深圳大学学报理工版

量子反常霍尔效应是一种存在于二维电子气中,具有无带隙的手性边缘态但体态绝缘的物理现象.不同于强磁场下量子化朗道能级引起的量子霍尔效应,量子反常霍尔效应可通过引入自旋轨道耦合相互作用以及交换场来实现.作者回顾了量子反常霍尔效应的研究进展,评述了石墨烯中的量子反常霍尔效应.通过理论模型预言在石墨烯体系中引入交换场破坏时间反演对称性,通过考虑Rashba自旋-轨道耦合,可在狄拉克点打开一个拓扑非平庸的量子反常霍尔效应体能隙,进一步分析解释其物理根源.讨论了几种实验原型,尝试通过外部操控在石墨烯中实现量子反常霍尔效应.

Quantum anomalous Hall effect is a physical phenomenon of two-dimensional systems characterized by the insulating bulk states and chirally propagating gapless edge modes. Different from the quantum Hall effect caused by quantized Landau-level due to the strong magnetic field, the quantum anomalous Hall effect can be realized by the joint effect of spin-orbit coupling and local magnetization in the absence of Landau-level. In this paper, we, after briefly introducing the history and current status of the quantum anomalous Hall effect, mainly focus on the graphene which is a famous two-dimensional material possesses intriguing electronic and magnetic properties. We first give a simple theoretical model where the exchange field is present to break the time reversal symmetry and then the Rashba spin-orbit coupling opens an energy gap to realize quantum anomalous Hall effect in graphene. Then we further explain the microscopic mechanism. At last, we discuss several possible experimental prototypes aimed at realizing the quantum anomalous Hall effect in realistic.

引言
1 石墨烯及其特性
2 石墨烯中量子反常霍尔效应的理想
3 实验原型设计
4 结语

图1 石墨烯自由度示意图<br/>Fig.1 Freedoms of graphene

图1 石墨烯自由度示意图
Fig.1 Freedoms of graphene

图2 二维拓扑绝缘体的边缘态示意图[18]<br/>Fig.2 Edge states of 2D topological insulator[18]

图2 二维拓扑绝缘体的边缘态示意图[18]
Fig.2 Edge states of 2D topological insulator[18]

图3 石墨烯在自旋轨道耦合作用和交换场存在情况下的能带图[10]<br/>Fig.3 Energy bands of graphene with Rashba spin orbit coupling and exchange field[10]

图3 石墨烯在自旋轨道耦合作用和交换场存在情况下的能带图[10]
Fig.3 Energy bands of graphene with Rashba spin orbit coupling and exchange field[10]

图4 倒空间中的贝利曲率[10]<br/>Fig.4 Berry curvatures of graphene in first Brillouin zone(a)and along x-axis(b)[10]

图4 倒空间中的贝利曲率[10]
Fig.4 Berry curvatures of graphene in first Brillouin zone(a)and along x-axis(b)[10]

图5 石墨烯条带的能带结构<br/>Fig.5 Band structure of graphene nanoribbon

图5 石墨烯条带的能带结构
Fig.5 Band structure of graphene nanoribbon

图6 K和K'谷不同的价带电子态的自旋和赝自旋织构[28]<br/>Fig.6 Texture of real spin and pseudospins of different enregy bands in K and K' valleys[28]

图6 K和K'谷不同的价带电子态的自旋和赝自旋织构[28]
Fig.6 Texture of real spin and pseudospins of different enregy bands in K and K' valleys[28]

图7 铁原子吸附在4×4的石墨烯超元胞后的能带结构及产生的贝利曲率的分布[30]<br/>Fig.7 Energy bands and Berry curvature distribution of graphene with Fe atoms adsorbed in 4×4 supercells[30]

图7 铁原子吸附在4×4的石墨烯超元胞后的能带结构及产生的贝利曲率的分布[30]
Fig.7 Energy bands and Berry curvature distribution of graphene with Fe atoms adsorbed in 4×4 supercells[30]

图8 3×3超元胞正格矢和倒格矢示意图[30]<br/>Fig.8 Lattice and reciprocal lattice for 3×3 supercell of graphene[30]

图8 3×3超元胞正格矢和倒格矢示意图[30]
Fig.8 Lattice and reciprocal lattice for 3×3 supercell of graphene[30]

