We study the bound states of two spin-$\frac{1}{2}$ fermions interacting via a contact attraction (characterized by a scattering length) in the singlet channel in three-dimensional space in presence of a uniform non-Abelian gauge field. The configuration of the gauge field that generates a Rashba-type spin-orbit interaction is described by three coupling parameters $({\lambda }_x,{\lambda }_y,{\lambda }_z)$. For a generic gauge field configuration, the critical scattering length required for the formation of a bound state is negative, i.e., shifts to the “BCS side” of the resonance. Interestingly, we find that there are special high-symmetry configurations (e.g., ${\lambda }_x={\lambda }_y={\lambda }_z$) for which there is a two-body bound state for any scattering length however small and negative. Remarkably, the bound-state wave functions obtained for such configurations have nematic spin structure similar to those found in liquid ${}^3\mathrm{He}$. Our results show that the BCS-BEC (Bose-Einstein condensation) crossover is drastically affected by the presence of a non-Abelian gauge field. We discuss possible experimental signatures of our findings both at high and low temperatures.

• Received 20 December 2010
• Corrected 16 March 2011

DOI:https://doi.org/10.1103/PhysRevB.83.094515