Origin of dispersive effects of the RamanDband in carbon materials

The origin and dispersion of the anomalous disorder-induced Raman band $(D$ band) observed in all ${\mathrm{sp}}^{2}$ hybridized disordered carbon materials near 1350 ${\mathrm{cm}}^{\ensuremath{-}1}$ is investigated as a function of incident laser energy. This effect is explained in terms of the coupling between electrons and phonons with the same wave vector near the K point of the Brillouin zone. The high dispersion is ascribed to the coupling between the optic phonons associated with the D band and the transverse acoustic branch. The large Raman cross section is due to the breathing motion of these particular phonons near the K point. Our model challenges the idea that the Raman D peak is due to laser-energy-independent features in the phonon density of states, but rather is due to a resonant Raman process.