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Based on the two-dimensional (2D) attractive Fermi-Hubbard model with Rashbaspin-orbit coupling (SOC), the SOC strength and Zeeman field dependences of thephase diagram are investigated by calculating the pairing gapself-consistently. The results reveal that the phase transition from the BCSsuperfluid to the topological superfluid happens under proper Zeeman fieldstrength and SOC strength. In particular, in contrast to the BCS superfluiddecreasing monotonically as the SOC strength increasing, the topologicalsuperfluid region shows a dome with the SOC strength increasing. An optimalregion in the phase diagram to find the topological superfluid can be found,which is important to realize the topological superfluid in optical latticeexperimentally. Then we obtain the change of both band structure and density ofstates (DOS) during the topological phase transition, and explain the fourpeaks of DOS in the topological superfluid by the topology change of thelow-energy branch of quasiparticle energy spectra. Moreover, the topologicalsuperfluid can be suppressed by the doping concentration.

Phase diagram, band structure and density of states in two-dimensional attractive Fermi-Hubbard model with Rashba spin-orbit coupling