Cooper pair delocalization in disordered media

Abstract

We discuss the effect of disorder on the coherent propagation of the bound state of two attracting particles. It is shown that a result analogous to the Anderson theorem for dirty superconductors is also valid for the Cooper problem, namely, that the pair wave function is extended beyond the single-particle localization length if the latter is large. A physical justification is given in terms of the Thouless block-scaling picture of localization. These arguments are supplemented by numerical simulations. With increasing disorder we find a transition from a regime in which the interaction delocalizes the pair to a regime in which the interaction enhances localization.