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

“…The proximity of the region , which was shown to give rise to a sizeable radiative energy loss in doped graphene in the THz-MIR frequency range [ 22 , 23 , 24 ], renders the issue of the nonrelativistic approximation rather nontrivial in the present context. Nevertheless, we expect that our results will be applicable for the incident electron energies in the low–keV range, and may be of a semiquantitative utility for typical incident energies in the monochromated STEM-EELS with ultrahigh energy resolution [ 19 , 32 ].…”

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

“…44,45 The EELS technique has been extensively used, both in the transmission 46 and high-resolution reflection mode, 47 to investigate collective excitations in isotropic 2D materials, such as graphene, over a broad range of frequencies and wavenumbers, including plasmon 37,[48][49][50][51][52][53] and phonon modes. 42 In the theoretical modeling of EELS, graphene was described as isotropic sheet with an in-plane optical conductivity, which was modeled both phenomenologically 50,54 and via ab initio calculations. 51,55 Although nonretarded calculations of EELS reproduced the experimental data for graphene quite well for energy losses ≳1 eV, 50,56 a relativistic formulation of the interaction of a fast charged particle with graphene was developed to assess the role of retardation in energy losses 54,57,58 and to investigate the TR spectra from graphene in a broad range of frequencies, from the THz to the VUV.…”

“…42 In the theoretical modeling of EELS, graphene was described as isotropic sheet with an in-plane optical conductivity, which was modeled both phenomenologically 50,54 and via ab initio calculations. 51,55 Although nonretarded calculations of EELS reproduced the experimental data for graphene quite well for energy losses ≳1 eV, 50,56 a relativistic formulation of the interaction of a fast charged particle with graphene was developed to assess the role of retardation in energy losses 54,57,58 and to investigate the TR spectra from graphene in a broad range of frequencies, from the THz to the VUV. 57,[59][60][61] At the same time, there were only few experimental EELS studies of BP, which were limited to the range of electron energy losses ≳1 eV, and were accompanied by ab initio calculations of the loss function for multi-layer BP in the nonretarded regime.…”