Plasmons in isolated single-walled carbon nanotubes

The collective excitation modes of individual single-walled carbon nanotubes are studied theoretically in the nearest-neighbour tight-binding approximation. Umklapp terms are taken into account and local-field effects are studied. Plasmon mode dispersion relations for carbon nanotubes with radius R ∼7 Å are obtained. We report a strong dependence of the plasmon dispersion on the chirality of the carbon nanotubes. In particular, armchair and zigzag tubes have dispersive plasmons, but some of the chiral tubes have essentially dispersionless plasmons. Our results offer an alternative explanation to the origin of the experimentally observed low-energy dispersionless modes found in momentum-dependent EELS experiments. Important differences between a tight-binding model and free electron gas model are discussed and it is shown that some important qualitative features cannot be captured by a free electron gas model. An acoustic plasmon mode is found in all metallic carbon nanotubes, giving support to the experimental findings in Raman scattering.