Power-law localization in two-dimensional systems theory and experiment

It is shown that all the non-metallic transport phenomena in the weak-disorder limit for small length scales result from a quasi-extended wave function [Equation Found]- For large length scales, Φ_E changes into pure power-law states, Φ_E = C/r^S. For S< 1, diffusive transport is predicted with σ_dif - T^S/(S+1). For stronger disorder, S increases and for S> 1, hopping conduction is predicted. In this region the negative magnetoreisistance should disappear. Experimental evidence is given for all the above predictions. We also construct a two-parameter scaling function, appropriate to power-law localization, which is in agreement with experiment. We show that all the available data support the existence of power-law localized states which are separated by a mobility edge from exponential localized states.