Ab initiophonon dispersions of single-wall carbon nanotubes

Phonon-dispersion curves for a series of single-wall carbon nanotubes (SWCNT’s) have been obtained by ab initio supercell approach. Force constants are calculated using norm-conserving pseudopotential plane-wave method in the framework of the density-functional theory and local-density approximation. Cumulant force-constant method is used instead of interatomic force-constant method to construct the dynamical matrices. We get much better low-frequency dispersions than existing results with no soft phonon mode presented. Good accuracy is shown in the full frequency range. Residue forces in the relaxed SWCNT structures are filtered out by a linear fitting force-constant scheme. Raman and IR active modes are reanalyzed by $D_{2nd}$ group symmetry. The frequencies are found to agree excellently with the experimental observations. Our results confirm the reported frequency drop of the $A_{1g}$ mode. Some issues in the low-temperature specific-heat experiment and the neutron-scattering experiment are well explained by our phonon dispersions. Phonon dispersions of graphite are also calculated using the same method, being in good agreement with experiment. Theoretical analysis is also presented to explain the advantages of cumulant force-constant method to get better low-frequency dispersions.