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.