Theoretical analysis of telescopic oscillations in multi-walled carbon nanotubes

A simplified theory of the telescopic oscillations in multiwalled carbon nanotubes is developed. The explicit expressions for the telescopic force constants (longitudinal rigidity) and the frequencies of telescopic oscillations are derived. The contribution of small-amplitude telescopic oscillations to the nanotubes low temperature specific heat is estimated.Comment: 14 pages, 5 figure

Lattice thermal conductivity of graphene with conventionally isotopic defects

The thermal conductivity of doped graphene flake of finite size is investigated with emphasis on the influence of mass of substituting atoms on this property. It is shown that the graphene doping by small concentrations of relatively heavy atoms results in a disproportionately impressive drop of lattice thermal conductivity.Comment: 12 pages, 3 figure

Phonons in graphene with point defects

The phonon density of states (DOS) of graphene with different types of point defects (carbon isotopes, substitution atoms, vacancies) is considered. Using a solvable model which is based on the harmonic approximation and the assumption that the elastic forces act only between nearest neighboring ions we calculate corrections to graphene DOS dependent on type and concentration of defects. In particular the correction due to isotopic dimers is determined. It is shown that a relatively small concentration of defects may lead to significant and specific changes in the DOS, especially at low frequencies, near the Van Hove points and in the vicinity of the K-points of the Brillouin zone. In some cases defects generate one or several narrow gaps near the critical points of the phonon DOS as well as resonance states in the Brillouin zone regular points. All types of defects are characterized by the appearance of one or more additional Van Hove peaks near the (Dirac) K points and their singular contribution may be comparable with the effect of electron-phonon interaction. Besides, for low frequencies and near the critical points the relative change in density of states may be many times higher than the concentration of defects.Comment: 19 pages, 7 figure