Hall voltage and current distributions in an ideal two-dimensional system

The redistribution of charge, which generates the Hall voltage, cannot occur only at the edges in a two-dimensional system but must occur in the bulk. Using a Hartree approximation we derive a self-consistent equation which describes the charge, current, and Hall voltage distributions in a two-dimensional electron gas with filled Landau levels. These distributions are weighted toward the sample edges with a decay length into the bulk which depends on sample size and magnetic field strength.