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 $J$ . The leading thermodynamic instabilities lie in the channels of ferromagnetism hybridized with the ferronematic order with $J={1}^{+}$ 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 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 $J$. The leading thermodynamic instabilities lie in the channels of ferromagnetism hybridized with the ferronematic order with $J={1}^{+}$ 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.

arXiv:1201.1607Physical Review BMay 14, 201222 citations

Unconventional symmetries of Fermi liquid and Cooper pairing properties with electric and magnetic dipolar fermions

Yi Li, Congjun Wu

The rapid experimental progress of ultra-cold dipolar fermions opens up a whole new opportunity to investigate novel many-body physics of fermions. In this article, we review theoretical studies of the Fermi liquid theory and Cooper pairing instabilities of both electric and magnetic dipolar fermionic systems from the perspective of unconventional symmetries. When the electric dipole moments are aligned by the external electric field, their interactions exhibit the explicit d(r(2)-3z(2)) anisotropy. The Fermi liquid properties, including the single-particle spectra, thermodynamic susceptibilities and collective excitations, are all affected by this anisotropy. The electric dipolar interaction provides a mechanism for the unconventional spin triplet Cooper pairing, which is different from the usual spin-fluctuation mechanism in solids and the superfluid (3)He. Furthermore, the competition between pairing instabilities in the singlet and triplet channels gives rise to a novel time-reversal symmetry breaking superfluid state. Unlike electric dipole moments which are induced by electric fields and unquantized, magnetic dipole moments are intrinsic proportional to the hyperfine-spin operators with a Lande factor. Its effects even manifest in unpolarized systems exhibiting an isotropic but spin-orbit coupled nature. The resultant spin-orbit coupled Fermi liquid theory supports a collective sound mode exhibiting a topologically non-trivial spin distribution over the Fermi surface. It also leads to a novel p-wave spin triplet Cooper pairing state whose spin and orbital angular momentum are entangled to the total angular momentum J = 1 dubbed the J-triplet pairing. This J-triplet pairing phase is different from both the spin-orbit coupled (3)He-B phase with J = 0 and the spin-orbit decoupled (3)He-A phase.The rapid experimental progress of ultra-cold dipolar fermions opens up a whole new opportunity to investigate novel many-body physics of fermions. In this article, we review theoretical studies of the Fermi liquid theory and Cooper pairing instabilities of both electric and magnetic dipolar fermionic systems from the perspective of unconventional symmetries. When the electric dipole moments are aligned by the external electric field, their interactions exhibit the explicit d(r(2)-3z(2)) anisotropy. The Fermi liquid properties, including the single-particle spectra, thermodynamic susceptibilities and collective excitations, are all affected by this anisotropy. The electric dipolar interaction provides a mechanism for the unconventional spin triplet Cooper pairing, which is different from the usual spin-fluctuation mechanism in solids and the superfluid (3)He. Furthermore, the competition between pairing instabilities in the singlet and triplet channels gives rise to a novel time-reversal symmetry breaking superfluid state. Unlike electric dipole moments which are induced by electric fields and unquantized, magnetic dipole moments are intrinsic proportional to the hyperfine-spin operators with a Lande factor. Its effects even manifest in unpolarized systems exhibiting an isotropic but spin-orbit coupled nature. The resultant spin-orbit coupled Fermi liquid theory supports a collective sound mode exhibiting a topologically non-trivial spin distribution over the Fermi surface. It also leads to a novel p-wave spin triplet Cooper pairing state whose spin and orbital angular momentum are entangled to the total angular momentum J = 1 dubbed the J-triplet pairing. This J-triplet pairing phase is different from both the spin-orbit coupled (3)He-B phase with J = 0 and the spin-orbit decoupled (3)He-A phase.

arXiv:1501.00540Journal of Physics Condensed MatterNov 17, 201410 citations

COLLECTIVE SPIN MODES IN FERMI LIQUIDS WITH SPIN-ORBIT COUPLING

Журнал Экспериментальной и Теоретической ФизикиOct 1, 20220 citations

Ferromagnetic and nematic non-Fermi liquids in spin-orbit-coupled two-dimensional Fermi gases

Jonathan Ruhman, Erez Berg

We study the fate of a two-dimensional system of interacting fermions with Rashba spin-orbit coupling in the dilute limit. The interactions are strongly renormalized at low densities, and give rise to various fermionic liquid crystalline phases, including a spin-density wave, an in-plane ferromagnet, and a nonmagnetic nematic phase, even in the weak-coupling limit. The nature of the ground state in the low-density limit depends on the range of the interactions: for short-range interactions it is the ferromagnet, while for dipolar interactions the nematic phase is favored. Interestingly, the ferromagnetic and nematic phases exhibit strong deviations from Fermi liquid theory, due to the scattering of the fermionic quasiparticles off long-wavelength collective modes. Thus, we argue that a system of interacting fermions with Rashba dispersion is generically a non-Fermi liquid at low densities.We study the fate of a two-dimensional system of interacting fermions with Rashba spin-orbit coupling in the dilute limit. The interactions are strongly renormalized at low densities, and give rise to various fermionic liquid crystalline phases, including a spin-density wave, an in-plane ferromagnet, and a nonmagnetic nematic phase, even in the weak-coupling limit. The nature of the ground state in the low-density limit depends on the range of the interactions: for short-range interactions it is the ferromagnet, while for dipolar interactions the nematic phase is favored. Interestingly, the ferromagnetic and nematic phases exhibit strong deviations from Fermi liquid theory, due to the scattering of the fermionic quasiparticles off long-wavelength collective modes. Thus, we argue that a system of interacting fermions with Rashba dispersion is generically a non-Fermi liquid at low densities.

arXiv:1408.6250Physical Review BDec 10, 201422 citations

J

. The leading thermodynamic instabilities lie in the channels of ferromagnetism hybridized with the ferronematic order with

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.