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

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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)-->3.315 h(2)/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 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>0 in a BCS superconductor.