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

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 (x) over cap -direction and the tunneling between nearest tubes in the (y) over cap -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.