Abstract
A nonequilibrium distribution of carrier concentration across the sample caused by the Lorenz force is the origin of the Hall electric field. This distribution as well as the electrical and chemical potential profiles in the Hall direction are calculated for both three- and two-dimensional electron gases. In the three-dimensional case the deviation of electron concentration from its equilibrium value is rather small and located only near the sample edges. In the two-dimensional case the difference in electron concentrations at opposite sample edges is much more considerable and does not saturate with the sample size. At high magnetic field when the quantum Hall effect occurs, the difference in Fermi quasi-levels at the sample edges must be equal to the Landau level separation times an integer in large intervals of applied voltage, which has been observed in the experiment.
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