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

TL;DR

This paper investigates the groundstate evolution from BCS superconductivity to Bose-Einstein condensation in a $d_{x^{2}-y^{2}}$ wave superconductor, highlighting the conditions for bosonic behavior emergence and its effects on groundstate properties.

Contribution

It provides a detailed analysis of the BCS-BEC crossover in a $d_{x^{2}-y^{2}}$ superconductor, emphasizing the role of density and the exclusion principle.

Findings

Bosonic degrees of freedom emerge only in the dilute limit.

Significant changes in the one-particle distribution function occur with bosonic behavior.

Groundstate properties vary notably with density and pairing symmetry.

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.