We model Raman processes in silicene and germanene involving scattering of quasiparticles by, either, two phonons, or, one phonon and one point defect. We compute the resonance Raman intensities and lifetimes for laser excitations between 1 and 3$,$eV using a newly developed third-nearest neighbour tight-binding model parametrized from first principles density functional theory. We identify features in the Raman spectra that are unique to the studied materials or the defects therein. We find that in silicene, a new Raman resonance arises from the $2.77,rm$eV $pi-sigma$ plasmon at the M point, measurably higher than the Raman resonance originating from the $2.12,rm$eV $pi$ plasmon energy. We show that in germanene, the lifetimes of charge carriers, and thereby the linewidths of the Raman peaks, are influenced by spin-orbit splittings within the electronic structure. We use our model to predict scattering cross sections for defect induced Raman scattering involving adatoms, substitutional impurities, Stone-Wales pairs, and vacancies, and argue that the presence of each of these defects in silicene and germanene can be qualitatively matched to specific features in the Raman response.
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