We present a fully relativistic formulation of the energy loss of a charged particle traversing a number of graphene layers under normal incidence. We focus on the THz frequency range, using a Drude model to describe the conductivity of graphene. We distinguish two types of contributions to the electron energy loss (EEL): the energy deposited in graphene layers in the form of electronic excitations (Ohm losses), which include the excitation of Dirac plasmon polaritons (DPP) and corresponding dissipative processes, and the energy that is emitted in the form of transition radiation (TR).

Neglecting interlayer electron hopping, we study in detail the contribution of each layer to the ohmic losses and analyze the directional decomposition of the radiation emitted in the half-spaces defined by the graphene planes. We also study the hybridization of graphene's DPPs. Performing a layer decomposition of ohmic energy losses, which include excitation of hybridized DPPs (HDPPs), we inspect the contribution of each separate layer into the excitation of those HDPPs. In this relativistic EEL study, we find several exciting results. For instance, by increasing the interlayer distance and changing the relative doping densities in graphene layers, we find surprisingly strong asymmetries in both the directional and layer-wise decomposition with respect to the direction of motion of the external electron.

Last but not least, we investigate the energy loss and transition radiation from interaction of a single layer graphene with an external moving charged particle under oblique incidence. In this part of our study we deeply explore the role of longitudinal and transverse plasmon excitations and their contributions into ohmic loss and TR.

Keywords:

graphene, plasmon, energy loss, transition radiation, electron beam, relativistic effects