We use a determinant quantum Monte Carlo simulation and a mean-field approach to study the Rashba spin-orbit coupled Fermi gases in square optical lattice. Notably, we show that the Berezinskii-Kosterlitz-Thoules phase transition temperature can be enhanced by the spin-orbit coupling. The superfluidity is always dominated by spin-singlet pairing when the attraction or the spin-orbit coupling increases. Moreover, the spin susceptibility is shown to be anisotropic and attends a steady value in the presence of the spin-orbit coupling.
We use a determinant quantum Monte Carlo simulation and a mean-field approach to study the Rashba spin-orbit coupled Fermi gases in square optical lattice. Notably, we show that the Berezinskii-Kosterlitz-Thoules phase transition temperature can be enhanced by the spin-orbit coupling. The superfluidity is always dominated by spin-singlet pairing when the attraction or the spin-orbit coupling increases. Moreover, the spin susceptibility is shown to be anisotropic and attends a steady value in the presence of the spin-orbit coupling.
We study the effect of spin-orbit coupling on both the zero-temperature and nonzero-temperature behavior of a two-dimensional Fermi gas. We include a generic combination of Rashba and Dresselhaus terms into the system Hamiltonian, which allows us to study both the experimentally relevant equal-Rashba-Dresselhaus (ERD) limit and the Rashba-only (RO) limit. At zero temperature, we derive the phase diagram as a function of the two-body binding energy and Zeeman field. In the ERD case, this phase diagram reveals several topologically distinct uniform superfluid phases, classified according to the nodal structure of the quasiparticle excitation energies. Furthermore, we use a momentum-dependent SU(2) rotation to transform the system into a generalized helicity basis, revealing that spin-orbit coupling induces a triplet pairing component of the order parameter. At nonzero temperature, we study the Berezinskii-Kosterlitz-Thouless (BKT) phase transition by including phase fluctuations of the order parameter up to second order. We show that the superfluid density becomes anisotropic due to the presence of spin-orbit coupling (except in the RO case). This leads both to elliptic vortices and antivortices, and to anisotropic sound velocities. The latter prove to be sensitive to quantum phase transitions between topologically distinct phases. We show further that at a fixed nonzero Zeeman field, the BKT critical temperature is increased by the presence of ERD spin-orbit coupling. Subsequently, we demonstrate that the Clogston limit becomes infinite: TBKT remains nonzero at all finite values of the Zeeman field. We conclude by extending the quantum phase transition lines to nonzero temperature, using the nodal structure of the quasiparticle spectrum, thus connecting the BKT critical temperature with the zero-temperature results.
The admixture of spin-singlet and spin-triplet pairing states in superconductors can be typically induced by breaking spatial inversion symmetry. Employing the numerically exact auxiliary-field quantum Monte Carlo method, we study such mixed-parity pairing phenomena of attractive fermions with Rashba spin-orbit coupling (SOC) in a two-dimensional optical lattice at finite temperature. We systematically explore the evolution of the essential pairing structure in both singlet and triplet channels versus the temperature, fermion filling, and SOC and interaction strengths, via computing the finite-size results of the condensate fraction and pair wave function. Our numerical results reveal that the singlet channel dominates in the fermion pairing and the triplet pairing has a relatively small contribution to the superfluidity for physically relevant parameters. In contrast to the singlet channel mainly consisting of the on-site Cooper pairs, the triplet pairing has plentiful patterns in real space with the largest contributions from several nearest neighbors. As the SOC strength increases, the pairing correlation is first enhanced and then suppressed for triplet pairing while it is simply weakened in the singlet channel. We have also obtained the Berezinskii-Kosterlitz-Thouless transition temperatures through the finite-size analysis of the condensate fraction. Our results can serve as a quantitative guide for future optical lattice experiments as well as accurate benchmarks for theories and other numerical methods.
