Theory of Magneto--Acoustic Transport in Modulated Quantum Hall Systems Near $\nu=1/2$

TL;DR

This paper develops a theoretical model explaining anomalous magneto-transport phenomena in a modulated 2DEG near filling factor 1/2, linking observed effects to deformation of the composite fermion Fermi surface caused by density modulation.

Contribution

It introduces a new model of a deformed composite fermion Fermi surface to explain experimental anomalies in magneto-transport near =1/2.

Findings

Nonlinear wave vector dependence of conductivity

Peaks in SAW velocity shift and attenuation

Anisotropic response due to flattened Fermi surface regions

Abstract

Motivated by the experimental results of Willett et al [Phys.Rev. Lett., {\bf 78}, 4478 (1997)] we develop a magneto-transport theory for the response of a two dimensional electron gas (2DEG) in the Fractional Quantum Hall Regime near Landau level filling factor $\nu = 1/2$ 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 $\nu = 1/2$, and we show that the deformation of the (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 non-local case which corresponds to the SAW experiments. We introduce a new 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 $\nu = 1/2:$ 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 CF-FS which are flattened by the applied modulation.