Scale-tailored localization and its observation in non-Hermitian electrical circuits

Cui-Xian Guo, Luhong Su, Yongliang Wang, Li Li, Jinzhe Wang, Xinhui Ruan, Yanjing Du, Dongning Zheng (), Shu Chen () and Haiping Hu ()
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Cui-Xian Guo: Chinese Academy of Sciences
Luhong Su: Chinese Academy of Sciences
Yongliang Wang: Chinese Academy of Sciences
Li Li: Chinese Academy of Sciences
Jinzhe Wang: Chinese Academy of Sciences
Xinhui Ruan: Chinese Academy of Sciences
Yanjing Du: Chinese Academy of Sciences
Dongning Zheng: Chinese Academy of Sciences
Shu Chen: Chinese Academy of Sciences
Haiping Hu: Chinese Academy of Sciences

Nature Communications, 2024, vol. 15, issue 1, 1-9

Abstract: Abstract Anderson localization and non-Hermitian skin effect are two paradigmatic wave localization phenomena, resulting from wave interference and the intrinsic non-Hermitian point gap, respectively. In this study, we unveil a novel localization phenomenon associated with long-range asymmetric coupling, termed scale-tailored localization, where the number of induced localized modes and their localization lengths scale exclusively with the coupling range. We show that the long-range coupling fundamentally reshapes the energy spectra and eigenstates by creating multiple connected paths on the lattice. Furthermore, we present experimental observations of scale-tailored localization in non-Hermitian electrical circuits utilizing adjustable voltage followers and switches. The circuit admittance spectra possess separate point-shaped and loop-shaped components in the complex energy plane, corresponding respectively to skin modes and scale-tailored localized states. Our findings not only expand and deepen the understanding of peculiar effects induced by non-Hermiticity but also offer a feasible experimental platform for exploring and controlling wave localizations.

Date: 2024
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DOI: 10.1038/s41467-024-53434-8

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