图9 吸附原子对石黑烯能带结构的影响[35]<br/>Fig.9 Influence of adatoms on energy bands of graphene[35]

图9 吸附原子对石黑烯能带结构的影响[35]
Fig.9 Influence of adatoms on energy bands of graphene[35]

图10 随机吸附对3×3超元胞输运性质的影响[35]<br/>Fig.10 Effect of random adsorption on transport properties[35]

图10 随机吸附对3×3超元胞输运性质的影响[35]
Fig.10 Effect of random adsorption on transport properties[35]

[1] Hall E H.On a new action of the magnet on electric currents[J].American Journal of Mathematics, 1987, 2(3): 287-292.
[2] Ando T, Fowler A B,Stern F. Electronic properties of two-dimensional systems[J].Reviews of Modern Physics, 1982, 54(2): 437- 672.
[3] Klitzing K V. The quantized hall effect[J].Physica B+C, 1984, 126(1/2/3): 242-249.
[4] Zhang Yuanbo, Tan Yanwen, Stormer H L, et al. Experimental observation of the quantum Hall effect and Berry's phase in graphene [J].Nature, 2005, 438: 201-204.
[5] Thouless D J, Kohmoto M, Nightingale M P, et al. Quantized Hall conductance in a two-dimensional periodic potential [J].Physical Review Letters, 1982, 49: 405- 408.
[6] Haldane F M. Model for a quantum Hall effect without Landau levels: condensed-matter realization of the “parity anomaly”[J]. Physical Review Letters, 1988, 61(18): 2015-2018.
[7] Onoda M, Nagaosa N. Quantized anomalous Hall effect in two-dimensional ferromagnets: quantum Hall effect in metals[J]. Physical Review Letters, 2003, 90(20): 206601-1-206601- 4.
[8] Liu Chaoxing, Qi Xiaoliang, Dai Xi, et al.Quantum anomalous Hall effect in Hg1-yMnyTe quantum wells[J]. Physical Review Letters, 2008, 101(14): 146802-1-146802-5.
[9] Yu Rui, Zhang Wei, Zhang Haijun, et al.Quantized anomalous Hall effect in magnetic topological insulators[J].Science,2010,329(5987):61- 64.
[10] Qiao Zhenhua, Yang Shengyuan, Feng Wanxiang, et al. Quantum anomalous Hall effect in graphene from Rashba and exchange effects[J]. Physical Review B, 2010, 82(16): 161414-1-161414- 4.
[11] Novoselov K S, Geim A K, Morozov S V, et al. Two-dimensional gas of massless Dirac fermions in graphene[J]. Nature, 2005, 438(765): 197-200.
[12] Hasan M Z, Kane C L.Colloquium: topological insulators[J].Reviews of Modern Physics,2010,82(4):3045-3067.
[13] Nomura K, Nagaosa N.Surface-quantized anomalous Hall current and the magnetoelectric effect in magnetically disordered topological insulators[J].Physical Review Letters,2011,106(16):166802-1-166802-5.
[14] Zhang Hongbin, Lazo C, Blügel S, et al. Electrically tunable quantum anomalous Hall effect in graphene decorated by 5d transition-metal adatoms[J].Physical Review Letters, 2012, 108(5): 056802-1-056802- 4.
[15] Ezawa M. Valley-polarized metals and quantum anomalous Hall effect in silicene[J].Physical Review Letters, 2012, 109(5): 055502-1-055502-5.
[16] Garrity K F,David V. Chern insulators from heavy atoms on magnetic substrates [J].Physical Review Letters, 2012, 110(11): 116802-1-116802-5.
[17] Wang Z F, Liu Zheng, Liu Feng. Quantum anomalous Hall effect in 2D organic topological insulators[J].Physical Review Letters, 2013, 110(13):196801-1-196801-5.
[18] Kane C L, Mele E J.Quantum spin Hall effect in graphene[J].Physical Review Letters,2005,95(22):226801-1-226801- 4.
[19] Murakami S, Nagaosa N, Zhang Shoucheng.Spin-Hall insulator[J].Physical Review Letters,2004,93(15):156804-1-156804- 4.
[20] König M, Wiedmann S, Brüne C, et al.Quantum spin hall insulator state in HgTe quantum wells[J].Science,2007,318(5851):766-770.
[21] Hsieh D, Qian D, Wray L, et al.A topological Dirac insulator in a quantum spin Hall phase[J].Nature,2008,452(7190):970-974.
