Flexural phonons in supported graphene: from pinning to localization
We identify graphene layer on a disordered corrugated substrate as a system where localization of phonons can be observed. In this case, the scattering time induced by a substrate for the out of plane vibrations, so-called flexural phonons, for vanishing wave vector tends to a finite limit. One may, therefore, expect that physics of the flexural phonons exhibits features characteristic for electron localization in two dimensions, albeit without complications caused by the electron-electron interactions. We confirmed this idea by calculating statistical properties of the Anderson localization of flexural phonons for a model of elastic sheet in the presence of the pinning centers. We discussed possible manifestations of the flexural phonons, including the localized ones, in the electronic thermal conductance.