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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.
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A seminal gedankenexperiment by Laughlin describes the charge transport in quantum Hall systems via the pumping of flux. Here, we propose an optical scheme which probes and manipulates quantum Hall systems in a similar way: When light containing orbi
We report on numerical studies into the interplay of disorder and electron-electron interactions within the integer quantum Hall regime, where the presence of a strong magnetic field and two-dimensional confinement of the electronic system profoundly
Statistical properties of critical wave functions at the spin quantum Hall transition are studied both numerically and analytically (via mapping onto the classical percolation). It is shown that the index $eta$ characterizing the decay of wave functi
Using scanning tunneling spectroscopy in ultra-high vacuum at low temperature (T = 0.3 K) and high magnetic fields (B < 12 T), we directly probe electronic wave functions across an integer quantum Hall transition. In accordance with theoretical predi