Graphite and Graphene Nano-films: Phonons Localization and Propagation

The nature of flexural rigidity of graphene monolayers and a formation of the quasi-flexural modes in a graphite and the graphene nano-films is explained. It is shown, that in the major part of the band of quasi-continuous spectrum, quasi-flexural modes do not practically couple with the modes polarized in the plane of the layer. The frequencies of propagone zone are determined for the phonons with various polarizations. The existence of high-frequency propagation zone is demonstrated for quasi-flexural phonons. The conditions for a formation of quasi-local vibrations and boson peaks are analyzed for modes with different polarization. The conditions for the formation of the quasi-local vibrations and boson peaks in the modes of different polarization are analyzed.