Topological semimetal and superfluid of s-wave interacting fermionic atoms in an orbital optical lattice

Recent advanced experimental implementations of optical lattices with highly tunable geometry open up new regimes for quantum many-body states of matter that previously had not been accessible. Here we introduce a symmetry-based method of utilizing the geometry of optical lattice to systematically control topologically non-trivial orbital hybridization. Such an orbital mixing leads to an unexpected and yet robust topological semimetal at single-particle level for a gas of fermionic atoms. When considering s-wave attractive interaction between atoms as for instance tuned by Feshbach resonance, topological superfluid state with high Chern number is unveiled in the presence of on-site rotation. This state supports chiral edge excitations, manifesting its topological nature. An experimental realization scheme is designed, which introduces a systematic way of achieving a new universality class (such as Chern number of 2) of orbital-hybridized topological phases beyond geometrically standard optical lattices.