Localization Length and Inverse Participation Ratio of Two Dimensional Electron in the Quantized Hall Effect

Abstract

The inverse participation ratio, whose nonvanishing value represents the localized state, is calculated for the two dimensional lowest Landau level in the presence of a random potential. In the band tail, an exact value for the inverse participation ratio is obtained for the Gaussian while noise random potential and the state becomes localized. By the large order perturbational analysis, the exponent for the localization length around the band center is estimated. A 1/N expansion is also considered for the inverse participation ratio.