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

TL;DR

This paper demonstrates how to simulate the quantum spin Hall effect in a topological Lieb lattice using a radio-frequency circuit, revealing tunable topological phases through capacitor-inductor networks.

Contribution

It introduces a method to realize a topological Lieb lattice in circuits and explores tunable topological phase transitions by varying circuit parameters.

Findings

Successfully simulated topological Lieb lattice in RF circuits

Identified tunable topological phase transitions with capacitance changes

Extended phase change analysis to arbitrary values

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.