We investigate a mix-dimensional Fermi-Fermi mixture in which one species is confined in twodimensional(2D) space while the other is free in three-dimensional space(3D). We determine the superfluid transition temperature Tc for the entire BCS-BEC crossover including the important effects of noncondensed pairs. We find that the transition temperature reduces while the imbalance of mass is increased or lattice constant (dz) is reduced. In population imbalance case, the stability of superfluid is sharply destroyed by increasing the polarization.
We investigate topological superfluids in a coupled layer system, in which transitions between different topological superfluids can be realized by controlling the binding energy, interlayer tunneling and layer asymmetry etc. These topological transitions are characterized by energy gap closing and reopening at the critical points at zero momentum where the Chern number and sign of Pfaffian undergo a discontinuous change. In a hard wall boundary the bulk-edge correspondence ensures that the number of edge modes exactly equals the Chern number, whereas all the edge modes localized at the same edge propagate along the same direction. However, in a trapped potential these edge modes are spatially localized at the interfaces between different topological superfluids, where the number of edge modes exactly equals the Chern number difference between the left and right interface. These topological phases can be detected by spin texture at or near zero momentum, which changes discretely across the phase transition points due to band inversion. The model can be easily generalized to multilayer system in which the Chern number can equal any positive integer. These large Chern number topological superfluids provide fertile grounds for exploring new quantum matters in context of ultracold atoms.
Topological nodal superconductors are generally realized based on unconventional pairings. In this work, we propose a minimal model to realize these topological nodal phases with only s-wave interaction. In our model the linear and quadratic spin-orbit couplings along the two directions break the isotropy in momentum space and introduce effective unconventional pairings on the Fermi surface. This model may support different nodal superconducting phases characterized by either winding number in BDI class or Pfaffian in D class at the particle-hole invariant axes. In the vicinity of the nodal points the effective Hamiltonian can be described by either type-I or type-II Dirac equation; and the crossover between these two nodal points can be driven by external Zeeman fields. We show that these nodal phases are robust against weak disorders, thus are possible to be realized in experiments with real materials. The smoking-gun evidences to verify these phases based on scanning tunneling spectroscopy are also briefly discussed.
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