Scaling of the critical current in the quantum Hall effect: A probe of current distribution

The critical current ${\mathit{I}}_{\mathit{c}}$ 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, and hence current, across the channel. A new perspective on the breakdown mechanism is obtained. In particular, inter-Landau-level transitions, previously thought to predict values of ${\mathit{I}}_{\mathit{c}}$ much too high, are actually shown to be in quantitative agreement with experiments interpreted in this manner.