Hybrid folded phonons in twisted graphene

Abstract

We theoretically investigated phonon dispersion and specific heat in AA-stacked, AB-stacked and twisted bilayer graphene with various rotation angles. Twisting bilayer graphene leads to emergence of new phonon branches – termed hybrid folded phonons – which originate from mixing of phonon modes from different high-symmetry directions in the Brillouin zone. The frequencies of the hybrid folded phonon depend strongly on the rotation angle and can be used for non-contact identification of the twist angles in graphene samples. It was also shown that the dispersion of the out-of-plane acoustic phonons – referred to as ZA phonons – deviates strongly from a parabolic law starting from the frequencies as low as ~100 cm-1. This leads to the frequency-dependent ZA phonon density of states and the breakdown of the linear dependence of the specific heat on temperature.