Resonant anti-Stokes Raman scattering in single-walled carbon nanotubes

The dependence of the anti-Stokes Raman intensity on the excitation laser energy in carbon nanotubes is studied by resonant Raman spectroscopy. The complete resonant anti-Stokes and Stokes Raman profiles of the high-energy longitudinal phonon (${G}^{+}$) are obtained for (8,3), (7,5), (6,4), and (6,5) single chirality enriched samples. A high asymmetry between the intensity of the incoming and outgoing resonance is observed in the resonant Raman profiles. In contrast to Stokes scattering, anti-Stokes scattering is more intense at the outgoing resonance then at the incoming resonance. The resonance profiles are explained by a Raman process that includes the phonon-mediated interactions with the dark excitonic state. The chirality dependence of the Raman profiles is due to the variation in the exciton-phonon matrix elements, in agreement with tight-binding calculations. Based on the asymmetric Raman profiles we present the resonance factors for the Stokes/anti-Stokes ratios in carbon nanotubes.