We have addressed one of the most important and basic results in disordered systems, namely the complete localization of noninteracting electrons in two dimensions even at infinitesimal disorder. We present a proof of this assertion by combining some finer aspects of the behavior of self-avoiding random walks with Anderson’s original approach to localization where a renormalized perturbation expansion of self-energy, whose terms have the self-avoiding random-walk character, was analyzed.

• Received 18 October 2005

DOI:https://doi.org/10.1103/PhysRevB.73.033404