本文研究了磁场作用下双层石墨烯中的拓扑相。当考虑内禀自旋轨道耦合时，系统中出现许多拓扑相，通过调节双层石墨烯的层间电压和费米能可以实现拓扑相变。另外，还研究了时间反演对称性破缺的自旋霍尔效应的稳定性，发现它对于对称性破缺的扰动是非常稳定的。在内禀自旋轨道耦合和塞曼劈裂共同作用下，当塞曼劈裂很强时，自旋霍尔态会被破坏而自旋过滤的霍尔态将依然保持。这些研究结果在自旋电子器件方面有着巨大的潜在应用价值。%We report the investigation of topological phases in biased bilayer graphene at a magnetic field. Vari-ous kinds of topological phases can be obtained when considering the intrinsic spin-orbit coupling. Topological phase transition between these phases can be realized by tuning the bias voltage and Fermi energy. Besides, the stability of time-reversal symmetry-broken quantum spin Hall effect is investigated, which is robust against symmetry-breaking per-turbations. The combined effect of intrinsic SOC and Zeeman splitting is also explored, and we find that the QSH phase is broken by a large Zeeman splitting whereas the spin-filtered QH phase remains. These results could have great potential for applications in spintronics devices.
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