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

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.

10+16 pages, 5+11 figures

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Cited by in corpus (12)

• Erratic non-Hermitian skin localization
• Numerical instability of non-Hermitian Hamiltonian evolutions
• Interaction-Induced Second-Order Skin Effect
• Scale-free localization versus Anderson localization in unidirectional quasiperiodic lattices
• Controlled probing of localization effects in the non-Hermitian Aubry-André model via topolectrical circuits
• Anisotropic-scaling localization in higher-dimensional non-Hermitian systems
• Super-enhanced Sensitivity in Non-Hermitian Systems at Infernal Points
• Non-equilibrium dynamics of localization phase transition in the non-Hermitian Disorder-Aubry-André model
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• Concurrent Skin-scale-free Localization and Criticality under Möbius Boundary Conditions in a Non-Hermitian Ladder