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

## TL;DR

This paper theoretically investigates the properties of a two-dimensional resonantly interacting p-wave Fermi superfluid, focusing on Tan's contact parameters and breathing mode frequency, revealing how effective range influences these observables near resonance.

## Contribution

It provides the first detailed analysis of Tan's contact and breathing mode behavior in 2D p-wave Fermi gases, including the effects of finite effective range.

## Key findings

- The many-body component of Tan's contact peaks above resonance.
- Breathing mode frequency dips near resonance due to contact behavior.
- Frequency deviation from scale invariance depends logarithmically on effective range.

## Abstract

Inspired by the renewed experimental activities on $p$-wave resonantly interacting atomic Fermi gases, we theoretically investigate 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 $^{40}$K and $^{6}$Li 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, $k_{F}R_{p}\ll1$, where $k_{F}$ is the Fermi wavevector 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, $\delta\omega_{B}\simeq-(\omega_{0}/4)\ln^{-1}(k_{F}R_{p})$.