Collective excitations in a single-layer carbon nanotube

Abstract

The inter-\ensuremath{\pi}-band response function of a single-layer carbon nanotube is calculated within the random-phase approximation. Such a cylindrical system exhibits rich inter-\ensuremath{\pi}-band excitations. The decoupled \ensuremath{\pi} 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 \ensuremath{\pi} plasmon frequency is \ensuremath{\sim}6--8 eV, which is insensitive to the nanotube geometry such as the radius and chiral angle. Comparison with recent experiments is discussed. \textcopyright{} 1996 The American Physical Society.