Surface acoustic wave propagation in graphene

Surface acoustic wave (SAW) propagation is a powerful method to investigate two-dimensional (2D) electron systems. We show how SAW observables are influenced by coupling to the 2D massless Dirac electrons of graphene and argue that Landau oscillations in SAW propagation can be observed as function of gate voltage for constant field. Contrary to other transport measurements, the zero-field SAW propagation gives the wavevector dependence of graphene conductivity for small wave numbers. We predict a crossover from Schrodinger to Dirac-like behavior as a function of gate voltage, with no attenuation in the latter for clean samples.