Condensed Matter Theory

Abstract:

We review the network model for the integer quantum Hall effect. The model provides a simplified description of Anderson localization in this context. It represents non-interacting electrons moving in two dimensions under the combined influence of a strong magnetic field and a smooth disordered potential. In this setting, electron eigenstates form disorder-broadened Landau levels and their character varies with energy across the Landau level. States in both the low-energy and the high-energy tails of the Landau level are localized, with a spatial extent characterized by the localization length. At the center of the Landau level there is a transition between phases with different quantized values of the Hall conductance and the localization length is divergent. The network model captures universal features of this transition.