Prediction of Aharonov-Bohm oscillations on the quantum hall plateaus of small and narrow rings

It is shown, by use of a Landauer-type formulation of the quantum Hall transport, that in small and narrow two-dimensional rings, the Hall quantization of xy is accompanied by a finite, but small, xx which exhibits periodic Aharonov-Bohm oscillations. These oscillations arise as a subtle consequence of the possible elastic backscattering of the current-carrying electrons in narrow channels.