Quantized magnetoresistance in multiply connected perimeters in two-dimensional systems

It is shown that multiply connected perimeter contacts of a two-dimenisonal system in the quantized-Hall-effect (QHE) regime have two-terminal resistance values equal to a well-defined rational fraction of $\frac{h}{e^2}$, depending on the interconnection configurations. A phenomenological model is presented to account for the results which is consistent with quantized dissipation in the vicinity of current-carrying contacts. It is further demonstrated that the interior of the system is dissipationless and the effect is not affected by the inclusion of macroscopic inhomogeneities.