Strain gradient polarization in graphene

Flexoelectricity phenomenon is the response of electric polarization to an applied strain gradient and is developed as a consequence of crystal symmetry in all materials. In this study, we show that the presence of strain gradient in non-piezoelectric graphene sheet does not only affect the ionic positions, but also the asymmetric redistribution of the electron density, which induce strong polarization in the graphene sheet. Using quantum mechanics calculations, the resulting axial and normal piezoelectric coefficients of the graphene sheet were determined using two loading conditions: (i) a graphene sheet containing non-centrosymmetric pores subjected to an axial load, and (ii) a pristine graphene sheet subjected to a bending moment. Particular emphases were placed on the role of edge and corner states of pores arising due to the functionalization. We also investigated the electronic structure of graphene sheet under different in-plane strain distributions using quantum mechanics calculations and tight-binding approach. The findings of our work reveal that the respective axial and normal electromechanical couplings in graphene can be engineered by changing the size of non-centrosymmetric pores and radii of curvature. Our fundamental study highlights the possibility of using graphene sheets in nanoelectromechanical systems as sensors or actuators.