Evidence for Size-Dependent Discrete Dispersions in Single-Wall Nanotubes

Raman scattering spectra of single-wall nanotubes with mean radii 0.55, 0.65, and 1.0 nm show size-dependent multiple splittings of the optical phonon peak corresponding to the ${E}_{2g}$ mode in graphite. These splittings constitute the first experimental evidence for the unique feature of nanotubes that they exhibit discrete and diameter-dependent dispersions arising from their cylindrical symmetry. The observed dispersion is well explained on the basis of graphite, and shows possibilities of predicting and controlling the basic property of nanotubes in the zone-folding scheme.