The influence of electrical contacts on the magnetotransport in the quantized Hall regime is measured and calculated for various geometries in GaAs-${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As heterostructures. The observed effects are interpreted in terms of a local resistivity tensor without taking into account the possible existence of macroscopic quantum states or localization. We approximate the experimental geometries by a network of simple rectangles with (or without) contacts. We shows that this simple approach leads to a good picture of the physics behind the potential distribution. To test our approach, we measure the voltages on two multiply connected Hall bars. In special geometries with large contacts we measure a two-terminal resistance that is smaller than the Hall resistivity. Both observations can be reproduced in our calculations. Furthermore the effects of large Hall contacts in a normal Hall bar geometry are calculated and it is shown that the measured Hall resistance can be smaller than the true Hall resistance, with their difference proportional to the magnetoresistance. The dip which is often observed at the strong-field side of Hall plateaus can also be explained by the influence of (large) contacts. This shows that many of the experimental observations can be described successfully, extending our interpretation in terms of a (inhomogeneous) local resistivity tensor to real samples with metal contacts.

• Received 8 July 1988

DOI:https://doi.org/10.1103/PhysRevB.38.13297