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 .

我们对比了人工磁场下光晶格中 SU(3) 和 SU(2) 费米子的拓扑绝缘相。为此，我们将固定颜色轨道耦合的SU(3) 彩色费米子（D ¹⁰表示）的化学势与颜色翻转场的相图与化学势与自旋翻转场的相图进行比较用于固定自旋轨道耦合的SU(2) 自旋费米子（D ¹表示）。为了对涌现的拓扑相进行分类，我们获得了陈矩阵并确定了 SU(3) 有色费米子的三个不同的拓扑不变量：电荷-电荷、色荷和色-色陈数。这与 SU(2) 自旋形成鲜明对比 在这种情况下，只需要两个拓扑不变量：电荷-电荷和自旋-电荷陈数。虽然我们关注 SU(3) 有色和 SU(2) 自旋费米子，但我们的结果表明存在三个独立的陈数与量子霍尔响应相关联，用于更高的费米子不可约表示D ^p和D ^{p 0} ( p > 1)分别为 SU(2) 和 SU(3)。我们建议使用超冷费米原子 ytterbium-173和 strontium-87的内部状态来研究这种比较。