Coulomb interactions and the integer quantum Hall effect: Screening and transport

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Abstract
We examine the influence of Coulomb interactions on the integer quantum Hall effect in high-mobility, wide spacer-layer heterostructures. In these devices, the potential due to disorder is expected to be smooth on the scale of the spacer-layer thickness, which can be much larger than the magnetic length. Screening of this potential is accompanied by large fluctuations in electron density and has dramatic consequences. In particular, the screened potential can be pinned to the Fermi energy in regions of the sample, and these regions can percolate over a range of Landau-level filling fractions. We present a theory for transport that includes screening within the Thomas-Fermi approximation. Considering the Hall conductance as a function of filling fraction, we show that risers between quantized Hall plateaus acquire a finite width in the presence of Coulomb interactions. We also show that, under certain circumstances, current flows within the sample only along narrow strips, concentrated around particular contours of the equilibrium electron density.