Second-order Raman spectra of single and multiwalled carbon nanotubes

From second-order Raman scattering we find that the maximum in the phonon density of states of single-walled nanotubes softens by 30 cm^-1 over the value of graphite. A comparison of the phonon-dispersion curves of nanotubes in the literature shows that the ab initio approach best describes this softening. The excitation-energy dependence of the D and D^ modes in single-walled nanotubes is 38 and 90 cm^-1/eV, respectively, similar to the multiwalled species.