Polarization of a quasi-two-dimensional repulsive Fermi gas with Rashba spin-orbit coupling: A variational study

Motivated by the remarkable experimental control of synthetic gauge fields in ultracold atomic systems, we investigate the effect of an artificial Rashba spin-orbit coupling on the spin polarization of a two-dimensional repulsive Fermi gas. By using a variational many-body wave function, based on a suitable spinorial structure, we find that the polarization properties of the system are indeed controlled by the interplay between spin-orbit coupling and repulsive interaction. In particular, two main effects are found: (1) The Rashba coupling determines a gradual increase of the degree of polarization beyond the critical repulsive interaction strength, at variance with conventional two-dimensional Stoner instability. (2) The critical interaction strength, above which finite polarization is developed, shows a dependence on the Rashba coupling, i.e., it is enhanced in case the Rashba coupling exceeds a critical value. A simple analytic expression for the critical interaction strength is further derived in the context of our variational formulation, which allows for a straightforward and insightful analysis of the present problem.

Figure 1

Optimal variational parameters ${\overline{n}}_{+}$ and $\overline{\zeta }$, plotted in function of $g$ for different values of ${\lambda }_R$. Units are specified in the text.

Figure 2

Polarization of the optimal variational state, plotted in function of $g$ for different values of ${\lambda }_R$. Solid black lines indicate the phase transition (shifted in the case of ${\lambda }_R=2)$. Units are specified in the text.

Figure 3

Critical repulsive interaction coupling constant $g_{c,{\lambda }_R}$ as a function ${\lambda }_R$. The dashed vertical line separates the regimes of constant and variable $g_{c,{\lambda }_R}$. Units are specified in the text.