We report theoretical analysis of the electronic flexoelectric effect associated with nanostructures of sp(2) carbon (curved graphene). Through the density functional theory calculations, we establish the universality of the linear dependence of flexoelectric atomic dipole moments on local curvature in various carbon networks (carbon nanotubes, fullerenes with high and low symmetry, and nanocones). The usefulness of such dependence is in the possibility to extend the analysis of any carbon systems with local deformations with respect to their electronic properties. This result is exemplified by exploring of flexoelectric effect in carbon nanocones that display large dipole moment, cumulative over their surface yet surprisingly scaling exactly linearly with the length, and with sine-law dependence on the apex angle, dflex ~ L sin(α). Our study points out the opportunity of predicting the electric dipole moment distribution on complex graphene-based nanostructures based only on the local curvature information.
Keywords: density functional theory; dipole moment; flexoelectricity; pyramidalization angle.