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.
For an ultra-thin Bi2Se3 film sandwiched between two ferromagnetic insulators (FIs), we investigate how its topological properties change with the angle between the magnetizations of the two FIs. The Chern numbers are calculated from the low-energy effective Hamiltonian for electrons in the surface states, and the bulk energy band and the edge states are simulated from the tight-binding model of a long ribbon with armchair edges on a two-dimensional honeycomb lattice, from which the topological phase of the system can be determined. It is found that with the magnetizations of the FIs varying from parallel to antiparallel, there appears a topological phase transition from the anomalous quantum Hall phase to the trivial insulating one at a critical angle.