Simulating Quantum Spin Hall Effect in Topological Lieb Lattice of Linear Circuit

Abstract

Inspired by the topological insulator circuit proposed and experimentally verified by Jia., et al. \cite{1}, we theoretically realized the topological Lieb lattice, a line centered square lattice with rich topological properties, in a radio-frequency circuit. We open the topological nontrivial band-gap through specific capacitor-inductor network, which resembles adding intrinsic spin orbit coupling term into the tight binding model. Finally, we discuss the extension of the $\phi=\pi/2$ phase change of hopping between sites to arbitrary value, and investigate the topological phase transition of the band structure vary with capacitance, thereby paving the way for designing tunable lattices using the presented framework.