One-parameter scaling in the lowest Landau band: Precise determination of the critical behavior of the localization length

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Abstract
The localization properties of noninteracting electrons in the lowest Landau band of a disordered two-dimensional system are investigated using a new version of the numerical finite-size scaling method which includes a quantitative statistical procedure of data evaluation. In contrast to other suggestions, universal one-parameter scaling behavior is obtained. The localization length diverges at the center of the band with a critical exponent ν=2.34±0.04. The critical region is determined to be about half of the bandwidth. Comparison with experimental quantum-Hall-effect data yields the temperature exponent of the phase breaking time p=2.0±0.2.