Phase diagram of a spin–orbit coupled Fermi gas in a bilayer optical lattice

We investigate the stability of helical superfluid phase in a spin–orbit coupled Fermi gas loaded in a bilayer optical lattice. The phase diagram of the system is constructed in the mean-field framework. We investigate the topological properties of the superfluid phases by a nontrivial application of the Fermi surface topological invariant to our time-reversal invariant system with degeneracies on the Fermi surface. We find that there is a first-order phase boundary in the phase diagram of half-filling case and the superfluid phases are all topological trivial. The superfluid phase is topological nontrivial when the filling fraction deviates from the half-filling. In the topological nontrivial superfluid phase, a full pairing gap exists in the bulk and gapless helical Majorana edge states exist at the boundary. (paper)