We present a computational study of the 2D Raman band of single-layer and bilayer graphene within a density-functional-based non-orthogonal tight-binding model. The phonon dispersion is derived perturbatively and the 2D band intensity is calculated in fourth-order quantum perturbation theory within this model. The 2D band intensity is enhanced through resonant processes in which the laser excitation matches an electronic transition and the energy and momentum of the scattered phonons match the difference of those of pairs of electronic states. As a result, the 2D band is dispersive, i.e., its position depends on the laser excitation. Here, we calculate the shift and shape, as well as the dispersion rate, of the 2D band for both single-layer graphene and bilayer graphene. The results are compared to available experimental data.
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