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

TL;DR

This paper introduces a new wave localization phenomenon called scale-tailored localization, which depends on the coupling range, and demonstrates its experimental observation in non-Hermitian electrical circuits, expanding understanding of non-Hermitian effects.

Contribution

The study uncovers scale-tailored localization linked to long-range asymmetric coupling and provides experimental evidence using non-Hermitian electrical circuits.

Findings

Localization length scales with coupling range

Energy spectra show multiple connected paths

Circuit admittance spectra reveal skin and localized states

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.