Dynamic-polarization forces on fast ions and molecules moving over supported graphene
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We use a two-dimensional, two-fluid hydrodynamic model to describe the high-frequency plasmon excitations of the carbon valence electrons responding to fast ions and electric dipoles, which move parallel to a single sheet of graphene supported by an insulating substrate. We calculate the stopping and the image forces on ions and dipoles, as well as the dynamic torque on dipoles about their center of mass, resulting from the dynamic polarization of graphene. While the results for ions are similar to those obtained earlier for ion channeling through carbon nanotubes in dielectric media, the stopping and the image forces on dipoles show strong directional dependencies. The torque on point dipoles implies a strong alignment effect in the direction of motion at lower speeds, as well as a tendency of the dipole to roll over the graphene at high speeds.