ONE-PARAMETER SCALING IN THE LOWEST LANDAU BAND

The localization properties of non-interacting 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. A statistical procedure of data evaluation is presented that allows to estimate the errors of the results and to check quantitatively whether the data are compatible with the scaling relations assumed. In contrast to other suggestions, universal one-parameter scaling behaviour is obtained. The localization length diverges at the centre of the band with a critical exponent v = 2.34±0.04. The critical region is determined to be about half of the bandwidth. Comparison with experimental quantum Hall effect data yields p = 2.0±0.2 for the temperature exponent of the phase breaking time. © 1990.