Stabilizing topological superfluidity of cold fermions in two-dimensional optical lattices

Theoretical studies have shown that identical fermions in a two-dimensional lattice can form a topological superfluid state, most notably a chiral p-wave pairing state, in the presence of attractive interactions. But the critical temperature is rather low as the system develops an instability towards phase separation with increasing interactions. This makes it experimentally challenging to realize a topological superfluid phase. We study the stability of the chiral p-wave phase against phase separation for spinless fermions in different lattices and find that the competition is common in the presence of nearest-neighbor attractions. Therefore, preventing phase separation is important to acquire higher critical temperatures for lattice fermions. To this end, we consider adding a longer-range repulsion to the short-range attraction in the system and find a strong suppression of the phase separation instability in favor of the chiral p-wave superfluid phase. We also discuss how to engineer the desired interactions in experiments with dipolar fermions.