Topological superfluids for spin-orbit coupled ultracold Fermi gases

We examine the topological superfluid phases for ultracold fermions in the presence of two-dimensional (2D) synthetic spin-orbit (SO) couplings which have been well realized in recent experiments. Specifically, we focus on the 2D Dirac semimetal and the SO coupled quantum anomalous Hall model, together with an attractive Hubbard interaction which can induce a superfluid phase in SO coupled systems. The superfluid phases are studied systematically based on self-consistent theories. In particular, an interesting transition between (pi, pi)-momentum superfluid phase and zero center-of-mass momentum superfluid phase is predicted as the strength of SO coupling is increased. The full phase diagrams of the superfluid phases are obtained, with the nontrivial topological superfluids being determined by precisely calculating the topological invariants. We also determine the optimal parameter conditions of the topological superfluid phases, which could be helpful for future real experimental studies.