Energy Losses and Transition Radiation in Multilayer Graphene Traversed by a Fast Charged Particle

Abstract

We present a fully relativistic formulation of the energy loss of a charged particle traversing a number of graphene layers and apply it to the case of two spatially separated layers probed by an energetic electron. We focus on the THz frequency range, using a Drude model to describe the conductivity of graphene and allowing for different doping density in each layer. We distinguish two types of contributions to the electron energy loss: the energy deposited in graphene layers in the form of electronic excitations (Ohm losses), which include the excitation of Dirac plasmon polaritons (DPP), and the energy that is emitted in the form of transition radiation. 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. 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 decompositions with respect to the direction of motion of the external electron. A modal decomposition is also performed in the limit of vanishing damping in graphene, exposing quite intricate roles of bonding and antibonding hybridization between DPPs in ohmic losses.