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 wavefunction φE=ψ(1) ext+ ψ(2) ext/r. For large length scales, φE changes into pure power-law states, φE = C/r S. For S > 1, diffusive transport is predicted with σdif ∼T S/(S+1). For stronger disorder, S increases and for S < 1, hopping conduction is predicted. In this region the negative magnetoresistance 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.