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.

Shaping quantum photonic states using free electrons

“…This way, our formalism and predictions can contribute to the growing interest of recent years in novel free-electron light sources based on nanophotonic structures and high Q cavities (61), for example, Smith-Purcell sources such as the "light well" (62), some requiring low electron energies (63), reaching the infrared telecom wavelength (64), and the deep UV (65). Other interaction geometries with nanophotonic structures and materials involve metamaterials (66,67), metasurfaces (68), and 2D materials (69)(70)(71) for generating light in various spectral regimes up to x-rays and gamma rays. Such nanophotonic light sources are attractive because of their tunable wavelength.…”

A Review on Graphene-Based Light Emitting Functional Devices

“…The realization of ultrafast plasmons-based optical signal source at the nanoscale is considered as a longstanding goal, the potential of the graphene-based emitter to revolutionize optoelectronics, thus allowing ultrafast optical signal processing for communication [ 49 ]. When the electron beam is exposed to the optically excited surface plasmons of graphene, the unidirectional, chromatic, and tunable emission from IR to X-ray was realized from the graphene [ 50 , 51 , 52 ]. The theoretical investigation and experimental demonstration of this mechanism predict the existence of plasmons at VIS and IR wavelengths [ 53 ].…”

“…The theoretical investigation and experimental demonstration of this mechanism predict the existence of plasmons at VIS and IR wavelengths [ 53 ]. Besides, the plasmons-assisted light emission from graphene in VIS, and even shorter wavelength was illustrated by the interaction of surface plasmons and charged particles [ 50 , 54 ]. Significantly, the 2D quantum Čerenkov effect (ČE) can also be achieved in graphene, due to the unique properties of high field confinement, surface plasmons, and low phase velocity.…”

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

“…On the other hand, the result for the radiative energy loss, which is nonzero only inside the light cone ( k < k d ), may be expressed as F rad = F ↑ rad + F ↓ rad , where contributions from the TR in the upper and lower half-spaces are evaluated from the fluxes of the Poynting vector, , taken across two distant parallel planes, z → ±∞, giving . 57 In order to relate this result to the angle-resolved measurements of radiation in SEM, one should switch to polar coordinates, and write F rad ( k , ω ) = F rad ( k , φ , ω ). 61 Then, for the TR emitted at a frequency ω in the direction defined by the angle θ with respect to ẑ and the polar angle φ with respect to x̂ , one can substitute and define the spectral angular distribution of TR as .…”