SIZE-DEPENDENT NONOHMIC BEHAVIOR AT A QUANTUM HALL PLATEAU

The longitudinal resistivity of quantum Hall plateaus has been studied for different sample width and sample currents. The critical currents for the breakdown of the quantum Hall effect was found to be proporti onal to the width of the samples. A subcritical rise of the mid-platea u resistivity was found to be exponentially dependent on the current d ivided by the sample width, and the exponent was found to scale with t he critical current. We explain this subcritical behaviour in terms of thermally activated electrons at points of maximal field gradients. T he critical current is due to a thermal run-away.