The strength of the radial-breathing mode in single-walled carbon nanotubes

We present calculations of the absolute Raman cross section of the radial breathing mode (RBM) of single‐walled carbon nanotubes. We included all matrix elements explicitely as obtained from first principles calculations. Our results show a systematic dependence on diameter and chiral angle as well as on v = (n1 − n2) mod3, which we explain with the help of a zone folding model. Thus, the comparison of relative Raman intensities can serve as an independent check for chirality assignments. The dependencies come mainly from the electron‐phonon matrix elements Me‐ph, which have to be taken into account when dealing with absolute Raman intensities. We compare our calculations to measurements of the absolute Raman cross section of individual nanotubes and find an agreement to within one order of magnitude. The obtained intensities are consistent with the fact that the Raman signal of a single nanotube can be detected experimentally.