We have measured a strictly linear $\pi$ plasmon dispersion along the axis of individualized single-wall carbon nanotubes, which is completely different from plasmon dispersions of graphite or bundled single-wall carbon nanotubes. Comparative ab initio studies on graphene-based systems allow us to reproduce the different dispersions. This suggests that individualized nanotubes provide viable experimental access to collective electronic excitations of graphene, and it validates the use of graphene to understand electronic excitations of carbon nanotubes. In particular, the calculations reveal that local field effects cause a mixing of electronic transitions, including the “Dirac cone,” resulting in the observed linear dispersion.

We performed ab initio calculations of the optical absorption spectrum and the wave-vector-dependent dielectric and energy-loss functions of graphite in the framework of the random-phase approximation. In the absorption spectrum, the most prominent peaks were analyzed in terms of interband transitions from specific regions of the Brillouin zone. The inclusion of the crystal local-field effects (LFE) in the response had an important influence on the absorption spectrum for light polarization parallel to the $\mathbf{c}$ axis. The calculated electron energy-loss spectra, even without LFE, were in very good agreement with existing momentum-dependent energy-loss experiments concerning the peak positions of the two valence-electron plasmons. Important aspects of the line shape and anisotropy of the energy-loss function at large momentum transfer $q$ were also well described: the splitting of the total $(\pi +\sigma )$ plasmon and the appearance of peaks originating from interband transitions. Finally, the role of the interlayer interaction was studied, in particular with regard to its effect on the absorption spectrum for light polarization parallel to $\mathbf{c}$, and to the position of the higher-frequency $\pi +\sigma$ plasmon.

We performed ab initio calculations of the anisotropic dielectric response of small-diameter single-walled carbon nanotubes in the framework of time-dependent density-functional theory. The calculated optical spectra are in very good agreement with experiment, both concerning absolute peak positions and anisotropy effects. The latter can only be described correctly when crystal local-field effects (“depolarization” effects) are fully taken into account. Moreover, interactions between the tubes can strongly modify their absorption and electron energy-loss spectra.

We determined the anisotropic dielectric response of graphite by means of time-dependent density-functional theory and high-resolution valence electron energy-loss spectroscopy. The calculated loss function was in very good agreement with the experiment for a wide range of momentum-transfer orientations with respect to the graphitic basal planes, provided that local-field effects were included in the response. The calculations also showed strong effects of the interlayer Coulomb interaction on the total $\pi +\sigma$ plasmon. This finding must be taken into account for the explanation of recent loss spectra of carbon nanotube materials.