Commensurability oscillations in the SAW induced acousto-electric effect in a 2DEG

We study the acousto-electric (AE) effect generated by surface acoustic waves (SAW) in a high mobility 2D electron gas (2DEG) with isotropic and especially small-angle impurity scattering. In both cases the acousto-electric effect exhibits Weiss oscillations periodic in $B^{-1}$ due to the commensurability of the SAW period with the size of the cyclotron orbit and resonances at the SAW frequency $\omega=k\omega_{c}$ multiple of the cyclotron frequency. We describe how oscillations in the acousto-electric effect are damped in low fields where $\omega_{c}\tau_{\ast}\lesssim1$ (with the time scale $\tau_{\ast}$ dependent on the type of scattering) and find its non-oscillatory part which remains finite to the lowest fields.