Energy losses and transition radiation produced by the interaction of charged particles with a graphene sheet

Abstract

We present a fully relativistic formulation of the energy loss of a charged particle traversing a conductive monoatomic layer and apply it to the case of graphene in a transmission electron microscope (TEM). We use two models of conductivity appropriate for different frequency regimes: (a) THz (terahertz) frequency range and (b) optical range. In each range we distinguish two types of contributions to the electron energy loss: the energy deposited in graphene in the form of electronic excitations (Ohm losses), and the energy that is emitted in the form of radiation. We find strong relativistic effects in the electron energy loss spectra, which are manifested, e.g., in the increased heights of the principal π and σ+π peaks that may be observed in TEM in the optical range. While the radiative energy losses are suppressed in the optical range in comparison to the Ohmic losses, we find that these two contributions are comparable in magnitude in the THz range, where the response of doped graphene is dominated by the Dirac plasmon polariton (DPP). In particular, relative contributions of the Ohmic and radiative energy losses are strongly affected by the damping of DPP. In the case of a clean graphene with low damping, the angular distribution of the radiated spectra at the sub-THz frequencies exhibit strong and possibly observable skewing towards graphene.