Resonant-Raman intensities and transition energies of theE11transition in carbon nanotubes

Abstract

We observed the lowest optical transitions $({E}_{11}^{S})$ in separated carbon nanotubes by resonant Raman spectroscopy. Radial breathing mode spectra were collected varying the excitation energy in the near-infrared from $1.15\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}1.48\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$. From resonance profiles we obtained the ${E}_{11}^{S}$ energies of 11 nanotubes, extending the experimental Kataura plot. Strong Raman signal from tubes with $\ensuremath{\nu}=(n\ensuremath{-}m)\mathrm{mod}3=+1$ and from tubes that were absent in photoluminescence support the theory of exciton resonance. The measured Raman intensities agree well with the calculated optical absorption and electron-phonon coupling obtained with first-principles and empirical methods. A remaining factor of $\ensuremath{\sim}3$ can be due to a higher abundance of armchairlike tubes or differences of the absorption and vibrational coupling between correlated (excitons) and uncorrelated electron-hole pairs.