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

Jorge Quintanilla; Balazs L. Györffy; James F. Annett; Jonathan P. Wallington

doi:10.1103/PhysRevB.66.214526

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

Jorge Quintanilla, Balazs L. Györffy, James F. Annett, Jonathan P. Wallington

DOI 10.1103/PhysRevB.66.214526 · Physical Review B

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Abstract

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 r0, and the breaking of the rotational symmetry is the result of an interplay between r0 and the interparticle distance rs. 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 kBTc→3.315ħ2/2m*[n/2(2l+1)]2/3, which coincides with the usual result only for l=0; for l>0, it differs in the degeneracy factor 1/(2l+1), which lowers Tc. 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>0 in a BCS superconductor.