Cooper pairing with finite angular momentum: BCS versus Bose limits

We revisit the old problem of exotic superconductivity as Cooper pairing with finite angular momentum emerging from a central potential.

Based on some general considerations, we suggest that the phenomenon

is associated with interactions that keep electrons at some particular,

finite distance r(0), and occurs at a range of intermediate densities

n similar to 1/r(0)(3). We discuss the ground state and the critical

temperature in the framework of a standard functional-integral theory

of the BCS to Bose crossover. We find that, due to the lower energy

of two-body bound states with l = 0, the rotational symmetry of the

ground state is always restored on approaching the Bose limit. Moreover

in that limit the critical temperature is always higher for pairs

with l = 0. The breaking of the rotational symmetry of the continuum

by the superfluid state thus seems to be a property of weakly-attractive,

non-monotonic interaction potentials, at intermediate densities.