Superfluid Phases of Dipolar Fermions in Harmonically Trapped Optical Lattices

We describe the emergence of superfluid phases of ultracold dipolar fermions in optical lattices for two-dimensional systems. Considering the many-body screening of dipolar interactions at intermediate and larger filling factors, we show that several superfluid phases with distinct pairing symmetries naturally arise in the singlet channel: local s-wave $(sl)$, extended s-wave $(se)$, d-wave $(d)$ or time-reversal-symmetry breaking $(sl + se \pm id)$-wave. We obtain the temperature versus filling factor phase diagram and show that d-wave pairing is favored near half-filling, that $(sl + se)$-wave is favored near zero or full filling, and that time-reversal-breaking $(sl + se \pm id)$-wave is favored in between. The inclusion of a harmonic trap reveals that a sequence of phases can coexist in the cloud depending on the filling factor at the center of the trap. Most notably in the spatial region where the $(sl + se \pm id)$-wave superfluid occurs, spontaneous currents are generated, and may be detected using velocity sensitive Bragg spectroscopy.