Title: Flexural phonons in supported graphene: from pinning to localization,
Abstract: We identify graphene layer on a disordered substrate as a possible system
where Anderson localization of phonons can be observed. Generally, observation
of localization for scattering waves is not simple, because the Rayleigh
scattering is inversely proportional to a high power of wavelength. The
situation is radically different for the out of plane vibrations, so-called
flexural phonons, scattered by pinning centers induced by a substrate. In this
case, the scattering time 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 confirm
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. Finally, we discuss possible manifestations of the flexural phonons,
including the localized ones, in the electronic thermal conductance.