Theory of magnetoacoustic transport in modulated quantum Hall systems nearν=1/2

Abstract

Motivated by the experimental results of Willett et al. [Phys. Rev. Lett. $78,$ 4478 (1997)], we develop a magnetotransport theory for the response of a two-dimensional electron gas (2DEG) in the fractional quantum Hall regime near Landau-level filling factor $\ensuremath{\nu}=1/2$ to the surface acoustic wave (SAW) in the presence of an added periodic density modulation. We assume there exists a composite fermion Fermi surface (CF-FS) at $\ensuremath{\nu}=1/2,$ which is a circle, and we show that the deformation of the circular CF-FS due to the density modulation can be at the origin of the observed transport anomalies for the experimental conditions. Our analysis is carried out particularly for the nonlocal case, which corresponds to the SAW experiments. We introduce a concrete model of a deformed CF-FS. The model permits us to explain anomalous features of the response of the modulated 2DEG to the SAW near $\ensuremath{\nu}=1/2:$ namely, the nonlinear wave-vector dependence of the electron conductivity, the appearance of peaks in the SAW velocity shift and attenuation, and the anisotropy of the effect, all of which originate from contributions to the conductivity tensor due to the regions of the originally circular CF-FS, which are flattened by the applied modulation.