Topological superfluid phase of a two-dimensional fermi gas with equal Rashba-Dresselhaus Spin-Orbit Coupling

Abstract The equal Rashba-Dresselhaus (ERD) spin-orbit coupling, as the first type to be implemented in cold atom experiments, provides a unique platform for exploring topological quantum phases. This work investigates the ground state of a two-dimensional Fermi gas featuring both ERD coupling and a Zeeman field, mapping out its topological phase diagram throughout the BCS-BEC crossover. We classify the homogeneous superfluid phases into topologically trivial gapped or nontrivial gapless phase based on the nodal structure of the quasiparticle excitation spectrum. We reveal the evolution of topological superfluid states under various conditions by systematically characterizing the phase distribution across key parameters including the spin-orbit coupling strength, two-body binding energy, Zeeman field, and chemical potential. Our findings indicate that spin-orbit coupling enhances triplet pairing and stabilizes the gapless superfluid phase. Moreover, small binding energy, and strong Zeeman field are found to promote the emergence of the gapless phase, particularly the US-II phase identified in this work. These results elucidate the phase transition mechanisms in low-dimensional quantum systems.