Edge voltages and distributed currents in the quantum Hall effect

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Abstract
It is shown from rather general assumptions that the current density at low temperatures in the interior of a quantum Hall device follows the electric field distribution, smeared out over an appropriate localization length. This is not in conflict with Laughlin’s result that the total Hall current depends only on the potential difference between the edges, but must be used to complement it. It is illustrated by a discussion of edge and bulk currents for a Hall bar under the conditions of the integer quantum Hall effect. It is argued that these results can be extended to the fractional quantum Hall effect.