Liu Zheng-Fang, Wu Qing-Ping, Chen Ai-Xi, Xiao Xian-Bo, Liu Nian-Hua, Miao Guo-Xing
Department of Applied Physics, East China Jiaotong University, Nanchang 330013, People's Republic of China. Institute for Quantum Computing, University of Waterloo, Waterloo, ON N2L 3G1, Canada.
J Phys Condens Matter. 2017 Feb 1;29(4):045304. doi: 10.1088/1361-648X/29/4/045304. Epub 2016 Nov 29.
We investigated the edge states and quantum phase transition in graphene under an in-plane effective exchange field. The result shows that the combined effects of the in-plane effective exchange field and a staggered sublattice potential can induce zero-energy flat bands of edge states. Such flat-band edge states can evolve into helical-like ones in the presence of intrinsic spin-orbit coupling, with a unique spin texture. We also find that the bulk energy gap induced by the spin-orbit coupling and staggered sublattice potential can be closed and reopened with the in-plane effective exchange field, and the reopened bulk gap can be even larger than that induced by only the spin-orbit coupling and staggered sublattice potential, which is different from the case of an out-of-plane effective exchange field. The calculated spin-dependent Chern numbers suggest that the bulk gap closing and reopening is accompanied by a quantum phase transition from a trivial insulator phase across a metal phase into a spin-dependent quantum Hall phase.
我们研究了面内有效交换场作用下石墨烯中的边缘态和量子相变。结果表明，面内有效交换场和交错亚晶格势的联合作用可诱导边缘态的零能平带。在存在本征自旋轨道耦合的情况下，这种平带边缘态可演化为类螺旋边缘态，具有独特的自旋纹理。我们还发现，由自旋轨道耦合和交错亚晶格势诱导的体能隙可通过面内有效交换场关闭并重新打开，且重新打开的体能隙甚至可能大于仅由自旋轨道耦合和交错亚晶格势诱导的体能隙，这与面外有效交换场的情况不同。计算得到的自旋相关陈数表明，体能隙的关闭和重新打开伴随着从平凡绝缘体相穿过金属相到自旋相关量子霍尔相的量子相变。
