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 disorder-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 0.025 $m_e$ 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 ${\omega }_{\mathrm{AS}}$ for D and $D^{*}$ modes, and predicts its dependence on the Raman excitation frequency.