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

A superfluid-insulator transition is known to occur in strongly disordered Fermi gases, in both the BCS and BEC regimes; here, we address the properties of this transition across the BEC-BCS crossover. We argue that the critical disorder strength at which superfluidity is lost changes non-monotonically with detuning from Feshbach resonance, and that a reentrant superfluid phase arises for detunings near the fermionic mobility edge. Our analysis of the intermediate regime is quantitatively valid for narrow resonances and near four dimensions, and provides a simple physical picture of this regime, in terms of two distinct but coexisting insulators.