Topological properties of linear circuit lattices

TL;DR

This paper introduces a simplified topological circuit lattice model that emulates quantum spin Hall insulators, enabling the simulation of complex topological phenomena like non-Abelian Aharonov-Bohm effects with tunable parameters.

Contribution

It presents a new circuit design with fewer elements that replicates the properties of quantum spin Hall insulators and allows for simulation of complex topological effects.

Findings

The circuit's frequency matrix is unitarily equivalent to a QSHI hopping matrix.

Identifies perturbations that preserve edge mode backscatter immunity.

Demonstrates simulation of non-Abelian Aharonov-Bohm effect.

Abstract

Motivated by the topologically insulating (TI) circuit of capacitors and inductors proposed and tested in arXiv:1309.0878, we present a related circuit with less elements per site. The normal mode frequency matrix of our circuit is unitarily equivalent to the hopping matrix of a quantum spin Hall insulator (QSHI) and we identify perturbations that do not backscatter the circuit's edge modes. The idea behind these models is generalized, providing a platform to simulate tunable and locally accessible lattices with arbitrary complex spin-dependent hopping of any range. A simulation of a non-Abelian Aharonov-Bohm effect using such linear circuit designs is discussed.