Liu Zhu-Xi, Li Zhi-Hua, Wang An-Min
Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China.
J Phys Condens Matter. 2019 Mar 27;31(12):125402. doi: 10.1088/1361-648X/aaff16. Epub 2019 Jan 16.
We propose a model of two-leg ladder topological insulator in which the spin-orbit couplings are presented in both intra-chain and inter-chain interactions. The topological phase supports four fractional charged edge states localized at opposite ends of the ladder, which belongs to the chiral symplectic (CII) class protected by time-reversal symmetry and chiral symmetry. In our model, the presence of time-reversal and chiral symmetry generates fourfold degeneracy for the edge states, and the two edge states with same chirality at one end of the ladder each carries half charge. In contrast to the two edge states spatially localized at one end of the ladder being not distinguished, these two edge states can be detected by the momentum density. The experimental scheme for realizing our model with cold atoms in optical lattice is discussed. By introducing a magnetic field in the x direction, the system is driven from CII class to AIII class. In AIII class, there exist two distinct topological phases that exhibit four degenerate edge states and two degenerate edge states in the gap, respectively. As same as the system in CII class, each edge state carries a half charge in AIII class.
我们提出了一种两腿梯子型拓扑绝缘体模型，其中自旋轨道耦合同时存在于链内和链间相互作用中。该拓扑相支持四个分数带电边缘态，它们局域在梯子的两端，属于受时间反演对称性和手征对称性保护的手征辛（CII）类。在我们的模型中，时间反演对称性和手征对称性的存在导致边缘态出现四重简并，梯子一端具有相同手征性的两个边缘态各携带半个电荷。与空间局域在梯子一端的两个边缘态无法区分不同，这两个边缘态可以通过动量密度来检测。讨论了在光学晶格中用冷原子实现我们模型的实验方案。通过在x方向引入磁场，系统从CII类被驱动到AIII类。在AIII类中，存在两个不同的拓扑相，分别在能隙中呈现四个简并边缘态和两个简并边缘态。与CII类中的系统一样，AIII类中的每个边缘态都携带半个电荷。
