Resonantly interacting p-wave Fermi superfluid in two dimensions: Tan's contact and the breathing mode

Inspired by the renewed experimental activities on p-wave resonantly interacting atomic Fermi gases, we investigate theoretically some experimental observables of such systems at zero temperature in two dimensions, using both mean-field theory and Gaussian pair fluctuation theory. These observables include the two p-wave contact parameters and the breathing mode frequency, which can be readily measured in current cold-atom setups with K-40 and Li-6 atoms. We find that the many-body component of the two contact parameters exhibits a pronounced peak slightly above the resonance and consequently leads to a dip in the breathing mode frequency. In the resonance limit, we discuss the dependence of the equation of state and the breathing mode frequency on the dimensionless effective range of the interaction k(F)R(P )<< 1, where k(F) is the Fermi wave vector and R-P is the effective range. The breathing mode frequency omega(B) deviates from the scale-invariant prediction of omega(c) = 2 omega(0), where omega(0) is the trapping frequency of the harmonic potential. This frequency shift is caused by the necessary existence of the effective range. In the small range limit, we predict that the mode frequency deviation at the leading order is given by delta omega(B) similar or equal to -(omega(0)/4) ln(-1)(k(F)R(P)).