Interactions of slowly moving charges with graphene: The role of substrate phonons

We study dynamic polarization of single-layer graphene lying on a strongly polar substrate, such as SiC, induced by an external charged particle that moves slowly parallel to graphene. Calculations of the total electrostatic potential in the graphene plane, as well as of the stopping and image forces on the external particle are performed by means of graphene's dielectric function within the random phase approximation. We find that the excitation of surface phonons in the substrate may exert quite strong influences on the wake effect in the potential at low particle speeds, as well as on the magnitudes of both forces at high particle speeds.