Localization length at the resistivity minima of the quantum Hall effect

Abstract

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 $\xi$ of such states at even filling factors $\nu = 2 N$. 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, $\xi \propto N^\alpha$ with the exponent $\alpha$ between one and ${10/3}$, depending on the model. In particular, for a ``white-noise'' random potential $\xi$ roughly coincides with the classical cyclotron radius. Our results are in reasonable agreement with experimental data on low and moderate mobility samples.