Multifractality of the quantum Hall wave functions in higher Landau levels

TL;DR

This study investigates the multifractality of quantum Hall wave functions in higher Landau levels, revealing persistent parabolic spectra and scaling behaviors consistent with universality in quantum critical phenomena.

Contribution

It demonstrates that the multifractal spectrum retains a parabolic form in higher Landau levels, extending the understanding of universality in quantum Hall systems.

Findings

Multifractal spectrum $f()$ varies with Landau level $N$.

Parabolic form of $f()$ persists in higher Landau levels.

Asymptotic single-parameter scaling observed with increasing potential range.

Abstract

To probe the universality class of the quantum Hall system at the metal-insulator critical point, the multifractality of the wave function $\psi$ is studied for higher Landau levels, $N=1,2$, for various range $(\sigma )$ of random potential. We have found that, while the multifractal spectrum $f(\alpha)$ (and consequently the fractal dimension) does vary with $N$, the parabolic form for $f(\alpha)$ indicative of a log-normal distribution of $\psi$ 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 $\sigma$ is seen, in agreement with Huckestein's irrelevant scaling field argument.