Exotic superfluid of trapped Fermi gases with spin–orbit coupling in dimensional crossover

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We investigate the ground state properties of Fermi gases in a planar array of one-dimensional potential tubes with spin–orbit coupling where the motion of atoms is free in the -direction and the tunneling between nearest tubes in the -direction is permitted. By using the mean-field method, the phase diagrams of the system at the dimensional crossover from quasi-one dimension to quasi-two dimensions is obtained. We find the existence of the topological state and Majorana mode in the weak tunneling case, and a rich phase diagram including two kinds of nodal superfluid phase and gapped superfluid phase, in the opposite case. The results show that topological pairing is favored in quasi-one dimension while nodal pairing state is favored in quasi-two dimensions.