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 $l=2\mathrm{}$ 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 $l=2\mathrm{}$ 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 $k_B{T}_c\to 3.315{ħ}^2{/2m}^{*}[n/2\mathrm{}(2l+1)\mathrm{}{]}^{2/3},$ which coincides with the usual result only for $l=0;$ for $l>\mathrm{}0,$ 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 $l>\mathrm{}0\mathrm{}$ in a BCS superconductor.

• Received 19 June 2001

DOI:https://doi.org/10.1103/PhysRevB.66.214526