Electrostatics of graphene: Charge distribution and capacitance

The distribution of net electric charge in graphene is investigated, using both a constitutive atomic charge–dipole interaction model and an approximate analytical solution to Laplace’s equation. These approximations, unlike first-principle calculations, are applicable to graphene sizes that are consistent with experiments. It is found that the analytical model gives a good description of the charge distribution, except for the very edge atoms because of the atomic edge state, which can instead be treated by the numerical model.