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

TL;DR

This study examines how quantum Hall extended states behave as magnetic field approaches zero, revealing disorder-dependent levitation saturation consistent with some experimental observations.

Contribution

It demonstrates that the levitation of the $n=0$ critical states persists in a continuum model with correlated disorder when considering at least two Landau bands, introducing a unified parameter for analysis.

Findings

Levitation of $n=0$ states occurs with two Landau bands.

Critical state levitation saturates depending on disorder strength.

Results align with certain experimental findings.

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 $\eta$ 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.