Valley-Chern Effect with LC-Resonators: A Modular Platform

TL;DR

This paper demonstrates a valley-Chern effect in a modular LC-resonator circuit platform that mimics graphene's electronic properties, enabling topological control of electromagnetic modes with high Q-factors.

Contribution

It introduces a novel LC-resonator lattice platform that replicates graphene's Hamiltonian and exhibits the valley-Chern effect through symmetry breaking.

Findings

Valley-Chern effect successfully demonstrated in LC-resonator lattice.

High Q-factors up to 10^4 achievable with practical materials.

Optimal circuit configuration identified for topological mode localization.

Abstract

The valley Chern-effect is theoretically demonstrated with a novel alternating current circuitry, where closed-loop LC-resonators sitting at the nodes of a honeycomb lattice are inductively coupled along the bonds. This enables us to generate a dynamical matrix which copies identically the Hamiltonian driving the electrons in graphene. The valley-Chern effect is generated by splitting the inversion symmetry of the lattice. After a detailed study of the Berry curvature landscape and of the localization of the interface modes, we derive an optimal configuration of the circuit. Furthermore, we show that Q-factors as high as $10^4$ can be achieved with reasonable materials and configurations.