Evolution from Bardeen–Cooper–Schrieffer to Bose–Einstein condensate superfluidity in the presence of disorder

Abstract

We describe the effects of disorder on the critical temperature of s-wave superfluids from the Bardeen–Cooper–Schrieffer (BCS) to the Bose–Einstein condensate (BEC) regime, with direct application to ultracold fermions. We use the functional integral method and the replica technique to study Gaussian correlated disorder due to impurities, and we discuss how this system can be generated experimentally. In the absence of disorder, the BCS regime is characterized by pair breaking and phase coherence temperature scales that are essentially the same, allowing strong correlations between the amplitude and phase of the order parameter for superfluidity. As non-pair-breaking disorder is introduced, the largely overlapping Cooper pairs seek to maintain phase coherence such that the critical temperature remains essentially unchanged, and Anderson's theorem is satisfied. However, in the BEC regime, the pair breaking and phase coherence temperature scales are very different such that non-pair-breaking disorder can dramatically affect phase coherence, and thus the critical temperature, without the requirement of breaking tightly bound fermion pairs simultaneously. In this case, Anderson's theorem does not apply, and the critical temperature can be more easily reduced in comparison to the BCS limit. Lastly, we find that the superfluid is more robust against disorder in the intermediate region near unitarity between the two regimes.