Reconfigurable Defect States in Non-Hermitian Topolectrical Chains with Gain and Loss

TL;DR

This paper explores how non-Hermitian effects, PT symmetry, and gain-loss engineering can dynamically reconfigure defect states in topological electrical chains, enabling controllable localization for advanced signal processing.

Contribution

It introduces a method to reconfigure defect state localization in non-Hermitian topoelectrical systems using gain and loss, extending previous work on defect engineering.

Findings

Defect states can localize at the defect, edges, or become delocalized depending on parameters.

Staggered gain and loss restore symmetric localization of topological states.

Experimental circuit simulations confirm tunable defect state localization.

Abstract

We investigate the interplay between the non-Hermitian skin effect (NHSE), parity-time (PT) symmetry, and topological defect states in a finite non-Hermitian Su-Schrieffer-Heeger (SSH) chain. In the conventional NHSE regime, non-reciprocal hopping leads to an asymmetric localization of all eigenstates at one edge of the system, including the bulk and topological edge states. However, the introduction of staggered gain and loss restores the symmetric localization of topological edge states while preserving the bulk NHSE. We further examine the response of defect states in this system, demonstrating that their spatial localization is dynamically controlled by the combined effects of NHSE and PT symmetry. Specifically, we identify three distinct regimes in which the defect states localize at the defect site, shift to the system's edges, or become completely delocalized. These findings extend beyond previous works that primarily explored the activation and suppression of defect states through gain-loss engineering. To validate our theoretical predictions, we propose an experimental realization using a topolectrical circuit, where non-Hermitian parameters are implemented via impedance converter-based non-reciprocal elements. Circuit simulations confirm the emergence and tunability of defect states through voltage and admittance measurements, providing a feasible platform for experimental studies of non-Hermitian defect engineering. Our results establish a route for designing reconfigurable non-Hermitian systems with controllable topological defect states, with potential applications in robust signal processing and sensing.