The evolution from BCS to BEC superfluidity in the presence of disorder

TL;DR

This paper investigates how disorder impacts the critical temperature of s-wave superfluids across the BCS to BEC crossover, revealing that disorder affects superfluidity differently depending on the regime, with robustness near unitarity.

Contribution

It provides a detailed theoretical analysis of disorder effects on superfluid critical temperature across the BCS-BEC transition using functional integral and replica methods.

Findings

Disorder has minimal effect on critical temperature in the BCS regime due to Anderson's theorem.

In the BEC regime, disorder can significantly lower the critical temperature by disrupting phase coherence.

Superfluidity near unitarity is more resilient to disorder than in the pure BCS or BEC limits.

Abstract

We describe the effects of disorder on the critical temperature of $s$-wave superfluids from the BCS to the 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 which 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 conspire 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 affect dramatically 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.