Simulating quantum spin Hall effect in the topological Lieb lattice of a linear circuit network

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