  Based on the two-dimensional (2D) attractive Fermi-Hubbard model with Rashba
spin-orbit coupling (SOC), the SOC strength and Zeeman field dependences of the
phase diagram are investigated by calculating the pairing gap
self-consistently. The results reveal that the phase transition from the BCS
superfluid to the topological superfluid happens under proper Zeeman field
strength and SOC strength. In particular, in contrast to the BCS superfluid
decreasing monotonically as the SOC strength increasing, the topological
superfluid region shows a dome with the SOC strength increasing. An optimal
region in the phase diagram to find the topological superfluid can be found,
which is important to realize the topological superfluid in optical lattice
experimentally. Then we obtain the change of both band structure and density of
states (DOS) during the topological phase transition, and explain the four
peaks of DOS in the topological superfluid by the topology change of the
low-energy branch of quasiparticle energy spectra. Moreover, the topological
superfluid can be suppressed by the doping concentration.
