BCS–BEC crossover and potential vs kinetic energy driven pairing in anisotropic superconductors

Abstract

The crossover from a BCS superconductor to a Bose-like condensate has been studied in a two-dimensional t - J model that incorporates hopping anisotropies of the charge carriers. The claim for the crossover phenomenon in the anisotropic system is supported by calculating an important length scale that characterizes a condensate, viz the radius of the Cooper pairs ( ξ pair ). Interestingly, ξ pair shrinks from a few thousands of lattice spacings in the isotropic case to as low as a few lattice spacings in the limit of extreme hopping anisotropy. Thus a system of large and overlapping Cooper pairs (BCS regime) corresponding to the isotropic case smoothly evolves into one that is characterized by short and tightly bound pairs (reminiscent of a Bose superfluid) in the presence of large anisotropies. Further, to question a recently made conjecture on a kinetic energy driven superfluid transition in the context of a Bose condensate, as opposed to a conventional potential energy driven superconductivity, we compute the condensation energy for the anisotropic case. We found that the kinetic energy does not play a key role in the superconducting transition, rather the superconductivity is still driven by potential energy.