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We propose a physical scheme for the realization of two-dimensionaltopological odd-parity superfluidity in a spin-independent bond-centered squareoptical lattice based upon interband fermion pairing. The D4 point-groupsymmetry of the lattice protects a quadratic band crossing, which allows one toprepare a Fermi surface of spin-up fermions with odd parity close to thedegeneracy point. In the presence of spin-down fermions with even paritypopulating a different energetically well separated band, odd-parity pairing isfavored. Strikingly, as a necessary prerequisite for pairing both Fermisurfaces can be tuned to match well. As a result, topological superfluid phasesemerge in the presence of merely s-wave interaction. Due to the Z2 symmetry ofthese odd-parity superfluids, we infer their topological features simply fromthe symmetry and the Fermi-surface topology as confirmed numerically.

Odd-parity topological superfluidity for fermions in a bond-centered square optical lattice