Topological piezoelectric response in moir\'e graphene systems

TL;DR

This paper predicts that moiré graphene systems exhibit nearly quantized piezoelectric responses linked to their topological valley Chern numbers, offering a new way to experimentally probe their topological properties.

Contribution

It introduces the concept that piezoelectric effects in topologically non-trivial moiré graphene can be nearly quantized and connects this to valley Chern numbers, supported by numerical calculations.

Findings

Piezoelectric tensor components are nearly quantized by valley Chern numbers.

Tuning displacement field or twist angle induces topological phase transitions.

Plateau shapes and abrupt jumps in response signal topological changes.

Abstract

We theoretically study the piezoelectric effects in moir\`e graphene systems. Since the strain couples to the electrons in the system as a pseudo vector potential, which has opposite signs for the $K$ and $K'$ valleys of graphene, its effects on the two valleys with opposite Chern numbers do not cancel out, but adds up. As a result, some components of the piezoelectric tensor in these systems, which typically have non-trivial topology in their flat bands, are nearly quantized in terms of the valley Chern numbers. Such a conclusion is verified by numerical calculations of the in-plane piezoelectric response of hBN-aligned twisted bilayer graphene, twisted bilayer-monolayer graphene, and twisted double bilayer graphene systems using both continuum model and atomistic tight-binding model. We find that by tuning the vertical displacement field and/or twist angle, which may induce gap closures between the flat bands and remote bands in these systems, plateau shapes of the piezoelectric response are obtained, with abrupt jumps across the topological phase transitions. We propose that such nearly quantized piezoelectric response may serve as a direct experimental probe for the valley Chern numbers of the flat bands in moir\'e graphene systems.