Resistance maps for a submicron Hall electrosensor in the diffusive regime

The response of a mesoscopic Hall cross to a local potential barrier is calculated from which we derive two-dimensional resistance maps. At zero magnetic field a double butterfly Hall resistance pattern arises in the Hall cross that is attributed to barrier-induced inhomogeneous current flow. Small, i.e., nonquantizing magnetic fields smoothen out the two wings of the butterfly into a single elongated feature. The longitudinal resistance pattern shows the strongest changes in the current leads leading to two well separated (by the cross area) bumps. Symmetry properties are found for the resistance maps (Hall and longitudinal) with respect to the position of the local introduced potential barrier.