Topological properties of linear circuit lattices

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.