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Phonons in Twisted Bilayer Graphene

We theoretically investigated phonon dispersion in AA-stacked, AB-stacked and twisted bilayer graphene with various rotation angles. The calculations were performed using the Born-von-Karman model for the intra-layer atomic interactions and the Lennard-Jones potential for the inter-layer interactions. It was found that the stacking order affects the out-of-plane acoustic phonon modes the most. The difference in the phonon densities of states in the twisted bilayer graphene and in AA- or AB-stacked bilayer graphene appears in the phonon frequencies range 90 - 110 1/cm. Twisting bilayer graphene leads to emergence of new phonon branches - termed entangled phonons - which originate from mixing of phonon modes from different high-symmetry directions in the Brillouin zone. The frequencies of the entangled phonon depend strongly on the rotation angle and can be used for non-contact identification of the twist angles in graphene samples. The obtained results and tabulated frequencies of phonons in twisted bilayer graphene are important for interpretation of experimental Raman data and determining thermal conductivity of these materials systems.