  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.
