Linear plasmon dispersion in single-wall carbon nanotubes and the collective excitation spectrum of graphene

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.