Critical localization in two-dimensional Landau quantization

The localization in two-dimensional disordered electron systems in strong magnetic fields is investigated by the finite-size scaling method. The scaling function numerically obtained for macroscopically long systems shows that the single-parameter scaling is invalid. The inverse localization length is found to have a novel critical behavior near the center of the Landau band, in which the Landau-index--dependent critical exponent determines the behavior of conductivity.