Fermionic superfluidity with positive scattering length

Superfluidity in an ultracold Fermi gas is usually associated with either a negative scattering length or the presence of a two-body bound state. We show that none of these ingredients is necessary to achieve superfluidity. Using a narrow Feshbach resonance with strong repulsive background interactions, the effective interactions can be repulsive for small energies and attractive for energies around the Fermi energy, similar to the effective interactions between electrons in a metallic superconductor. This can result in BCS-type superfluidity while the scattering length is positive.

Figure 1

(Color online) Critical temperature $T_c$ in the crossover region as a function of $(k_{F}a{)}^{-1}$ in the case of broad and narrow Feshbach resonances with different background interaction strengths $k_F{a}^P$. Dashed line: broad resonance where $(k_{F}a{)}^{-1}$ is the only relevant parameter. Solid, dash-dotted, and dotted lines: narrow resonance where $\tilde{C}=1$ and $k_F{a}^P=+0.5$, 0, and $-0.5$ respectively.

Figure 2

(Color online) Critical temperature $T_c$ in the BCS limit, for small negative and positive scattering lengths $k_{F}a$, in the case of a narrow Feshbach resonance with $k_F{a}^P=+1$ (solid line) and of a broad resonance (dashed line). Inset: chemical potential ${\mu }_c$ at $T_c$ for identical parameters.

Figure 3

(Color online) Phase shift $\varphi \left(k\right)\equiv \varphi (\mathbf{q},2{ϵ}_k+\frac{1}{2}{ϵ}_q-2\mu )$ for $k_{F}a=+0.3$. The resonance parameters are identical to those of Fig. 2. Inset: scattering length as a function of magnetic field. The shaded area indicates the region where $a>0$, but there are no molecules in the system.