Current distribution in antidot arrays near the breakdown of the quantum Hall effect

Breakdown currents of the quantum Hall effect (QHE) in two-dimensional electron systems containing an array of antidots were found to scale linearly with the sample widths. Therefore, we apply a local Drude type model with Hall angle theta approximate to 90 degrees to calculate using the continuity equation, for a given average current, the current density and the potential. We find that, with increasing tan theta, the current density is increasingly expelled from the regions occupied by the antidots, and twisted vortex structures evolve around the antidots. From the distribution of hot spots and cold regions in the antidot array we can understand many of the recent experimental results. (C) 1998 Elsevier Science B.V. All rights reserved.