Determination of Exciton-Phonon Coupling Elements in Single-Walled Carbon Nanotubes by Raman Overtone Analysis

Raman excitation profiles are obtained and compared for carbon nanotube radial breathing mode (RBM) fundamental and overtone vibrations for 5 specific chiralities. Fitting of the Raman excitation data is performed using Raman transform theory. The Huang-Rhys factors obtained from the modeling are directly related to the magnitude of the RBM exciton-phonon coupling element, which is shown to be in a weak coupling limit. The values of exciton-phonon coupling strengths and the possible role of revealed non-Condon effects are in agreement with quantum-chemical modeling.

Figure 1

Fundamental and first overtone (inset) Raman spectra of the RBM region for 766 nm excitation.

Figure 2

Top panels show PLE spectra (points) and the functions used as input to Raman transform theory models (solid lines). Bottom panels show experimental Raman excitation profiles for the RBM fundamental (circles) and overtone (triangles), along with fits obtained using Raman transform methods and parameters presented in Table . Raman intensities are for RBM and overtone frequencies, respectively, observed for the following chiralities at: (a) (12,1): $236{\mathrm{cm}}^{-1}/473{\mathrm{cm}}^{-1}$, (b) (10,5): $226{\mathrm{cm}}^{-1}/452{\mathrm{cm}}^{-1}$, (c) (10,2): $266{\mathrm{cm}}^{-1}/531{\mathrm{cm}}^{-1}$, (d) (9,4): $257{\mathrm{cm}}^{-1}/514{\mathrm{cm}}^{-1}$, and (e) (8,6): $245{\mathrm{cm}}^{-1}/489{\mathrm{cm}}^{-1}$. Overtone intensities have been multiplied by a factor of 10 for clarity.