论文标题
超电孔耦合SU的特征性，Chern数字和相图（3）光学晶格中
Eigenspectrum, Chern Numbers and Phase Diagrams of Ultracold Color-orbit Coupled SU(3) Fermions in Optical Lattices
论文作者
论文摘要
我们研究具有$ {\ rm su（3）} $对称性在光学晶格中的三个内部状态，红色，绿色和蓝色的三个内部状态，当有颜色轨道耦合和颜色叉场时。该系统对应于具有$ {\ rm su（2）} $对称性在有旋转轨道耦合和旋转式flipping zeeman字段的情况下对两层状态费米子的概括。我们研究了特征性和Chern数字，以描述在光学晶格中颜色轨道耦合费米子的相图中出现的不同拓扑阶段。我们获得了可以独立控制的人工磁，色轨和色叉场的函数。对于固定的人造磁通比，我们在化学电位与色闪光场或颜色轨道耦合的相图中确定拓扑量子相和相变，其中手性和中间段边缘状态的数量变化。拓扑非平凡的阶段分为三组：第一组具有非零的手性，仅表现出量子电荷效果；第二组具有总非零性手性，并且表现出量子电荷和量子色大厅的影响。第三组具有零性手性，但表现出量子色大厅的效果。这些阶段是量子厅和量子旋转大厅相的概括，用于带电$ 1/2 $ fermions。最后，我们还描述了状态的颜色密度以及总填充因子和固定颜色轨道，色叉和磁通比的化学潜力中的楼梯结构。我们在合理填充因子上表明了不可压缩状态的存在，该因子精确地通过了一个间隙标记定理给出，该定理将填充因子与磁通量比和拓扑量子数相关联。
We study ultracold color fermions with three internal states Red, Green and Blue with ${\rm SU(3)}$ symmetry in optical lattices, when color-orbit coupling and color-flip fields are present. This system corresponds to a generalization of two-internal state fermions with ${\rm SU(2)}$ symmetry in the presence of spin-orbit coupling and spin-flipping Zeeman fields. We investigate the eigenspectrum and Chern numbers to describe different topological phases that emerge in the phase diagrams of color-orbit coupled fermions in optical lattices. We obtain the phases as a function of artificial magnetic, color-orbit and color-flip fields that can be independently controlled. For fixed artificial magnetic flux ratio, we identify topological quantum phases and phase transitions in the phase diagrams of chemical potential versus color-flip fields or color-orbit coupling, where the chirality and number of midgap edge states changes. The topologically non-trivial phases are classified in three groups: the first group has total non-zero chirality and exhibit only the quantum charge Hall effect; the second group has total non-zero chirality and exhibit both quantum charge and quantum color Hall effects; and the third group has total zero chirality, but exhibit the quantum color Hall effect. These phases are generalizations of the quantum Hall and quantum spin Hall phases for charged spin-$1/2$ fermions. Lastly, we also describe the color density of states and a staircase structure in the total and color filling factors versus chemical potential for fixed color-orbit, color-flip and magnetic flux ratio. We show the existence of incompressible states at rational filling factors precisely given by a gap-labelling theorem that relates the filling factors to the magnetic flux ratio and topological quantum numbers.
