Valley Hall effect and kink states in topolectrical circuits

Abstract

We investigate the emergence of topological valley Hall and kink states in a two-dimensional topolectrical (TE) model as a result of broken chiral and reflection symmetries. The TE system consists of two segments hosting distinct topological states with opposite (similar) signs of the valley Hall index, and separated by a heterojunction to exhibit valley kink (Chern insulating) phases at the interface. In the practical circuit, the valley Hall index can be flipped between the two segments by modulating the on-site potential on the sublattice nodes of the respective segments. The presence of grounding connections in the circuit array subsequently leads to the emergence of gapped and gapless valley and kink states in the admittance spectra. These topological modes can be detected electrically by the impedance readouts of the system, which can be correlated to its admittance spectra. Finally, we confirm the robustness of the valley Hall and kink states via realistic LTspice simulation, taking into account the tolerance windows and parasitic effects inherent in circuit components. Our study demonstrates the applicability of TE circuit networks as a platform to realize and tune valley-dependent and kink topological phenomena.