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.

arXiv comment7 pages, 9 figures. Replaced with published version

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Cited by in corpus (6)

• Anderson Localization and Quantum Hall Effect: Numerical Observation of Two Parameter Scaling
• Anti-Levitation in the Integer Quantum Hall Systems
• Weakly chiral networks and 2D delocalized states in a weak magnetic field
• Levitation and percolation in quantum Hall systems with correlated disorder
• Phase diagram of weak-magnetic-field quantum Hall transition quantified from classical percolation
• A simple microscopic description of quantum Hall transition without Landau levels