Hopping anisotropies: A candidate for BCS-BEC crossover

In a two-dimensional t-J model that includes anisotropy in the hopping frequency of the charge carriers, the crossover scenario from a BCS superconductor to a condensate of tightly bound bosonic pairs is studied. The important length scales, such as the mean pair radius and penetration depth, are obtained as a function of the anisotropy parameter that distinguishes hopping in one direction with respect to the other. The results indicate a smooth evolution from a picture of highly overlapping Cooper pairs to a condensate of short-range bosonic pairs with increasing anisotropy. The claim for the crossover phenomena is supported by calculating the renormalized chemical potential which slips below the band minimum in the extreme anisotropy limit, implying the onset of a Bose phase.