Observation of impurity-induced scale-free localization in a disordered non-Hermitian electrical circuit

Abstract

One of unique features of non-Hermitian systems is the extreme sensitive to their boundary conditions, e.g., the emergence of non-Hermitian skin effect (NHSE) under the open boundary conditions, where most of bulk states become localized at the boundaries. In the presence of impurities, the scale-free localization can appear, which is qualitatively distinct from the NHSE. Here, we experimentally design a disordered non-Hermitian electrical circuits in the presence of a single non-Hermitian impurity and the nonreciprocal hopping. We observe the anomalous scale-free accumulation of eigenstates, opposite to the bulk hopping direction. The experimental results open the door to further explore the anomalous skin effects in non-Hermitian electrical circuits.

Graphical abstract

Keywords

non-Hermitian / scale-free localization / electrical circuit / non-Hermitian skin effect

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Declarations

The authors declare that they have no competing interests and there are no conflicts.

Acknowledgements

T.L. acknowledges the support from the Fundamental Research Funds for the Central Universities (Grant No. 2023ZYGXZR020), the Introduced Innovative Team Project of Guangdong Pearl River Talents Program (Grant No. 2021ZT09Z109), and the Startup Grant of South China University of Technology (Grant No. 20210012). W.B.J was supported by the National Natural Science Foundation of China (NSFC) (Grant No. U21A2093).

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