No 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 D 3h 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 D 3h or C 2v 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 (e 11 ≈ 4.5 × 10 −10 C/m and d 11 ≈ 1.5 pm/V for direct and * To whom correspondence should be addressed † Equipe de Chimie Physique, IPREM UMR5254, Université de Pau et des Pays de l'Adour, 64000 Pau, France ‡ Chemistry Department, Faculty of Science, Minia University, Minia 61519, Egypt ¶ Dipartimento di Chimica and Centre of Excellence NIS (Nanostructured Interfaces and Surfaces), Università di Torino, via Giuria 5, IT-10125 Torino (Italy) 1 converse piezoelectricity, respectively). This in-plane piezoelectric response of graphene is one-order of magnitude larger than the out-of-plane previously investigated one.