Superfluid density in the BCS-BEC crossover regime of a Fermi superfluid

We investigate the superfluid carrier density ρ_s in the BCS-BEC crossover regime of a Fermi superfluid at finite temperatures. Including pairing fluctuations within a Gaussian approximation, we calculate the superfluid order parameter, chemical potential, and ρ_s in a consistent manner in the whole BCS-BEC crossover region. In the weak-coupling BCS regime, the temperature dependence of ρ_s is dominated by single-particle excitations accompanied by thermal dissociation of Cooper pairs. In the strong-coupling BEC regime, we show that single-particle excitations become less dominant and thermal excitations of collective Bogoliubov mode become important for ρ_s. We clarify how the weak-coupling BCS result smoothly changes into the strong-coupling BEC result, as one increases the strength of a pairing interaction.