Cooper pair delocalization in disordered media

TL;DR

This paper investigates how disorder affects the delocalization of Cooper pairs, revealing a transition from delocalized to localized states influenced by disorder strength, supported by theoretical and numerical analysis.

Contribution

It extends the Anderson theorem to the Cooper problem, showing that pair wave functions can remain extended in disordered media under certain conditions.

Findings

Pair wave functions extend beyond single-particle localization length when the single-particle states are large.

A transition occurs from delocalization to enhanced localization of pairs as disorder increases.

Numerical simulations support the theoretical predictions about the localization transition.

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.