Conductivity models for electron energy loss spectroscopy of graphene in a scanning transmission electron microscope with high energy resolution

Launching Plasmons in a Two-Dimensional Material Traversed by a Fast Charged Particle

We use a dielectric-response formalism to compute the induced charge density and the induced potential in a conductive two-dimensional (2D) material, traversed by a charged particle that moves on a perpendicular trajectory with constant velocity. By analyzing the electric force on the material via the Maxwell stress tensor, we showed that the polarization of the material can be decomposed into a conservative part related to the dynamic image force, and a dissipative part describing the energy and momentum transfer to the material, which is ultimately responsible for launching the plasma oscillation waves in the material. After showing that the launching dynamics is fully determined by the Loss function of the material, we used a conductivity model suitable for the terahertz to the midinfrared frequency range, which includes both the intraband and interband electron transitions in the material, to compute the real-space and time animations of the propagating plasma waves in the plane of the material. Finally, we used a stationary phase analysis to show that the plasmon wave crests go into an overdamped regime at large propagation distances, which are comparable to the distances where retardation effects are expected to emerge due to hybridization of the plasmon dispersion with the light line at long wavelengths.

Directional effects in plasmon excitation and transition radiation from an anisotropic 2D material induced by a fast charged particle

We present a relativistic formulation of the energy loss of a charged particle traversing an anisotropic layer under arbitrary angle of incidence. We use a model for the conductivity tensor describing doped phosphorene, which supports plasmon polariton modes (PPMs) that exhibit a topological transition between elliptic and hyperbolic iso-frequency dispersion curves in the THz to the mid-infrared (MIR) frequency range. The total distribution of the momentum transfer and energy loss of the charged particle goes to excitation of the PPMs followed by their decay in phosphorene (Ohmic losses) and the energy that is emitted as transition radiation (TR). We show that the elliptic modes are efficiently excited in the THz range by relativistic particles, but the corresponding Ohmic distributions do not exhibit significant anisotropy. Contrastingly, hyperbolic modes are efficiently excited in the MIR range by slow particles moving under oblique incidence, producing Ohmic distributions that show strong directionality of propagation with large wavevectors associated with the asymptotes of the hyperbolic dispersion curves. The most dramatic effects of the anisotropic layer conductivity are seen in the angular spectra of the TR, with quite distinct and unexpected shapes of the radiation patterns emitted at the THz and MIR frequencies, even for a normal incidence of the charged particle. Those patterns are substantially skewed for oblique incidence, when they show a marked anisotropy relative to the principal axes of the layer. Such a rich variety of the TR spectra should be readily observable via angle-resolved measurements in a transmission electron microscope.