Quantized Multichannel Magnetotransport through a Barrier in Two Dimensions

Magnetoresistance measurements in a $\frac{{\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}}{\mathrm{GaAs}}$ heterojunction with a gate covering a small region of the sample reveal quantized values for certain ranges of gate voltage; these are explainable in terms of a Landauer resistance formula. The quantization occurs when the voltage probes are located in a region of dissipationless current flow, where the quantum Hall effect provides a physical realization of ideal leads. The measurements distinguish dramatically between different multichannel generalizations of the Landauer formula.