EDGE VOLTAGES AND DISTRIBUTED CURRENTS IN THE QUANTUM HALL-EFFECT

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