Disorder Induced BCS-BEC Crossover in an Ultracold Fermi Gas

We develop the formalism for BCS-BEC crossover in the presence of weak random impurity and calculate the effect of the random potentials on the basic mean-field quantities. The disorder has been included through the Nozieres and Schmitt-Rink theory of superconducting fluctuations, and we obtain the disorder induced superfluid order parameter and chemical potential through a self-consistent calculation. We also calculate the condensate fraction which reveals a distinct nonmonotonic behavior. The downturn in the latter result occurs at the crossover regime with gradual depletion on the BEC side. The non-monotonic feature in the condensate fraction data has been measured in clean systems. Motivated by the above result, we discuss the stability of a disordered fermionic superfluid in the crossover regime.