Localization length at the conductivity minima of the quantum Hall effect

Abstract

Abstract The quantum localization is known to be responsible for the deep conductivity minima of the quantum Hall effect. In this paper we calculate the localization length ξ as a function of magnetic field B at such minima for several models of disorder (“white-noise”, short-range, and long-range random potentials). We find that ξ∝B−α with the exponent α between one and 10 3 , depending on the model. In particular, for the “white-noise” random potential ξ roughly coincides with the classical cyclotron radius. Our results are in agreement with available experimental data.