Spin Chern numbers and time-reversal-symmetry-broken quantum spin Hall effect

The quantum spin Hall （QSH） effect is considered to be unstable to perturbations violating the time-reversal （TR） symmetry. We review some recent developments in the search of the QSH effect in the absence of the TR symmetry. The possibility to realize a robust QSH effect by artificial removal of the TR symmetry of the edge states is explored. As a useful tool to characterize topological phases without the TR symmetry, the spin-Chern number theory is introduced.     

Coupling-matrix approach to the Chern number calculation in disordered systems

The Chern number is often used to distinguish different topological phases of matter in two-dimensional electron systems. A fast and efficient coupling-matrix method is designed to calculate the Chern number in finite crystalline and disordered systems. To show its effectiveness, we apply the approach to the Haldane model and the lattice Hofstadter model, and obtain the correct quantized Chern numbers. The disorder-induced topological phase transition is well reproduced, when the disorder strength is increased beyond the critical value. We expect the method to be widely applicable to the study of topological quantum numbers.     

铁磁绝缘体间的极薄Bi2Se3薄膜的相变研究

研究一个极薄三维拓扑绝缘体Bi₂Se₃薄膜处于两个铁磁绝缘体层之间, 其铁磁层的磁化方向都处于竖直平面, 系统拓扑性质随磁化方向夹角的变化. 从表面态电子低能有效哈密顿量出发计算系统的Chern 数, 和运用一个具有Armchair边界的单层六角晶格带的紧束缚模型模拟系统的体能带和边缘态, 来确定系统所处的拓扑相. 发现两个铁磁层的磁化方式从平行转到反平行的某一临界角度, 系统经历从反常量子霍尔相到普通绝缘相的转变.