Origin of the Fine Structure of the RamanDBand in Single-Wall Carbon Nanotubes

Experiments show that the D bands of bundles of single wall carbon nanotubes have a fine structure, apparently consisting of more than one subband. Using the double resonance theory, we calculate for the first time the D band for a sample of a given diameter distribution for seven different laser excitation energies in a wide range. In addition, a detailed theoretical explanation for the fine structure of the D band is provided. The calculated results agree well with experiments and show that the main factors in determining the fine structure are an enhanced trigonal warping of the phonon dispersion, the presence of a diameter distribution in the sample, and--most importantly--the resonance from the Van Hove singularities.