Origin of the unusual dependence of Raman D band on excitation wavelength in graphite-like materials

We have revisited the still unresolved puzzle of the dispersion of the Raman disordered-induced D band as a function of laser excitation photon energy E$_L$ in graphite-like materials. We propose that the D-mode is a combination of an optic phonon at the K-point in the Brillioun zone and an acoustic phonon whose momentum is determined uniquely by the double resonance condition. The fit of the experimental data with the double-resonance model yields the reduced effective mass of 0.025m$_{e}$ for the electron-hole pairs corresponding to the A$_{2}$ transition, in agreement with other experiments. The model can also explain the difference between $\omega_S$ and $\omega_{AS}$ for D and D$^{\star}$ modes, and predicts its dependence on the Raman excitation frequency.