Lattice dynamics and symmetry of double wall carbon nanotubes

Abstract

Stable configurations and full symmetry groups of double wall carbon nanotubes are determined. These are used to calculate phonon bands for commensurate tubes. In particular, the modes with rigid walls are analysed and weak interlayer interaction is confirmed. Taking infra-red measurements is found to be a suitable method for characterizing double wall tubes. The heat capacity in the low temperature region is predicted to be lower than for single wall layers.