Velocity Shift of Surface Acoustic Waves due to Interaction with Composite Fermions in a Modulated Structure

We study the effect of a periodic density modulation on surface acoustic wave (SAW) propagation along a 2D electron gas near Landau level filling $\nu =1\mathrm{}/2$. Within the composite fermion theory, the problem is described in terms of fermions subject to a spatially modulated magnetic field and scattered by a random magnetic field. We find that a few percent modulation induces a large peak in the SAW velocity shift, as observed recently by Willett et al. As further support of this theory we find the dc resistivity to be in good agreement with recent data of Smet et al.