Resonant Raman intensity of the radial-breathing mode of single-walled carbon nanotubes

The resonant Raman profile of the radial-breathing mode was calculated for all 300 single-walled carbon nanotubes in the radius range from 2 angstrom to 12 angstrom and for optical transition energies up to 3.5 eV within a symmetry-adapted non-orthogonal tight-binding model (V. N. Popov, New J. Phys. 6, 17 (2004)). In the calculations, the electron-phonon and electron-photon interactions were accounted for explicitly. The simulated Raman spectrum for a nanotube sample is in fair agreement with the experimentally observed one. It is shown that the simplifying assumption for tube-independent matrix elements of these interactions can lead to erroneous predictions of the Raman spectra.