Equipotential distribution in the quantum Hall effect

We have measured peripheral and interior contact voltages in modulation-doped GaAs-${\mathrm{Al}}_{\mathrm{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As heterojunctions while observing the quantum Hall effect. We find that even in plateau regions, large potential differences exist in the interior of the specimens and are not confined to the edges of the sample. Equipotential maps constructed from the data show why voltages measured on the periphery of the sample remain constant in plateau regions despite gross changes in the patterns in the specimen interior.