Hall potential distribution in a thin layer as a function of its thickness

A self-consistent equation is derived for the Hall potential distribution of an electron gas with filled Landau levels in a thin layer taking into account its thickness and the magnetic field B j generated by the current distribution inside the layer. It is found that for parameter values corresponding to quantum Hall effect experiments the weighting of the potential distribution toward the layer edges is considerably reinforced due to the field B j . This effect increases with decreasing layer thickness.