How does a synthetic non-Abelian gauge field influence the bound states of two spin-$\half$ fermions?

TL;DR

This paper investigates how a uniform non-Abelian gauge field, inducing spin-orbit coupling, alters the formation and properties of two-fermion bound states in three dimensions, revealing unique bound state behaviors and nematic spin structures.

Contribution

It demonstrates that non-Abelian gauge fields significantly modify bound state formation, including the existence of bound states at negative scattering lengths and nematic spin structures, advancing understanding of gauge field effects on fermionic pairing.

Findings

Critical scattering length shifts to the BCS side with generic gauge fields.

Special high-symmetry configurations support bound states at any negative scattering length.

Bound states exhibit nematic spin structures similar to liquid $^3$He.

Abstract

We study the bound states of two spin-$\half$ fermions interacting via a contact attraction (characterized by a scattering length) in the singlet channel in 3D 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 {\em 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 {\em 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 $^3$He. Our results show that the BCS-BEC 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.