Bending sound in graphene: origin and manifestation

It is proved that the acoustic-type dispersion of bending mode in graphene is generated by the fluctuation interaction between in-plane and out-of-plane terms in the free energy arising with account of non-linear components in the graphene strain tensor. In doing so we use an original adiabatic approximation based on the alleged (confirmed a posteriori) significant difference of sound speeds for in-plane and bending modes. The explicit expression for the bending sound speed depending only on the graphene mass density, in-plane elastic constants and temperature is deduced as well as the characteristics of the microscopic corrugations of graphene. The obtained results are in good quantitative agreement with the data of real experiments and computer simulations.
Comment: 10 pages, 3 figures