Zavalniuk V. Vibrational excitations in graphene and carbon nanotubes with point defects

The contributions of phonons in ideal and non-ideal graphene and carbon nanotubes (CNTs), and quasi-macroscopic oscillations of walls in multi-walled CNTs on formation of thermal properties of concerned objects are studied. Using a solvable model which is based on the harmonic approximation and the assumption that the elastic forces act only between nearest neighboring atoms the corrections to the graphene density of states (DOS) dependent on the type and concentration of point defects are found. 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. The thermal conductivity of doped graphene flake of finite size is investigated with emphasis on the influence of the mass of the substituting atoms on this property. It is shown that graphene doping by small concentrations of relatively heavy atoms results in a disproportionately large drop in lattice thermal conductivity. The axial stiffness and wall telescopic oscillations in multi-walled CNTs (MWCNTs) were investigated within the continuum model based on Lennard-Jones intertube interaction. The axial stiffness of MWCNTs was considered as a function of the number of walls and their geometrical parameters. It was shown that the axial stiffness is determined only by several external shells (usually 3-5 and up to 15 for the extremely large nanotubes and high elongations) which is in a good agreement with the experimentally observed inverse relation between the radius and Young modulus (i.e., stiffness) of MWCNTs. Explicit expressions are derived for the telescopic force constants (longitudinal rigidity) and the frequencies of telescopic oscillations. The contribution of small-amplitude oscillations to the low-temperature specific heat of nanotubes was estimated. It was shown that this contribution is of the same order and higher than the phonon specific heat at temperatures 1K.