Groundstate properties of the BCS-Bose Einstein crossover in a $d_{x^{2}-y^{2}}$ wave superconductor

Abstract

We examine the groundstate properties of the crossover between BCS superconductivity and Bose Einstein condensation within a model which exhibits $d_{x^{2} - y^{2}}$ pairing symmetry. We compare results for zero temperature with known features of s-wave systems and show that bosonic degrees of freedom are likely to emerge only in the dilute limit. We relate the change in properties of the groundstate as a function of density to the effect of the exclusion principle and show that the one particle distribution function undergoes a significant change when bosonic behavior appears.