Current distribution and Hall potential landscape at the breakdown of the Quantum Hall Effect

The Quantum Hall effect (QHE) is used since 1990 in metrology to provide a resistance standard. The breakdown of the QHE at high bias current level limits the precision, with which the standard value can be reproduced. For about a decade we have used a scanning probe technique under QHE conditions to determine the Hall potential landscape inside a two-dimensional electron system (2DES), embedded in a (Al,Ga)As heterostructure. We obtained a clear, detailed microscopic picture how the current is distributed, and how this distribution evolves when the magnetic field is changed. Within a Hall resistance plateau, the current flows in incompressible regions of the 2DES, realized by a region of completely filled Landau states under the local Fermi level, which obtain an additional drift velocity due to the local Hall field. This contradicts to the popular picture of current carrying edge states. Recently we investigated the evolution of the Hall potential landscape with increasing current bias, respectively, increasing Hall voltage, for different magnetic field values inside the QHE plateau. The results are now perfectly understood in terms of our microscopic picture, where the presence and evolution of the incompressible landscape inside the 2DES dominates the current distribution even under high bias.