Single-mode phonon transmission in symmetry broken carbon nanotubes

Normal mode phonon transmissions are studied in carbon nanotubes with the presence of Stone-Wales (SW) defect, using a mode-matching method and through the analysis of symmetry. The calculation shows that the transmission for low group velocity acoustic phonons is evidently reduced at high frequency range, and that this SW defect induced symmetry breaking strongly inhibits the transmission of long wave optical phonons in carbon nanotubes. The characteristic features of transmission for each phonon mode depend on the symmetry. These findings suggest that the local heating in the defective nanotubes may be contributed mainly from the low group velocity acoustic phonons and optical phonons near the $\Gamma$-point.