The realization of spin-orbit coupling (SOC) in ultracold atoms has triggered an intensive exploring of topological superfluids in the degenerate Fermi gases based on mean-field theory, which has not yet been reported in experiments. Here, we demonstrate the topological phase transitions in the system via the numerically exact quantum Monte Carlo method. Without prior assumptions, our unbiased real-space calculation shows that spin-orbit coupling can stabilize an unconventional pairing in the weak SOC regime, in which the Fulde-Ferrell-Larkin-Ovchinnikov pairing coexists with the Bardeen-Cooper-Schrieffer pairing. Furthermore, we use the jumps in the spin polarization at the time-reversal invariant momenta to qualify the topological phase transition, where we find the critical exponent deviated from the mean-field theory. Our results pave the way for the searching of unconventional pairing and topological superfluids with degenerate Fermi gases.
We theoretically investigate the superfluid density and Berezinskii-Kosterlitz-Thouless (BKT) transition of a two-dimensional Rashba spin-orbit-coupled atomic Fermi gas with both in-plane and out-of-plane Zeeman fields. It was recently predicted that, by tuning the two Zeeman fields, the system may exhibit different exotic Fulde-Ferrell (FF) superfluid phases, including the gapped FF, gapless FF, gapless topological FF, and gapped topological FF states. Due to the FF paring, we show that the superfluid density (tensor) of the system becomes anisotropic. When an in-plane Zeeman field is applied along the x direction, the tensor component along the y direction ns,yy is generally larger than ns,xx in most parameter space. At zero temperature, there is always a discontinuity jump in ns,xx as the system evolves from a gapped FF into a gapless FF state. With increasing temperature, such a jump is gradually washed out. The critical BKT temperature has been calculated as functions of the spin-orbit-coupling strength, interatomic interaction strength, and in-plane and out-of-plane Zeeman fields. We predict that the novel FF superfluid phases have a significant critical BKT temperature, typically at the order of 0.1TF, where TF is the Fermi degenerate temperature. Therefore, their observation is within the reach of current experimental techniques in cold-atom laboratories.
We investigate the single-particle and collective excitations of a Rashba spin-orbit-coupled atomic Fermi gas with attractive interaction, loaded in a two-dimensional (2D) square optical lattice, in the presence of an effective out-of-plane Zeeman field. Our numerical calculations show that the many-body physics of the Bardeen-Cooper-Schrieffer (BCS) side is strongly modified compared to the Fermi gases in the free space. The physics behind this statement lies in the fact that in the 2D lattice case the single-particle ground-state energy is four times degenerated, while without a lattice structure the ground state is infinitely degenerate, and because of that, the spin-orbit coupling (SOC) in optical lattices gives rise to unusual properties entirely different from the continuum. For example, in the continuum, the pairing gap as well as the condensate fraction is strongly enhanced by the SOC strength on the BCS side. In the presence of lattice geometry the gap and the condensate fraction increase as a function of the SOC strength only at small fillings and a weak attraction limit. Moreover, we found that the speed of sound also exhibits different behavior: in the 3D and 2D continua, the slope of the Goldstone mode decreases as a function of the SOC strength, while in the lattice case the speed of sound increases monotonically with the SOC strength.
We investigate the Berezinskii-Kosterlitz-Thouless (BKT) transition in a 2D Fermi gas with spin-orbit coupling (SOC), as a function of the two-body binding energy and a perpendicular Zeeman field. By including a generic form of the SOC, as a function of Rashba and Dresselhaus terms, we study the evolution between the experimentally relevant equal Rashba-Dresselhaus (ERD) case and the Rashba-only (RO) case. We show that in the ERD case, at a fixed nonzero Zeeman field, the BKT transition temperature T(BKT) is increased by the presence of SOC for all values of the binding energy. We also find a significant increase in the value of the Clogston limit compared to the case without SOC. Furthermore, we demonstrate that the superfluid density tensor becomes anisotropic (except in the RO case), leading to an anisotropic phase-fluctuation action that describes elliptic vortices and antivortices, which become circular in the RO limit. This deformation constitutes an important experimental signature for superfluidity in a 2D Fermi gas with ERD SOC. Finally, we show that the anisotropic sound velocities exhibit anomalies at low temperatures, in the vicinity of quantum phase transitions between topologically distinct uniform superfluid phases.