Theory of infrared-active phonons in carbon nanotubes

The phonons of single-wall carbon nanotubes are investigated within a generalized bond-charge model. The computed phonon dispersions generally agree with earlier results: two acoustic phonons (longitudinal and rotating), flexure modes at low frequencies, and radius-dependent radial breathing modes. Computation of the strength of the infrared active phonons reveals that only three modes have the first-order infrared activity in achiral tubes. We compare the observed modes with both experimental and group-theoretical results and discuss the characters of infrared-active modes.