Levitation of the quantum Hall extended states in the $Bto$ 0 limit

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 $eta$ is combined into a single dimensionless parameter $hateta=eta/l_B$. 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.