Finite-Size Scaling Study of Localization in Landau Levels

Abstract

The electron localization in the two-dimensional system 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, α, is shown to have a power law dependence on energy around the center of the Landau level, E N , with α( E )∝| E - E N | s . For short-range scatterers, the critical exponent, s , is found to be close to 2(4) for N =0(1) Landau level, while the localization is much stronger for long-range scatterers.