System size dependent topological zero modes in coupled topolectrical chains

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.

9 Pages, 5 Figures

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Cited by in corpus (7)

• Topological Non-Hermitian skin effect
• Dimensional transmutation from non-Hermiticity
• Universal competitive spectral scaling from the critical non-Hermitian skin effect
• Impedance responses and size-dependent resonances in topolectrical circuits via the method of images
• Competition of non-Hermitian skin effect and topological localization of corner states observed in circuits
• Engineering topological states and quantum-inspired information processing using classical circuits
• Protected chaos in a topological lattice