Landau level broadening without disorder, non-integer plateaus without interactions - an alternative model of the quantum Hall effect

Tobias Kramer

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arXiv · cond-mat/0601621

Landau level broadening without disorder, non-integer plateaus without interactions - an alternative model of the quantum Hall effect

Tobias Kramer

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Abstract

I review some aspects of an alternative model of the quantum Hall effect, which is not based on the presence of disorder potentials. Instead, a quantization of the electronic drift current in the presence of crossed electric and magnetic fields is employed to construct a non-linear transport theory. Another important ingredient of the alternative theory is the coupling of the two-dimensional electron gas to the leads and the applied voltages. By working in a picture, where the external voltages fix the chemical potential in the 2D subsystem, the experimentally observed linear relation between the voltage and the location of the quantum Hall plateaus finds an natural explanation. Also, the classical Hall effect emerges as a natural limit of the quantum Hall effect. For low temperatures (or high currents), a non-integer substructure splits higher Landau levels into sublevels. The appearence of substructure and non-integer plateaus in the resistivity is NOT linked to electron-electron interactions, but caused by the presence of a (linear) electric field. Some of the resulting fractions correspond exactly to half-integer plateaus.

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Tobias Kramer. 2006-01-31. Landau level broadening without disorder, non-integer plateaus without interactions - an alternative model of the quantum Hall effect. https://arxiv.org/abs/cond-mat/0601621

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