  Attractive interaction between spinless fermions in a two-dimensional lattice
drives the formation of a topological superfluid. But the topological phase is
dynamically unstable towards phase separation when the system has a high
density of states and large interaction strength. This limits the critical
temperature to an experimentally challenging regime where, for example, even
ultracold atoms and molecules in optical lattices would struggle to realize the
topological superfluid. We propose that the introduction of a weaker
longer-range repulsion, in addition to the short-range attraction between
lattice fermions, will suppress the phase separation instability. Taking the
honeycomb lattice as an example, we show that our proposal significantly
enlarges the stable portion of the topological superfluid phase and increases
the critical temperature by an order of magnitude. Our work opens a route to
enhance the stability of topological superfluids by engineering inter-particle
interactions.
