Two-dimensional Fermi gases at a p-wave resonance

We study the possibility of $p$-wave superfluid of two-dimensional Fermi gases at a $p$-wave resonance using a two-channel model. Supplemented by an $\epsilon$-expansion near two dimensions, a systematic analysis is carried out at the broad-resonance limit when the interchannel coupling is strong. We show that a homogeneous p-wave pairing expected at the mean-field level is actually unstable due to fluctuation effects, in contrast to the previously predicted $p+ip$ superfluid at the narrow-resonance limit. This implies an onset of instability when the interchannel coupling is increased.