Vibrational Spectrum of Carbon Nanotubes

Abstract
We calculate the vibrational densities of states (VDOS) for the two kinds of carbon nanotubes (armchair- and zigzag-type), using the recursion method and compare them with that for a single layer of graphite. The results show that the VDOS for the carbon nanotubes have more peaks than that for the graphene layer, but retain the strong peaks corresponded to those of the graphene layer. And the spectrums of the two kinds of nanotubes contain some feature peaks independent of the diameter.