Interband physics in an ultra-cold Fermi gas in an optical lattice

We study a gas of strongly polarized cold fermions in an optical lattice when the excited p-bands are populated. We derive the relevant Hamiltonian and discuss the expected phase diagram for both repulsive and attractive interactions. In the parameter regime covered here, checkerboard anti-ferromagnetic ordering is found to be possible for repulsive interactions while for attractive interactions, transitions between different types of paired phases are predicted.