Quantum interferences in the Raman cross section for the radial breathing mode in metallic carbon nanotubes

The line shapes of the Raman excitation profiles for radial breathing modes in carbon nanotubes are shown to be strongly affected by interference effects that arise whenever strong optical transitions are separated by a small energy. This is the case in metallic zigzag and chiral tubes, where one-dimensional singularities in the electronic joint density of states are split due to the trigonal warping of the electronic band structure of a two-dimensional graphene. It is shown that the proper modeling of these interferences is crucial for the identification of the $(n,m)$ indices using Raman spectroscopy.