Non-universal BCS-BEC crossover in resonantly interacting Fermi gases

We investigate the non-universal behavior of the BCS-BEC crossover model at the normal to superfluid transition. By using a finite temperature quantum field theoretical approach due to Nozieres and Schmitt-Rink and by making the effective range expansion of the effective two-body interaction we numerically calculate the crossover transition temperature as a function of the scattering length, $a_{F},$ and the effective range parameter, $r_{\mathrm{e}}.$ In an ultracold two-component atomic Fermi gas BCS-BEC crossover physics is expected to appear near magnetic-field-induced Feshbach resonances. By matching two-body scattering properties near a Feshbach resonance to a simple renormalized model potential, a broad resonance is characterized by a small effective range and the gas displays a universal BCS-BEC crossover behavior. On the other hand, for a narrow resonance thermodynamic quantities depend the effective range which may be large and negative at resonance. For increasing values of $-r_{\mathrm{e}}$ we find the transition temperature to be suppressed in the crossover region. We furthermore argue for existence of a lower bound of $T_{c}$ at fixed coupling for increasing $-r_{\mathrm{e}}$ in the crossover region.