The case of disordered two‐dimensional electron systems

Abstract

We investigate the question of the existence or nonexistence of mobility edges that separate the localized and extended states in two‐dimensional disordered electron systems treated within the Anderson model. Evidence is produced to show that the mobility edges exist if the amount of disorder is less than a critical value. The following three different agruments are presented: (1) exact enumeration of self‐avoiding walks that contribute to the renormalized perturbation series of self‐energy whose convergence (divergence) indicates localization (delocalization); (2) “quantum percolation” in a strongly disordered binary alloy; and (3) influence of magnetic field on localized and extended states (the quantum Hall Effect problem). Copyright © 1986 John Wiley & Sons, Inc.