Double-resonant Raman scattering in graphite: Interference effects, selection rules, and phonon dispersion

We present a comprehensive analysis of double-resonant Raman scattering in graphite and derive an analytical expression for the Raman cross section of the D mode in one dimension. The extension to two dimensions does not change the double-resonant phonon wave vectors. In the full integration of the Raman cross section, the contributions by phonons from exactly the K point cancel due to destructive interference. We calculate the D mode explicitly based on recent experimental data of the graphite phonon dispersion. Applying the selection rules, a mapping of additional disorder-induced and second-order Raman modes onto the Brillouin zone of graphite is obtained.