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

Abstract

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 ${\mathrm{\ensuremath{\Gamma}}}_{33}$. 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.