We present several applications of the layered electron gas model to electron
energy loss spectroscopy of free-standing films consisting of $N$ graphene
layers in a scanning transmission electron microscope. Using a two-fluid model
for the single-layer polarizability, we discuss the evolution of high-energy
plasmon spectra with $N$, and find good agreement with the recent experimental
data for both multi-layer graphene with $N<10$, and thick slabs of graphite.
Such applications of these analytical models help shed light on several
features observed in the plasmon spectra of those structures, including the
role of plasmon dispersion, dynamic interference in excitations of various
plasmon eigenmodes, as well as the relevance of the bulk plasmon bands, rather
than surface plasmons, in classifying the plasmon peaks.Comment: 11 pages, 6 figures. Accepted for publication in Phys. Rev.
We evaluate the stopping and image forces on a charged particle moving parallel to a doped sheet of graphene by using the dielectric response formalism for graphene's π-electron bands in the random phase approximation (RPA). The forces are presented as functions of the particle speed and the particle distance for a broad range of charge-carrier densities in graphene. A detailed comparison with the results from a kinetic equation model reveal the importance of inter-band single-particle excitations in the RPA model for high particle speeds. We also consider the effects of a finite gap between graphene and a supporting substrate, as well as the effects of a finite damping rate that is included through the use of Mermin's procedure. The damping rate is estimated from a tentative comparison of the Mermin loss function with a HREELS experiment. In the limit of low particle speeds, several analytical results are obtained for the friction coefficient that show an intricate relationship between the charge-carrier density, the damping rate, and the particle distance, which may be relevant to surface processes and electrochemistry involving graphene.
The propagator of a dynamically screened Coulomb interaction W in a sandwichlike structure consisting of two graphene layers separated by a slab of Al 2 O 3 (or vacuum) is derived from single-layer graphene response functions and by using a local dielectric function for the bulk Al 2 O 3. The response function of graphene is obtained using two approaches within the random phase approximation (RPA): an ab initio method that includes all electronic bands in graphene and a computationally less demanding method based on the massless Dirac fermion (MDF) approximation for the low-energy excitations of electrons in the π bands. The propagator W is used to derive an expression for the effective dielectric function of our sandwich structure, which is relevant for the reflection electron energy loss spectroscopy of its surface. Focusing on the range of frequencies from THz to mid-infrared, special attention is paid to finding an accurate optical limit in the ab initio method, where the response function is expressed in terms of a frequency-dependent conductivity of graphene. It was shown that the optical limit suffices for describing hybridization between the Dirac plasmons in graphene layers and the Fuchs-Kliewer phonons in both surfaces of the Al 2 O 3 slab, and that the spectra obtained from both the ab initio method and the MDF approximation in the optical limit agree perfectly well for wave numbers up to about 0.1 nm −1. Going beyond the optical limit, the agreement between the full ab initio method and the MDF approximation was found to extend to wave numbers up to about 0.3 nm −1 for doped graphene layers with the Fermi energy of 0.2 eV.
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