Multifractality of the quantum Hall wave functions in higher Landau levels

Abstract

To probe the universality class of the quantum Hall system at the metal-insulator critical point, the multifractality of the wave function $ψ$ is studied for higher Landau levels, $N=1,2$, for various range $(σ)$ of random potential. We have found that, while the multifractal spectrum $f(α)$ (and consequently the fractal dimension) does vary with $N$, the parabolic form for $f(α)$ indicative of a log-normal distribution of $ψ$ persists in higher Landau levels. If we relate the multifractality with the scaling of localization via the conformal theory, an asymptotic recovery of the single-parameter scaling with increasing $σ$ is seen, in agreement with Huckestein's irrelevant scaling field argument.