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arXiv:1112.2596 · Physical Review A

Spontaneous generation of spin-orbit coupling in magnetic dipolar Fermi gases

Takaaki Sogo, Mi­chael Urban, Peter Schuck, T. Miyakawa

Published Mar 9, 2012• 14 citations
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Abstract

The stability of an unpolarized two-component dipolar Fermi gas is studied within mean-field theory. Besides the known instability towards spontaneous magnetization with Fermi sphere deformation, another instability toward spontaneous formation of a spin-orbit coupled phase with a Rashba-like spin texture is found. A phase diagram is presented and consequences are briefly discussed.

DOI
10.1103/physreva.85.031601

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•Apr 4, 2013•0 citations
The stability of an unpolarized two-component dipolar Fermi gas is studied within mean-field theory. Besides the known instability towards spontaneous magnetization with Fermi sphere deformation, another instability toward spontaneous formation of a spin-orbit coupled phase with a Rashba-like spin texture is found. A phase diagram is presented and consequences are briefly discussed.
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We investigate Fermi liquid states of the ultracold magnetic dipolar Fermi gases in the simplest two-component case including both thermodynamic instabilities and collective excitations. The magnetic dipolar interaction is invariant under the simultaneous spin-orbit rotation but not under either the spin or the orbit one. Therefore, the corresponding Fermi liquid theory is intrinsically spin-orbit coupled. This is a fundamental feature of magnetic dipolar Fermi gases different from electric dipolar ones. The Landau interaction matrix is calculated and is diagonalized in terms of the spin-orbit coupled partial-wave channels of the total angular momentum JJJ. The leading thermodynamic instabilities lie in the channels of ferromagnetism hybridized with the ferronematic order with J=1+J={1}^{+}J=1+ and the spin-current mode with $J={1}^{\ensuremath{-}}$, where +++ and $\ensuremath{-}$ represent even and odd parities, respectively. An exotic propagating collective mode is identified as spin-orbit coupled Fermi surface oscillations in which spin distribution on the Fermi surface exhibits a topologically nontrivial hedgehog configuration.
We study the ferromagnetic transition of a two-component homogeneous dipolar Fermi gas with 1D spin–orbit coupling (SOC) at finite temperature. The ferromagnetic transition temperature is obtained as functions of dipolar constant λ d, spin–orbit coupling constant λ SOC and contact interaction constant λ s. It increases monotonically with these three parameters. In the ferromagnetic phase, the Fermi surfaces of different components can be deformed differently. The phase diagrams at finite temperature are obtained.
We use the self-consistent mean-field theory to analyze the effects of Rashba-type spin-orbit coupling (SOC) on the ground-state phase diagram of population-imbalanced Fermi gases throughout the BCS-Bose-Einstein condensate evolution. We find that the SOC and population imbalance are counteracting, and that this competition tends to stabilize the uniform superfluid phase against the phase separation. However, we also show that the SOC stabilizes (destabilizes) the uniform superfluid phase against the normal phase for low (high) population imbalances. In addition, we find topological quantum phase transitions associated with the appearance of momentum-space regions with zero quasiparticle energies, and study their signatures in the momentum distribution.
We show that unconventional spin order arises naturally in two-component dipolar Fermi gases of atoms or molecules, which recently became accessible experimentally, in optical lattices. Using an unbiased functional renormalization-group analysis, we find that dipolar interactions lead to an instability of the gas toward an $\ensuremath{\ell}=1$ spin-density wave state. This phase is the particle-hole analog of spin-triplet, ppp-wave Cooper pairs. The order parameter for such spin-density waves of ppp-wave orbital symmetry is a vector in spin space and, moreover, is defined on lattice bonds rather than on lattice sites. We determine the rich quantum phase diagram of dipolar fermions at half filling on the square lattice as a function of the dipolar orientation and discuss how these exotic spin-density waves emerge amidst competition with superfluid and charge-density wave phases.
We use the Bogoliubov-de Gennes (BdG) theory to study the interplay between the Zeeman field, spin-orbit coupling (SOC) and resultant skyrmion-like polarization textures in harmonically trapped two-dimensional Fermi gases. Our primary finding is that, in sharp contrast to the no-SOC case where only an easy-axis polarization is possible beyond a threshold Zeeman field (depending on the interaction strength), any non-zero combination of the Zeeman field and Rashba SOC induces not only an easy-axis polarization everywhere in the system but also a spatially-modulated transverse one near the edges. Our secondary finding is that the ground states of Rashba spin-orbit coupled systems are revealed to have stronger Fulde-Ferrell type non-uniform superfluid characters (i.e. phase modulations) but not a Larkin-Ovchinnikov one (i.e. amplitude modulations) under the in-plane Zeeman field, for which the phases of the superfluid order parameters modulate near the edges and most prominently along the transverse direction. The effects of the interaction, temperature, SOC anisotropy and Zeeman field anisotropy on the intricate polarization textures and superfluid order parameter are also discussed.