Role of the confinement-induced effective range on the thermodynamics of a strongly correlated Fermi gas in two dimensions

We theoretically investigate the thermodynamic properties of a strongly correlated two-dimensional Fermi gas with a confinement-induced negative effective range of interactions, which is described by a two-channel model Hamiltonian. By extending the many-body T-matrix approach by Nozi\`eres and Schmitt-Rink to the two-channel model, we calculate the equation of state in the normal phase and present several thermodynamic quantities as functions of temperature, interaction strength, and effective range. We find that there is a non-trivial dependence of thermodynamics on the effective range. In experiment, where the effective range is set by the tight axial confinement, the contribution of the effective range becomes non-negligible as the temperature decreases down to the degenerate temperature. We compare our finite-range results with recent measurements on the density equation of state, and show that the effective range has to be taken into account for the purpose of a quantitative understanding of the experimental data.