Inhomogeneity near Hall-bar intersections in the diffusive regime

Determine whether the assumption of a homogeneous two-dimensional electron system inside a Hall bar used in the Drude-based multi-terminal current-division model fails near contact intersections in the diffusive transport regime, and characterize the resulting spatial inhomogeneity of the in-plane electric fields E_x and E_y and its impact on the partitioning of the ohmic current component I_xx relative to the transverse component I_xy.

Background

Away from the quantum Hall plateaus, the authors observe that measured multi-terminal currents depend on contact configuration beyond the predictions of their Drude-based model, which assumes a homogeneous Hall bar and a homogeneous internal electric field. They argue that near intersections, both E_x and E_y become inhomogeneous, affecting the division of I_xx while I_xy remains bent into contacts.

To account for these deviations, they explicitly conjecture that their homogeneity assumption fails near intersections in the diffusive regime, motivating a more refined modeling of spatially varying fields and current division near junctions.