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Phonon dispersions and vibrational properties of monolayer, bilayer, and trilayer graphene: Density-functional perturbation theory
The phonon dispersions of monolayer and few-layer graphene ($AB$ bilayer, and $ABA$ and $ABC$ trilayers) are investigated using the density-functional perturbation theory. Compared with the monolayer, the optical phonon ${E}_{2g}$ mode at $\ensuremath{\Gamma}$ splits into two and three doubly degenerate branches for bilayer and trilayer graphene, respectively, due to the …