Phonon spectrum of double-wall carbon nanotubes

The results of studying the phonon spectra of carbon nanotubes within the framework of the periodic-cluster model are presented. Special attention is paid to the phonon spectrum of double-wall nanotubes. It is shown that the spectrum is separated into two subbands corresponding to the acoustic and optical vibrational modes. A specific feature of the phonon dispersion curves is their “doublet” character. The spectrum has an acoustic mode corresponding to longitudinal oscillations of the two walls of a double-wall carbon nanotube with respect to each other.