System size dependent topological zero modes in coupled topolectrical chains

TL;DR

This study explores how topological zero modes in coupled topolectrical chains depend on system size, revealing their emergence, disappearance, and controllability through circuit parameters and boundary conditions.

Contribution

It demonstrates the size-dependent emergence of topological zero modes in coupled non-Hermitian topolectrical chains and provides a framework for their physical detection and control.

Findings

Topological zero modes appear only in coupled chains, not in individual ones.

The zero modes vanish beyond a critical system size.

Sign modulation of inverse decay length controls zero mode emergence/disappearance.

Abstract

In this paper, we demonstrate the emergence and disappearance of topological zero modes (TZMs) in a coupled topolectrical (TE) circuit lattice. Specifically, we consider non-Hermitian TE chains in which TZMs do not occur in the individual uncoupled chains, but emerge when these chains are coupled by inter-chain capacitors. The coupled system hosts TZMs which show size-dependent behaviours and vanish beyond a certain critical size. In addition, the emergence or disappearance of the TZMs in the open boundary condition (OBC) spectra for a given size of the coupled system can be controlled by modulating the signs of its inverse decay length. Analytically, trivial and non-trivial phases of the coupled system can be distinguished by the differing ranks of their corresponding Laplacian matrix. The TE circuit framework enables the physical detection of the TZMs via electrical impedance measurements. Our work establishes the conditions for inducing TZMs and modulating their behavior in coupled TE chains.