Tricritical physics in two-dimensional p-wave superfluids near resonance

We study the effect of quantum fluctuations on the stability of two-dimensional (p+ip)-wave superfluids near resonance. The system is a Bardeen-Cooper-Schrieffer superfluid on one side of the resonance and a Bose-Einstein condensate on the other side. When the quantum fluctuations are strong, the interactions between Cooper pairs or bosonic molecules are substantially renormalized. As a result, the interactions between bosonic fields can become attractive at low energy and destabilize the superfluid phase even if the mean-field interactions are repulsive. We find that in the strong coupling limit, there exists a finite region near resonance where the superfluids are unstable and the system undergoes a first order phase transition at its boundary. The size of this region scales as exp(-c/g²), where g is the p-wave interaction constant and c is a numerical factor. Using a simple renormalization group analysis, we identify the tri-critical points which separate the continuous phase transition from the first order phase transition.