Calculating the discrepancy between the Stokes and anti-Stokes RamanDband of carbon nanotubes using double resonance theory

The correspondence between the Stokes and anti-Stokes Raman D band of graphitic materials in general, and bundles of single-wall carbon nanotubes (SWCNT's) in particular is investigated using the double resonance theory. The D band of bundles of SWCNT's is determined by the Van Hove singularity enhanced double-resonant Raman-scattering processes. We show that the experimentally observed 7--8 cm^-1 difference between the Stokes and anti-Stokes D band--corresponding to the energy of one phonon---can be fully explained by the double-resonant Raman-scattering processes.