Scaling Behavior of Level Spacing Distribution in the Lowest Landau Band of Two-Dimensional Disordered Electrons

Abstract

The spacing distributions of unfolded energy levels in the lowest Landau band formed in disordered two-dimensional electron systems are numerically studied for different energy regions. By fitting the distribution function to an appropriate interpolation formula, the level repulsion parameter β is obtained as a function of the unfolded energy x. The functional forms of β(x) for different system sizes are found to exhibit a certain scaling behavior. From this scaling property, it is possible to estimate the exponent of the localization length as a function of energy, which is found to be 2.4±0.2, consistent with previously reported values. Possible applications to other Anderson transitions are also discussed.