Inelastic electron scattering and magnetic collective response of mesoscopic carbon structures

We obtain analytically the self-consistent quasiparticle energy (QPE) spectra associated with certain fullerenes, e.g., ${\mathrm{C}}_{50}$, ${\mathrm{C}}_{60}$, ${\mathrm{C}}_{70}$, and the graphitic nanotubules. A random-phase approximation-level formalism for calculating the collective electronic excitations is then developed using the above QPE spectra as input. Multipole excitations are obtained for ${\mathrm{C}}_{60}$ and related quasispherical fullerenes. In the presence of a strong external magnetic field applied along the axis of the nanotubule, an extra peak in the de Haas–van Alphen oscillations predicted previously manifests itself as a discontinuity in the highest magnetoplasmon dispersion curve for the nanotubules in the infrared regime. The magnetic field breaks the degeneracy of the subbands such that each intersubband excitation branch is split into four distinct branches. An approximate plasmon dispersion relation in the high frequency regime is also derived. Furthermore, the inelastic electron scattering cross section characterized by the density-density correlation function is calculated. Our results are in good agreement with experiments on photoionization, gas phase electron-energy loss spectroscopy (EELS), transmission EELS, and high-resolution electron-energy loss spectroscopy.