Cooper pairing with finite angular momentum: BCS vs Bose limits

TL;DR

This paper explores exotic superconductivity with finite angular momentum pairing, analyzing the BCS to Bose crossover, and finds that symmetry is restored in the Bose limit with higher critical temperatures for s-wave pairs.

Contribution

It introduces a framework connecting finite angular momentum pairing to interactions at finite distances and examines symmetry restoration in the BCS-Bose crossover.

Findings

Symmetry is restored in the Bose limit due to lower energy s-wave bound states.

Critical temperature is higher for s-wave (l=0) pairs in the Bose limit.

Symmetry breaking occurs at intermediate densities with non-monotonic interactions.

Abstract

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 phenomenonn is associated with interactions that keep electrons at some particular, finite distance (r_{0}), and occurs at a range of intermediate densities (n\sim 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.