzing the time evolution, we demonstrate that quantum jumps between the skin states and the Anderson-localized states occur in the theoretical model. Further, to gain support for our theoretical predictions in an experimental platform, we propose a topolectrical circuit featuring an interface that separates two distinct electrical circuit networks. The voltage profile of the circuit exhibits confinement at the interface, analogous to the skin effect, while the phenomenon of Anderson localization in the circuit can be perceived via a predicted localization behavior near the excitation node, rather than exhibiting sudden non-Hermitian jumps, as observed in the tight-binding framework. This interplay leads to a spatially tunable localization of the output voltage of the circuit. Our findings provide deeper insights into the controlled confinement of the eigenstates of the non-Hermitian Aubry-Andr\'e model by designing analogous features in topolectrical circuits, opening avenues in the fabrication of advanced electronic systems such as highly sensitive sensors and efficient devices for information transfer and communication.