Chirality-dependent G-band Raman intensity of carbon nanotubes

The chirality-dependent G-band Raman intensity of single wall carbon nanotubes is calculated using a nonresonant theory for the Raman tensor. We obtain six or three intense Raman modes, respectively, for chiral or achiral nanotubes, whose relative intensities depend on the chiral angle of the nanotube. The longitudinal and transverse optical phonon modes in two-dimensional graphite become, respectively, transverse and longitudinal optical phonon modes in a one-dimensional nanotube. Confocal micro-Raman measurements of individual single wall carbon nanotubes show chirality-dependent spectra of the G-band intensity, as predicted by this theory.