Collective excitations in a single-layer carbon nanotube

The inter-π-band response function of a single-layer carbon nanotube is calculated within the random-phase approximation. Such a cylindrical system exhibits rich inter-π-band excitations. The decoupled π plasmons of different angular momenta (L’s) strongly depend on the transferred momenta (q’s). Furthermore, they exhibit a dimensionality crossover as the nanotube radius is increased. For small q’s and L’s, the π plasmon frequency is ∼6-8 eV, which is insensitive to the nanotube geometry such as the radius and chiral angle. Comparison with recent experiments is discussed.