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Levitation of the quantum Hall extended states in the $B\to$ 0 limit

Th. Koschny·L. Schweitzer
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Abstract

We investigate the fate of the quantum Hall extended states within a continuum model with spatially correlated disorder potentials. The model can be projected onto a couple of the lowest Landau bands. Levitation of the $n=0$ critical states is observed if at least the two lowest Landau bands are considered. The dependence on the magnetic length $l_B=(\hbar/(eB))^{1/2}$ and on the correlation length of the disorder potential $η$ is combined into a single dimensionless parameter $\hatη=η/l_B$. This enables us to study the behavior of the critical states for vanishing magnetic field. In the two Landau band limit, we find a disorder dependent saturation of the critical states' levitation which is in contrast to earlier propositions, but in accord with some experiments.

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Th. Koschny, L. Schweitzer. 2004-10-06. Levitation of the quantum Hall extended states in the $B\to$ 0 limit. https://doi.org/10.1103/physrevb.70.165301

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