Piezoelectricity in asymmetrically strained bilayer graphene

TL;DR

This paper presents a comprehensive method to analyze the electronic properties of commensurate bilayer graphene under various strains, revealing strain-dependent classes, charge transfer, and tunable piezoelectric effects, with potential extensions to multilayer systems.

Contribution

A novel, general approach for studying commensurate graphene heterostructures that captures strain effects, interlayer coupling, and piezoelectricity, applicable to multilayer systems.

Findings

Strain induces distinct classes of superstructures with different low-energy physics.

Significant charge transfer occurs between layers under strain.

Piezoelectric effects can be tuned with a perpendicular electric field.

Abstract

We study the electronic properties of commensurate faulted bilayer graphene by diagonalizing the one-particle Hamiltonian of the bilayer system in a complete basis of Bloch states of the individual graphene layers. Our novel approach is very general and can be easily extended to any commensurate graphene-based heterostructure. Here, we consider three cases: i) twisted bilayer graphene, ii) bilayer graphene where triaxial stress is applied to one layer, and iii) bilayer graphene where uniaxial stress is applied to one layer. We show that the resulting superstructures can be divided into distinct classes, depending on the twist angle or the magnitude of the induced strain. The different classes are distinguished from each other by the interlayer coupling mechanism, resulting in fundamentally different low-energy physics. For the cases of triaxial and uniaxial stress, the individual graphene layers tend to decouple and we find significant charge transfer between the layers. In addition, this piezoelectric effect can be tuned by applying a perpendicular electric field. Finally, we show how our approach can be generalized to multilayer systems.