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A superfluid-insulator transition is known to occur in strongly disorderedFermi gases, in both the BCS and BEC regimes; here, we address the propertiesof this transition across the BEC-BCS crossover. We argue that the criticaldisorder strength at which superfluidity is lost changes non-monotonically withdetuning from Feshbach resonance, and that a reentrant superfluid phase arisesfor detunings near the fermionic mobility edge. Our analysis of theintermediate regime is quantitatively valid for narrow resonances and near fourdimensions, and provides a simple physical picture of this regime, in terms oftwo distinct but coexisting insulators.

BEC-BCS crossover and the mobility edge: superfluid-insulator transitions and reentrant superfluidity in disordered Fermi gases