Polarization of supported graphene by slowly moving charges

Abstract

We describe the dynamic polarization of graphene's $\ensuremath{\pi}$ electrons by means of the Vlasov equations in the relaxation-time approximation and evaluate the stopping and the image forces on slow ions moving parallel to a supported graphene under the gating conditions. While the effects of temperature and the gate potential on these forces are conveniently included by means of a single scaling parameter, the effects of variation in size of the gap between graphene and the $\mathrm{Si}{\mathrm{O}}_{2}$ substrate are found to be quite large, pointing to the need for including this gap explicitly in modeling of polarization of graphene.