Double resonant Raman phenomena enhanced by van Hove singularities in single-wall carbon nanotubes

The behavior of the disorder-induced D band in the Raman spectrum of single-wall carbon nanotubes (SWCNT’s) was investigated both theoretically and experimentally. The measured maximum position of the D band for SWCNT bundles exhibits an oscillation superimposed on a linear shift, when the laser excitation energy $E_{\mathrm{laser}}$ varies in the range of 1.6–2.8 eV. We have shown theoretically by explicit integrations for the resonant Raman cross section that the D-band intensity of an isolated SWCNT has a sharp maximum when $E_{\mathrm{laser}}$ of either the incoming or the scattered photon matches a van Hove singularity in the joint density of states. This “resonance” must be considered in addition to the double resonance from a scattering by an impurity. Calculating the D band of a superposition of all the 114 SWCNT’s within a given diameter range, both the shift and the oscillation in the experimentally observed spectra were reproduced.