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 $\varphi =\pi /2$ 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.

arXiv comment9 pages, 5 figures, see also https://journals.aps.org/prb/abstract/10.1103/PhysRevB.97.075310

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• Topologically Enhanced Harmonic Generation in a Nonlinear Transmission Line Metamaterial
• Non-Hermitian exceptional Landau quantization in electric circuits
• Observation of Antichiral Edge States in a Circuit Lattice
• Boundary states of 4D topological matter: Emergence and full 3D-imaging of nodal Seifert surfaces
• Chern insulators for electromagnetic waves in electrical circuit networks
• Always-Real-Eigenvalued Non-Hermitian Topological Systems
• Strongly Nonlinear Topological Phases of Cascaded Topoelectrical Circuits
• Engineering topological states and quantum-inspired information processing using classical circuits
• Valley-Chern Effect with LC-Resonators: A Modular Platform
• Reentrant quantum spin Hall effect in the presence of an exchange field
• Altermagnetism and its induced higher-order topology on the Lieb lattice
• Non-Hermitian Topoelectrical Circuits: Expedient Tools for Topological State Engineering with Gain-Loss Modulation
• Topological edge states and disorder robustness in one-dimensional off-diagonal mosaic lattices