Electron pairing and evidence of a BCS-BEC crossover in d-wave superconductors

We have demonstrated that it is possible to access a crossover scenario starting with a weak coupling (BCS) d-wave superconductor to a strongly coupled Bose-Einstein condensate (BEC) phase as the exchange interaction is tuned in a two-dimensional system described by a t-J-U model via numerically solving the Bogoliubov-de Gennes (BdG) equations. While in the extreme dilute limit, the electronic pairing phenomenon is independent of the Coulomb repulsion, U, the superconductivity depends on U, and so does the crossover. Further, the effect of variation in the carrier density on the BCS-BEC crossover has also been investigated. The crossover picture is illustrated by computing the chemical potential, which when falls below the noninteracting band minimum, signals the onset of a phase with tightly bound, shorter pairs. As an evidence of the above feature, the Cooper pair radius is calculated which shows a significant shortening at the emergence of a BEC-like phase. Besides, in contrast to the previous work where a crossover was claimed only in the dilute limit, we have demonstrated it at large densities near half filling.