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 $\psi$ 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.

10 pages, revtex, 5 figures available on request from [email protected]

References in corpus (3)

• Scaling Theory of the Integer Quantum Hall Effect
• Mutifractal Analysis of Broadly Distributed Observables at Criticality
• Corrections to Scaling in the Integer Quantum Hall Effect

Cited by in corpus (6)

• Observation of multifractality in Anderson localization of ultrasound
• Quantum Hall plateau transition in graphene with spatially correlated random hopping
• Localization and conductance fluctuations in the integer quantum Hall effect: Real--space renormalization group approach
• Phase Structure of the Topological Anderson Insulator
• Universal Conductance and Conductivity at Critical Points in Integer Quantum Hall Systems
• Statistical properties of two-particle transmission at Anderson transition