It is shown that the Debye-Waller factor for graphene has a singularity. However, the singularity does not affect the zero-temperature value of the Debye-Waller factor. We calculate the zero-temperature limit of the mean-square displacement separately for planar and out-of-plane modes for graphene. These values give the Debye-Waller factor which can be used to model the scattering processes at temperatures much lower than the Debye temperature of graphene. Since the effective Debye temperature of graphene is quite high, 2312 and 1287 deg K, respectively, for the planar and the out of plane modes, the calculated values should be useful in most cases of practical interest.
Physics Letters B
graphene, phonon Green's function, Debye-Waller factor, correlation function, frequency spectrum