SCALING OF THE CRITICAL-CURRENT IN THE QUANTUM HALL-EFFECT - A PROBE OF CURRENT DISTRIBUTION

The critical current I(c) for the breakdown of the quantum Hall effect is found to scale logarithmically with the channel width for all Landau levels. We interpret this experimental result as a manifestation of a logarithmic distribution of the Hall potential across the channel. A new perspective on the breakdown mechanism is obtained. Inter-Landau-level transitions, previously thought to predict values of I(c) much too high, are shown to be in quantitative agreement with experiments interpreted in this manner.