[en] Recent low-temperature scanning-force-microscopy experiments on narrow Hall bars, under the conditions of the integer quantum Hall effect (IQHE) and its breakdown, have revealed an interesting position dependence of the Hall potential, which changes drastically with the applied magnetic field and the strength of the imposed current through the sample. The present paper shows, that inclusion of Joule heating into an existing self-consistent theory of screening and magneto-transport, which assumes translation invariant Hall bars with a homogeneous background charge due to doping, can explain the experimental results on the breakdown of the IQHE in the so called edge-dominated regime.

[en] A previously developed self-consistent screening and magneto-transport theory for laterally confined, translation-invariant quantum-Hall-systems is applied to two-dimensional electron systems created by a donor sheet with a lateral density modulation. The previous calculations, assuming a homogeneous donor charge density, could explain experimental results on the spatial distribution of an applied source-drain-current, and the resulting Hall potential, only for the ‘edge-dominated’ low-magnetic-field part of a quantum-Hall-plateau, where the current flows through incompressible stripes near the edges. For the high-magnetic-field regime of the plateau, they predicted current flow only in a narrow stripe in the center of the sample, whereas the experiments found current in a wide region of its bulk. Assuming a suitably modulated donor charge density, we can avoid this discrepancy, and we obtain a strong dependence of the distribution of the applied current on magnetic field, lattice temperature, and the current-strength. (paper)

[en] First, we present recent experimental results confirming previously predicted strong asymmetries of the current distribution in narrow Hall bars under conditions of the integer quantum Hall effect (IQHE). Then, using a previously developed self-consistent screening and transport theory of the IQHE, we investigate how these asymmetries, which are due to a nonlinear feedback effect of the imposed current on the electron distribution in the sample, depend on relevant parameters, such as strength of the imposed current, magnetic field, temperature and collision broadening of the Landau-quantized energy bands. We find that many aspects of the experimental results can be understood within this approach, whereas other aspects require explicit consideration of additional mechanisms, which may lead to the breakdown of the IQHE. (paper)