Topological Color-Hall Insulators: SU(3) Fermions in Optical Lattices

We discuss the emergence of topological color insulators in optical lattices as quantum phases of SU(3) ultra-cold neutral fermions. We construct the Chern matrix and classify all insulating phases in terms of three topological invariants: the charge-charge, the color-charge and the color-color Chern numbers. Our classification transcends that of SU(2) systems which require only the charge-charge (charge-Hall) and spin-charge (spin-Hall) Chern numbers. To illustrate the topological classification of the insulating phases of SU(3) fermions, we construct phase diagrams of chemical potential and color-orbit parameter versus color-flip fields for fixed magnetic flux ratio.