Ultracold fermions with several flavors

Ultracold atoms have attracted enormous interest recently, and Cooper pairing between fermionic alkali atoms may have been observed experimentally. Besides the demonstration of phenomena that we are acquainted with from solid state physics, ultracold atoms possibly exhibit interesting many-body ground states that do not have straightforward counterparts in solid state physics. The hyperfine degree of freedom of the atoms in combination with optical lattices may allow for the approximate realization of fermionic SU(N) Hubbard models where N counts the number of trapped hyperfine states ('flavors'). We analyze the ground states of this model on the two-dimensional square lattice using one-loop renormalization group and meanfield techniques. In the repulsive case for N > 6 and half band filling staggered flux order is found as the dominant instability, in agreement with the large-N limit. In the attractive case and odd N a full Fermi surface coexists with a superfluid in the ground state. We describe how these unconventional paired states can be identified in the density response of the fermions.