Topological superfluids usually refer to a superfluid state which is gapped in the bulk but metallic at the boundary. Here we report that a gapless, topologically nontrivial superfluid with an inhomogeneous Fulde-Ferrell pairing order parameter can emerge in a two-dimensional spin-orbit coupled Fermi gas, in the presence of both in-plane and out-of-plane Zeeman fields. The Fulde-Ferrell pairing-induced by the spin-orbit coupling and in-plane Zeeman field-is responsible for this gapless feature. This exotic superfluid has a significant Berezinskii-Kosterlitz-Thouless transition temperature and has robust Majorana edge modes against disorder owing to its topological nature.
The superfluid phases in the resonant dipolar Fermi gases are investigated by the standard meanfield theory. In contrast to the crossover from Bose-Einstein condensation (BEC) to Bardeen-CooperSchrieffer (BCS) superfluid in the Fermi gases with the isotropic interactions, the resonant dipolar interaction leads to two completely different BEC phases of the tight-binding Fermi molecules on both sides of the resonance, which are characterized by two order parameters with the distinct internal symmetries. We point that near the resonance, the two competitive phases can coexist, and an emergent relative phase between the two order parameters spontaneously breaks the time-reversal symmetry, which could be observed in the momentum resolved rf-spectroscopy. Introduction. -The unprecedented experimental progresses [1][2][3][4][5] in creating quantum gases of fermions with large dipole moment has stimulated extensive investigations of dipolar Fermi gases. Owing to the long-range and anisotropic nature of the dipole-dipole interaction (DDI), new quantum phenomena emerge in the dipolar Fermi gases, e.g., the ferro-nematic phase [6], the novel static and dynamical properties in the normal phase [7], and the p-wave dominated BCS superfluids induced by the partially attractive DDI [8][9][10][11]. Of particular interest, the recent studies demonstrated that in the two-species dipolar Fermi gases the competition between the shortrange contact interaction and DDI led to the coexistence of singlet-and triplet-paired superfluids [12][13][14].
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