Imbalanced ultracold Fermi gas in the weakly repulsive regime: Renormalization-group approach for p -wave superfluidity

We theoretically study a possible pairing mechanism for a two-dimensional population imbalanced Fermi gas with short-range repulsive interactions, which can be realized on the upper branch of a Feshbach resonance. We use a well-controlled renormalization-group approach, which allows an unbiased study of the instabilities of imbalanced Fermi liquid without assumption of a broken symmetry and gives a numerical calculation of the transition temperature from microscopic parameters. Our results show a leading superfluid instability in the $p$-wave channel for the majority species. The corresponding mechanism is that there are effective attractive interactions for the majority species, induced by the particle-hole susceptibility of the minority species, where the mismatch of the Fermi surfaces of the two species plays an important role. We also propose an experimental protocol for detecting the $p$-wave superfluidity and discuss the corresponding experimental signatures.