Abstract
We discuss the microscopic mechanism for the onset of dissipation in a quantum Hall system. Based on general results on the time dependence of the states in a disorder-broadened Landau band in the presence of a macroscopic electric field E , it is found that the mobility edges move from the band center towards the band tails when | E | is increased, in agreement with experiments. Since in real samples, | E | is space dependent, the mobility edges are also space dependent. Dissipation (i.e. breakdown of the quantum Hall effect) sets in at points ( x, y), where | E ( x, y)| has the value for which a mobility edge attains the Fermi energy. This value depends on the disorder potential and on the filling factor. Inside a sample, the conductivities depend on | E ( x, y)| and hence on space. We discuss experimental applications, including dissipation in opposite corners of a Hall bar and related breakdown phenomena.
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