Valence excitations in individual single-wall carbon nanotubes

We report on measurements of the plasmon losses of individual single-wall carbon nanotubes by electron energy-loss spectroscopy in a high-resolution transmission electron microscope. The experimental data are compared to simulated excitation probabilities calculated using the hydrodynamic theory of the interaction between a probe electron and a two-dimensional quasifree electron gas confined on a cylindrical shell. Depending on the nanotube geometry, the first- or the second-order oscillation mode dominates the loss spectrum. The resonance energy of the dominant resonance mode is found to depend on the radius of the nanotube.