Electron energy loss in carbon nanostructures

The response of fullerenes and carbon nanotubes is investigated by representing each carbon atom by its atomic polarizability. The polarization of each carbon atom produces an induced dipole that is the result of the interaction with a given external field plus the mutual interaction among carbon atoms. The polarizability is obtained from the dielectric function of graphite after invoking the Clausius-Mossotti relation. This formalism is applied to the simulation of electron energy loss spectra both in fullerenes and in carbon nanotubes. The case of broad electron beams is considered and the loss probability is analyzed in detail as a function of the electron deflection angle within a fully quantum-mechanical description of the electrons. A general good agreement with available experiments is obtained in a wide range of probe energies between 1 keV and 60 keV.Comment: 8 pages, 6 figures, submitted to PR

Surface Corrections to Bulk Energy Losses in Scanning Transmission Electron Microscopy of Spheres

The interaction of a fast electron penetrating a spherical target is studied, in the frame of the classical dielectric theory. Expressions for ω the Fourier component of the induced scalar field and energy loss probability are obtained. The reduction in the bulk loss probability due to the surface boundary correction is calculated to all orders in a multipole expansion. The dependence of this correction on the impact parameter and on the radius of the sphere is also studied and compared with the results for films

Target Geometry Dependence of Electron Energy Loss Spectra in Scanning Transmission Electron Microscopy (STEM)

In the frame of the Self-Energy formalism, we study the interaction between STEM electrons and small particles in the range of the valence electron excitations. We first calculate the energy loss probability for an isolated sphere and study the loss spectrum dependence on the size of the particle and on the relative impact parameter. Then we analyze the loss spectra in more realistic situations: (a) the effect of the coupling between the particle and supporting surface is studied in a simple geometrical model; and (b) we analyze the dependence of the losses on the geometrical shape of the target by considering hemispherical particle. Our results are in a good qualitative (and in simple cases, quantitative too) agreement with several experimental results which show anomalous excitations. We restate the suitability of the dielectric theory to study the surface excitations of these systems

One-dimensional potential for image-potential states on graphene

In the framework of dielectric theory the static non-local self-energy of an electron near an ultra-thin polarizable layer has been calculated and applied to study binding energies of image-states near free-standing graphene. The corresponding series of eigenvalues and eigenfunctions have been obtained by solving numerically the one-dimensional Schr{\"o}dinger equation. Image-potential-state wave functions accumulate most of their probability outside the slab. We find that a Random Phase Approximation (RPA) for the non-local dielectric function yields a superior description for the potential inside the slab, but a simple Fermi-Thomas theory can be used to get a reasonable quasi-analytical approximation to the full RPA result that can be computed very economically. Binding energies of the image-potential states follow a pattern close to the Rydberg series for a perfect metal with the addition of intermediate states due to the added symmetry of the potential. The formalism only requires a minimal set of free parameters; the slab width and the electronic density. The theoretical calculations are compared to experimental results for work function and image-potential states obtained by two-photon photoemission.Comment: 24 pages; 10 figures. arXiv admin note: text overlap with arXiv:1301.448

Electron energy loss and induced photon emission in photonic crystals

The interaction of a fast electron with a photonic crystal is investigated by solving the Maxwell equations exactly for the external field provided by the electron in the presence of the crystal. The energy loss is obtained from the retarding force exerted on the electron by the induced electric field. The features of the energy loss spectra are shown to be related to the photonic band structure of the crystal. Two different regimes are discussed: for small lattice constants $a$ relative to the wavelength of the associated electron excitations $\lambda$, an effective medium theory can be used to describe the material; however, for $a\sim\lambda$ the photonic band structure plays an important role. Special attention is paid to the frequency gap regions in the latter case.Comment: 12 pages, 7 figure

Dielectric response of pentagonal defects in multilayer graphene nano-cones

The dielectric response of pentagonal defects in multilayer graphene nano-cones has been studied by electron energy loss spectroscopy and ab initio simulations. At the cone apex, a strong modification of the dielectric response is observed below the energy of the π plasmon resonance. This is attributed to π → π* interband transitions induced by topology-specific resonant π bonding states as well as π*–σ* hybridization. It is concluded that pentagonal defects strongly affect the local electronic structure in such a way that multi-walled graphene nano-cones should show great promise as field emitters

Plasmon excitations at diffuse interfaces

Energy losses experienced by a fast electron probe moving through a dielectric medium have been studied both numerically and analytically, where the response function varies continuously with position in one transverse direction. The frequent assumption that the loss spectrum should exhibit a peak determined by the plasmon energy in a homogeneous medium with the composition found locally at the probe position can be incorrect. In free electron systems, inhomogeneous effects can cause spectral shape changes as well as peak shifts. Computations for diffuse interfaces between semiconductors with differing band gaps are also reported. Prospects for improved spatial resolution in valence loss spectroscopy at higher momentum transfer are discussed. © IOP Publishing Ltd.A Howie thanks Professor P Echenique and the staff of the Donostia International Physics Centre for excellent stimulation and hospitality. This work was supported in part by the Spanish MEC (contract No. FIS2004-06490-C03-02) and by the EU (project No. STRP-016881-SPANS).Peer Reviewe