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arXiv:1112.4731

Magnetization of a homogeneous two dimensional fermion gas with repulsive contact interaction and Rashba spin-orbit potential

Alberto Ambrosetti, Pier Luigi Silvestrelli, Flavio Toigo

Published Dec 20, 2011• 0 citations
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Abstract

The z axis magnetization of a two dimensional electron gas with contact repulsive interaction and in presence of a Rashba potential is computed by means of quantum field theory at second order. A striking effect of the pure Rashba interaction is that of hindering spin alignment along the z direction. Evidence of transition at critical repulsive interaction coupling constant is still found. The degree of magnetization, however, shows a clear dependence on the spin-orbit interaction strength. Furthermore, the transition to magnetized state appears to be smoothed by the presence of the Rashba interaction.

DOI
10.48550/arxiv.1112.4731

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The z axis magnetization of a two dimensional electron gas with contact repulsive interaction and in presence of a Rashba potential is computed by means of quantum field theory at second order. A striking effect of the pure Rashba interaction is that of hindering spin alignment along the z direction. Evidence of transition at critical repulsive interaction coupling constant is still found. The degree of magnetization, however, shows a clear dependence on the spin-orbit interaction strength. Furthermore, the transition to magnetized state appears to be smoothed by the presence of the Rashba interaction.
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.
Thanks to the recent experimental realization and control of artificial gauge fields, spin-orbit (SO) couplings are witnessing an ever increasing interest in the field of cold atoms. However, predicting their effect on spin polarization and energetic properties of interacting systems is a major challenge, due to the complex interplay between spin and position dynamics. In this work we exploit the diffusion Monte Carlo algorithm to compute energetic and polarization properties of a three-dimensional repulsive Fermi gas in the presence of Rashba spin-orbit coupling. We find that SO effects tend to contrast the spin alignment induced by the exchange interaction, slightly shifting the onset of the Stoner instability towards larger values of the scattering length. In addition, polarization and energy properties of the system can be tuned trough a combined control of the repulsive interaction and Rashba coupling.
We study a homogeneous two-component dipolar Fermi gas with 1D spin-orbit coupling (SOC) at zero temperature and find that the system undergoes a transition from the paramagnetic phase to the ferromagnetic phase under suitable dipolar interaction constant λ d, SOC constant λ SOC and contact interaction constant λ s. This phase transition can be of either 1st order or 2nd order, depending on the parameters. Near the 2nd-order phase transition, the system is partially magnetized in the ferromagnetic phase. With SOC, the ferromagnetic phase can even exist in the absence of the contact interaction. The increase in dipolar interaction, SOC strength, and contact interaction are all helpful to stabilize the ferromagnetic state. The critical dipolar interaction strength at the phase transition can be reduced by the increase in SOC strength or contact interaction. Phase diagrams of these systems are obtained.
We study the interacting Fermi-Hubbard model in two spatial dimensions with synthetic gauge coupling of the spin-orbit Rashba type, at half-filling. Using real-space mean-field theory, we numerically determine the phase as a function of the interaction strength for different values of the gauge-field parameter. For a fixed value of the gauge field, we observe that when the strength of the repulsive interaction is increased, the system enters into an antiferromagnetic phase, then undergoes a first-order phase transition to a noncollinear magnetic phase. Depending on the gauge-field parameter, this phase further evolves to the one predicted from the effective Heisenberg model obtained in the limit of large interaction strength. We explain the presence of the antiferromagnetic phase at small interaction from the computation of the spin-spin susceptibility, which displays a divergence at low temperatures for the antiferromagnetic ordering. We discuss, how the divergence is related to the nature of the underlying Fermi surfaces. Finally, the fact that the first-order phase transitions for different gauge-field parameters occur at unrelated critical interaction strengths arises from a Hofstadter-like situation, i.e., for different magnetic phases, the mean-field Hamiltonians have different translational symmetries.
We study how the Rashba spin-orbit interaction influences unconventional superconductivity in a two-dimensional electron gas partially spin polarized by a magnetic field. Somewhat surprisingly, we find that for all field orientations, only the larger Fermi surface is superconducting. When the magnetic field is oriented out of plane, the system realizes a topological p+ipp+ipp+ip pairing state. When the field is rotated in plane, the order parameter develops nodes along the field direction and finite center-of-mass-momentum pairing is realized. We demonstrate that the pairing symmetry of the system can be easily probed experimentally due to the dependence of various thermodynamic quantities on the magnetic field geometry, and calculate the electronic specific heat as an example.