SU(3) vs. SU(2) fermions in optical lattices: Color-Hall vs. spin-Hall topological insulators

Abstract

We contrast topological insulating phases of SU(3) and SU(2) fermions in optical lattices under artificial magnetic fields. For this purpose, we compare the phase diagram of chemical potential vs. color-flip fields for SU(3) colored fermions (D 10 representation) for fixed color-orbit coupling to the phase diagram of chemical potential vs. spin-flip fields for SU(2) spin- fermions (D 1 representation) for fixed spin-orbit coupling. To classify the emergent topological phases, we obtain the Chern matrix and identify three distinct topological invariants for SU(3) colored fermions: the charge-charge, the color-charge and the color-color Chern numbers. This is in sharp contrast to the SU(2) spin- case, where only two topological invariants are necessary: the charge-charge and the spin-charge Chern numbers. Although we focus on SU(3) colored and SU(2) spin- fermions, our results indicate the existence of three independent Chern numbers associated with the quantum Hall response for higher fermionic irreducible representations D p and D p0 (p > 1) of SU(2) and SU(3), respectively. We suggest to investigate this comparison using the internal states of ultracold Fermi atoms ytterbium-173 and strontium-87 .