Phonons in twisted bilayer graphene

We theoretically investigate phonon dispersion in AA-stacked, AB-stacked, and twisted bilayer graphene with various rotation angles. The calculations are performed using the Born-von Karman model for the intralayer atomic interactions and the Lennard-Jones potential for the interlayer interactions. It is 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 frequency range 90-110 cm(-1). Twisting bilayer graphene leads to the emergence of different phonon branches-termed hybrid folded phonons-which originate from the mixing of phonon modes from different high-symmetry directions in the Brillouin zone. The frequencies of the hybrid folded phonons depend strongly on the rotation angle and can be used for noncontact identification of the twist angles in graphene samples. The obtained results and the tabulated frequencies of phonons in twisted bilayer graphene are important for the interpretation of experimental Raman data and in determining the thermal conductivity of these material systems.