  We provide a theoretical model that describes the dielectric coupling of a 2D
layer of graphene, represented by a polarization function in the Random Phase
Approximation, and a semi-infinite 3D substrate, represented by a surface
response function in a non-local formulation. We concentrate on the role of the
dynamic response of the substrate for low-frequency excitations of the combined
graphene-substrate system, which give rise to the stopping force on slowly
moving charges above graphene. A comparison of the dielectric loss function
with experimental HREELS data for graphene on a SiC substrate is used to
estimate the damping rate in graphene and to reveal the importance of phonon
excitations in an insulating substrate. A signature of the hybridization
between graphene's pi plasmon and the substrate's phonon is found in the
stopping force. A friction coefficient that is calculated for slow charges
moving above graphene on a metallic substrate shows an interplay between the
low-energy single-particle excitations in both systems.
