Graphene Stopping Power for a Fast Charged Particle: Parallel Case

In this paper, we analyze the energy loss and stopping power of a fast charged particle probe of a 2-D graphene sheet. The fast particle motion is taken to be parallel to the 2-D graphene sheet, and the system is considered at the degenerate limit (zero temperature). The 2-D graphene layer response dynamics are described in the random phase approximation. We determine the energy loss for motion parallel to the 2-D graphene layer as a function of the distance of the fast particle from the layer and its velocity, calculating the stopping power.