Abstract

W. Zhao, K. S. Tikhonov, A. M. Finkel'stein

We identify graphene layer on a SiO_2 substrate as a system where Anderson localization of phonons can
be observed. Generally, observation of localization for scattering waves, e.g., acoustic phonons, is not
simple, because the Reighley scattering is inversely proportional to a high power of wavelength. For
example, in two dimensions (2D) the scattering rate of the acoustic phonons is proportional to the third
power of the wave vector. The situation is radically different for the out of plane vibrations (so-called
flexural phonons) scattered by the pinning centers induced by a substrate. In this case, the scattering
time for the vanishing wave vector tends to a constant limit. One may therefore expect that physics of
the flexural phonons exhibits features characteristic for electron localization in 2D, albeit without
complications induced by the electron-electron interactions. To check this we calculated numerically
statistical properties of the model of flexural phonons in the presence of the pinning centers. We argue
that not only localization at short distances for low-energy modes, but also the regime of weak
localization for higher energies is the same as in the two-dimensional disordered Anderson model.