Nonequilibrium distribution of edge and bulk current in a quantum Hall conductor

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Abstract
A quantitative model is presented that accounts for the experimental observation that four-terminal resistances of a high-mobility quantum Hall conductor cannot be related directly to a single resistivity tensor. The key ingredient is that the highest (partly occupied) Landau level is completely decoupled from the other levels except at the contacts. The current carried by the top level alone is related through a resistivity tensor to the longitudinal and the transverse electric-field components. Deviations from a homogeneous current distribution close to the contacts are taken into account. For the other (fully occupied) Landau levels the usual edge-channel description is used. It is shown how the electric field can be incorporated into this description in order to obtain a consistent model. A mechanism for the onset of nonlinear behavior is given.