Excitation and chirality dependence of the exciton-phonon coupling in carbon nanotubes

Based on the empirical nearest-neighbor tight-binding model, we predict that the dependence of the cross section of the resonance Raman scattering from the radial breathing mode of a carbon nanotube multiplied by the fourth power of the nanotube radius is a quadratic function of a newly introduced parameter characterizing nanotube chirality. This dependence reflects the dependence of the exciton-phonon coupling matrix element on the nanotube radius and chiral angle. We perform Raman scattering measurements on nanotubes in solution and confirm the predicted parabolic dependence assuming a close-to-uniform distribution of chiral angles in nanotube samples. The deviation of the experimental points from the parabola provides information about chirality distribution of nanotubes in a sample, which opens new horizons in characterization of samples containing nanotubes of different chiralities.