Intensities of the Raman-active modes in single and multiwall nanotubes

We investigated the phonon symmetries in the Raman spectra of single and multiwall nanotubes. By using linearly and circularly polarized light we measured the Raman tensor invariants on unoriented carbon nanotubes. The ratio between the antisymmetric and the isotropic invariant shows that Raman scattering in semiconducting single wall tubes is mainly due to fully symmetric $A_{1\left(g\right)\mathrm{}}$ phonons with a strongly uniaxial Raman tensor. With the help of recent experiments on aligned nanotubes we calculate the relative intensities for the high-energy modes of different symmetry. Compared to single wall tubes the intensity of the $E_{1\left(g\right)\mathrm{}}$ and $E_{2\left(g\right)\mathrm{}}$ symmetry phonons in multiwall tubes is 1.5 times stronger. The antisymmetric component of the resonant Raman process was found to be zero in all measurements.