Multifractality of the quantum Hall wave functions in higher Landau levels

Details Multifractality of the quantum Hall wave functions in higher Landau levels Multifractality of the quantum Hall wave functions in higher Landau levels

1996-06-24

arxiv.org/abs/cond-mat/9606164v1

Physics

Condensed Matter

10 pages, revtex, 5 figures available on request from aoki@phys.s.u-tokyo.ac.jp

Scientific paper

10.1103/PhysRevB.54.10350

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.

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