Localization length at the resistivity minima of the quantum Hall effect

The resistivity minima of the quantum Hall effect arise due to the localization of the electron states at the Fermi energy, when it is positioned between adjacent Landau levels. In this paper we calculate the localization length (Formula presented) of such states at even filling factors (Formula presented). The calculation is done for several models of disorder (“white-noise,” short-range, and long-range random potentials). We find that the localization length has a power-law dependence on the Landau level index, (Formula presented) with the exponent (Formula presented) between one and (Formula presented), depending on the model. In particular, for a “white-noise” random potential (Formula presented) roughly coincides with the classical cyclotron radius. Our results are in reasonable agreement with experimental data on low and moderate mobility samples.