Intraband electron-phonon scattering in single-walled carbon nanotubes

The intraband electron-phonon matrix elements of all single-walled carbon nanotubes in the radius range from 3.5to12Å were calculated within a nonorthogonal tight-binding model of the electronic band structure. All possible scattering processes for all phonons allowed by the selection rules were considered. The matrix elements for scattering by tangential optical phonons in the linear bands of armchair nanotubes are nonzero for either forward or backward scattering and tend to 12.8eV/Å (intravalley) and 18.1eV/Å (intervalley) in the large-radius limit. For scattering in the lowest-energy parabolic conduction band of any nanotube, the matrix elements have large-radius limits of 9.2eV/Å (intravalley) and 13.4eV/Å (armchair, intervalley). For twist and longitudinal acoustic phonons, they depend on the chiral angle θ as sin3θ and cos3θ in the large-radius limit. While the matrix elements show radius and chirality dependence, the scattering lengths are almost nanotube independent. For medium-radius metallic tubes, the scattering length in linear bands is 1.0–1.6μm (acoustic phonons), 0.16μm (longitudinal optical phonons), and 0.06μm (A′1 K-point phonons).