Phonon Dispersion for Armchair and Zigzag Carbon Nanotubes

Abstract

In this paper we present calculations of phonon dispersion of different types of single walled carbon nanotubes (SWCNT). In these calculations, the starting point has been the phonon dispersion of graphene. Zone folding scheme is then applied to obtain the phonon dispersion of CNT from that of graphene. Since the radial breathing modes in the phonon dispersion are not obtained by the zone-folding method, certain modifications are made in the lower branches to obtain these modes. These modifications produce results similar to those obtained by more sophisticated ab-initio methods.