Inducing a Finite In-Plane Piezoelectricity in Graphene with Low Concentration of Inversion Symmetry-Breaking Defects

Abstract

We show that a finite in-plane piezoelectricity can be induced in graphene by breaking its inversion center with any in-plane defect, in the limit of vanishing defect concentration. We first consider different patterns of BN-doped graphene sheets of D3h symmetry, whose electronic and piezoelectric (dominated by the electronic rather than nuclear term) properties are characterized at the ab initio level of theory. We then consider other in-plane defects, such as holes of D3h or C2v point symmetry, and confirm that a common limit value (for low defect concentration) of the piezoelectric response of graphene is obtained regardless of the particular chemical or physical nature of the defects (e11 ≈ 4.5 × 10–10 C/m and d11 ≈ 1.5 pm/V for direct and converse piezoelectricity, respectively). This in-plane piezoelectric response of graphene is one-order of magnitude larger than the out-of-plane previously investigated one.