# Cooper pairing with finite angular momentum via a central attraction: From the BCS to the Bose limits

Quintanilla, Jorge, Gyorffy, Balazs L., Annett, James F, Wallington, Jonathan P (2002) Cooper pairing with finite angular momentum via a central attraction: From the BCS to the Bose limits. Physical Review B: Condensed Matter and Materials Physics, 66 (21). p. 214526. ISSN 0163-1829. (doi:10.1103/PhysRevB.66.214526) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)

In the context of a simple model featuring an explicit, central interaction potential, and using a standard functional-integral technique, we study superconductivity with angular momentum quantum number l=2 as an emergent property of the many-body system. Our interaction potential is attractive at a finite distance r(0), and the breaking of the rotational symmetry is the result of an interplay between r(0) and the interparticle distance r(s). This interplay is generic to interactions of this type and is responsible for the existence of d-wave pairing for a range of densities. However, we find that l=2 pairing takes place only in the BCS limit. In contrast, as the Bose-Einstein (BE) limit is approached the internal energy of the preformed pairs'' becomes the dominant contribution and there is a quantum phase transition in which the s-wave symmetry is restored. We also find that the limiting value of the critical temperature is k(B)T(c)--&gt;3.315 h(2)/2m(*) [n/2(2l+1)](2/3), which coincides with the usual result only for l=0; for l&gt;0, it differs in the degeneracy factor 1/(2l+1), which lowers T-c. Our results thus place constraints on exotic pairing in the BE limit, while at the same time indicating a particularly interesting route to pairing with l&gt;0 in a BCS superconductor.