Raman spectra of commensurate double-walled carbon nanotubes

Using nonresonant bond-polarization theory, Raman spectra of periodic double-walled carbon nanotubes are calculated. Although the syrnmetry of these tubes is highly reduced in comparison with the symmetry of the layers, the intensities of Raman active modes do not show significant changes. In ZZ polarization, modes related to radial breathing and high energy modes of individual layers remain the most intensive ones, even though the number of totally symmetric modes could be quite high. The shift of all Raman active modes with notable intensity is discussed and special attention is given to the possibility of tube identification from Raman data. In the case of breathing-like modes, the frequency of the out of phase mode is found to be chirality dependent, while the in phase one remains only diameter dependent as in the case of individual layers.