Excitonic optical transitions characterized by Raman excitation profiles in single-walled carbon nanotubes

We examine the excitonic nature of the E-33 optical transition of the individual free-standing index-identified (23,7) single-walled carbon nanotube by means of the measurements of its radial-breathing-mode and G-mode Raman excitation profiles. We confirm that it is impossible to determine unambiguously the nature of its E-33 optical transition (excitonic vs band to band) based only on the excitation profiles. Nevertheless, by combining Raman scattering, Rayleigh scattering, and optical absorption measurements on strictly the same individual (23,7) single-walled carbon nanotube, we show that the absorption, Rayleigh spectra, and Raman excitation profiles of the longitudinal and transverse G modes are best fitted by considering the nature of the E-33 transition as excitonic. The fit of the three sets of data gives close values of the transition energy E-33 and damping parameter Gamma(33). This comparison shows that the fit of the Raman excitation profiles provides with good accuracy the energy and damping parameter of the excitonic optical transitions in single-walled carbon nanotubes.