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

Abstract

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

Repulsive atomic Fermi gas with Rashba spin-orbit coupling: A quantum Monte Carlo study

“…This behavior is consistent with the mean-field picture of Ref. [50], where nonzero polarization is developed in correspondence with a sudden increase of the variational parameter h. In fact, a finite value of h indicates a tendency of the system to choose a preferred spin orientation, inducing a nonzero polarization in the system.…”

“…In fact, for k F a → ∞ full polarization is expected, given the overwhelming effects of the two-body repulsion. Remarkably, qualitatively analogous results were found also in the twodimensional gas [50], making use of a variational procedure based on single-particle spinors of the form of Eq. (14).…”

“…However, the expectation of σ z on any of these single-particle states is identically zero. To retain information on the nonlocal spin structure and simultaneously allow for nonzero polarization, we make use of the following spinorial form [50]:…”

“…A very recent mean-field variational study of the two-dimensional Fermi gas with Rashba coupling [50] has indeed shown how SO effects can macroscopically influence the Stoner instability, leading to partially magnetized states. However, while a detailed theoretical understanding of the repulsive Fermi gas in the presence of a Rashba interaction would be extremely appealing, the intrinsically challenging calculations beyond the mean field are further complicated by the nonlocal nature of the SO coupling [50].…”

Itinerant chiral ferromagnetism in a trapped Rashba spin-orbit-coupled Fermi gas

“…Forλ 13, there exists a window of ferromagnetic phase at intermediate values of g. As g increases from zero to a lower critical value (represented by the red solid line with filled circles), the weakly correlated non-magnetic state becomes ferromagnetic. Note that this lower critical value is much smaller than g 0 MF = 2π 2 /M , the mean-field ferromagnetic critical interaction strength of a 2D homogeneous Fermi gas without SO coupling [17,18]. This can be understood from the Stoner's argument and the flat band singleparticle spectrum.…”