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).