Exotic pairing via a central attraction: from the BCS to the Bose limits

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 inter-particle distance r_s which we deem generic to interactions of this type. However such interplay, responsible for the preference of a d-wave state for a range of intermediate densities, 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(\hbar^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.