Moir\'e circuits: engineering magic-angle behaviors

TL;DR

This paper demonstrates the engineering of moiré physics in electric circuits, enabling the realization of flat bands, energy localization, and topological edge states, thus extending twistronics concepts beyond natural materials.

Contribution

It introduces a novel circuit platform to emulate moiré physics, including flat bands and topological states, with experimental validation and potential for advanced circuit applications.

Findings

Realization of flat bands at various twist angles

Observation of energy localization at magic coupling values

Detection of topological edge states induced by moiré patterns

Abstract

Moir\'e superlattices in the twisted bilayer graphene provide an unprecedented platform to investigate a wide range of exotic quantum phenomena. Recently, the twist degree of freedom has been introduced into various classical wave systems, giving rise to new ideas for the wave control. The question is whether twistronics and moir\'e physics can be extended to electronics with potential applications in the twist-enabled signal processing. Here, we demonstrate both in theory and experiment that lots of fascinating moir\'e physics can be engineered using electric circuits with extremely high degrees of freedom. By suitably designing the interlayer coupling and biasing of one sublattice for the twisted bilayer circuit, the low-energy flat bands with large bandgaps away from other states can be realized at various twist angles. Based on the moir\'e circuit with a fixed twist angle, we experimentally demonstrate the effect of band narrowing as well as the localization of electric energy when a magic value of the interlayer coupling is applied. Furthermore, the topological edge states, which originate from the moir\'e potential induced pseudomagnetic field, are also observed for the first time. Our findings suggest a flexible platform to study twistronics beyond natural materials and other classical wave systems, and may have potential applications in the field of intergraded circuit design.