Raman scattering in carbon nanotubes revisited

We explain the origin of the high-energy mode in the first-order Raman spectra of single-walled carbon nanotubes by double-resonant scattering. Following this interpretation, we calculate the multiple-peak structure as found in Raman experiments. The highest peak is above the graphite $\Gamma$-point frequency; its amplitude is larger than that of the second peak. We derive positive and negative frequency shifts as a function of excitation energy, which we observe experimentally as well. We predict a difference in frequency and shape of the high-energy mode in Stokes and anti-Stokes scattering.