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

We have studied the exotic superfluid phases of degenerated Fermi gases with spin-orbit coupling in a mixed dimensional system, where the motion of atoms are free in the x-direction and the tunneling between nearest tubes in the y-direction is permitted. Using the mean-field method, we obtain the phase diagrams of the system during the dimensional crossover between quasi one dimension to quasi two dimension. We find the existence of the topological state and Majorana edge 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. Our results show that topological pairing is favoured in quasi one dimension while nodal pairing state is favoured in quasi two dimension.