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

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 $l_B=(\hslash /(eB){)}^{1/2}$ and on the correlation length of the disorder potential $\eta$ is combined into a single dimensionless parameter $\hat{\eta }=\eta /l_B$. 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.

7 pages, 9 figures. Replaced with published version