Single-wall carbon nanotubes phonon spectra: Symmetry-based calculations

The phonon dispersions and atomic displacements for single-wall carbon nanotubes of arbitrary chirality are calculated. The full symmetry is implemented. The approach is based on the force constants of graphene, with the symmetry imposed modifications providing the twisting acoustic mode exactly. The functional dependence of frequencies of the Raman and infrared active modes on the wrapping angle and on the diameter are presented. The armchair tubes are found to be infrared inactive under the light linearly polarized along the tube axis. Also the overbending absolute value and the wave vector dependence on the tube geometry are found and the chirality selective method for the sample characterization is proposed. Finally, the specific heat calculations are carried out.