Effect of impurity interaction on the Anderson localization

Anderson localization is reexamined in the presence of interaction between impurities in two and three dimensions. The interaction gives rise to local order or, alternatively, to a correlated impurity probability distribution. This distribution is constructed explicitly with use of mean-field theory for a model system of a disordered binary alloy with one of the components modeling the impurities. The new probability distribution is then used to recalculate perturbatively the conductivity, starting from the metallic limit. When the interaction between impurities is repulsive, the conductivity is found to decrease relative to the noncorrelated case. The results are also analyzed with use of the renormalization group. If short-range interactions are considered, the critical exponents are unchanged but the value of the fixed-point coupling depends on some model parameters, which we relate to the experimental ones. Our results then fit qualitatively well the experimental data obtained for two quite different systems. In both cases, by varying the strength of the local order in a way specific to each experiment, a metal-insulator transition is induced even if, in the absence of any ordering, the system is metallic.