[22] Zhang Haijun, Liu Chaoxing, Qi Xiaoliang, et al. Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface[J]. Nature Physics, 2009, 5(6): 438- 442.
[23] Chang Cuizu, Zhang Jinsong, Feng Xiao, et al.Experimental observation of the quantum anomalous Hall effect in a magnetic topological insulator[J].Science,2013,340(6129):167-170.
[24] Castro Neto A H, Guinea F, Peres N M R, et al.The electronic properties of graphene[J].Reviews of Modern Physics,2009,81(1):109-162.
[25] Das Sarma S, Adam S, Hwang E H, et al.Electronic transport in two-dimensional graphene[J].Reviews of Modern Physics,2011,83(2):1- 69.
[26] Novoselov K S, Jiang Z, Zhang Y, et al. Room-temperature quantum Hall effect in graphene[J].Science,2007,315(5817):1379.
[27] McCann E,Koshino M.The electronic properties of bilayer graphene[J].Reports on Progress in Physics,2013,75(5):056503-1- 056503-31.
[28] Qiao Zhenhua, Jiang Hua, Li Xiao, et al.Microscopic theory of quantum anomalous Hall effect in graphene[J].Physical Review B,2012,85(11):115439-1-115439-10.
[29] Zhang Fang, MacDonald A H, Mele E J, et al.Valley Chern numbers and boundary modes in gapped bilayer graphene[J].Proceedings of the National Academy of Sciences of the United States of America,2013,110(26):10546-10551.
[30] Ding Jun, Qiao Zhenhua, Feng Wanxiang, et al.Engineering quantum anomalous/valley Hall states in graphene via metal-atom adsorption: an abinitio study[J].Physical Review B,2011,84(19):195444-1-195444-9.
[31] Kane C L, Mele E J.Z2 topological order and the quantum spin Hall effect[J].Physical Review Letters, 2005, 95(14):146802-1-146802- 4.
[32] Yao Yugui, Ye Fei, Qi Xiaoliang, et al.Spin-orbit gap of graphene: first-principles calculations[J].Physical Review B,2007,75(4):041401-1- 041401- 4.
[33] Dedkov Y S, Fonin M, Rüdiger U, et al. Rashba effect in the graphene/Ni(111)system[J]. Physical Review Letters,2008, 100(10): 107602-1-107602- 4.
[34] Tse W K, Qiao Zhenhua, Yao Yugui, et al.Quantum anomalous Hall effect in single-layer and bilayer graphene[J].Physical Review B, 2011, 83(15):155447-1-155447- 8.
[35] Jiang Hua, Qiao Zhenhua, Liu Haiwen, et al.Stabilizing topological phases in graphene via random adsorption[J].Physical Review Letters, 2012, 109(11):116803-1-116803-5.
[36] Qiao Zhenhua, Ren Wei, Chen Hua, et al.Quantum anomalous Hall effect in graphene proximity coupled to an antiferromagnetic insulator[J].Physical Review Letters, 2014, 112(11):116404-1-116404-5.
[37] Jiang Hua, Qiao Zhenhua, Liu Haiwen, et al.Quantum anomalous Hall effect with tunable Chern number in magnetic topological insulator film[J].Physical Review B, 2012, 85(4):045445-1- 045445- 8.
[38] Qiao Zhenhua, Li Xiao, Tse W K, et al.Topological phases in gated bilayer graphene: effects of Rashba spin-orbit coupling and exchange field[J].Physical Review B, 2013, 87(12):125405-1-125405-15.
[39] Min H, Hill J E, Sinitsyn N A, et al.Intrinsic and Rashba spin-orbit interactions in graphene sheets[J].Physical Review B, 2006, 74(16):165310-1-165310-5.
[40] Marchenko D, Varykhalov A, Scholz M R, et al.Giant Rashba splitting in graphene due to hybridization with gold[J].Nature Communications,2012,3:1232-1-1232-16.
[41] Eelbo T, Was'niowska M, Thakur P, et al. Adatoms and clusters of 3d transition metals on graphene: electronic and magnetic configurations[J].Physical Review Letters, 2013, 110(13):136804-1-136804- 8.

备注

引言

1 石墨烯及其特性

2 石墨烯中量子反常霍尔效应的理想

3 实验原型设计

4 结语

期刊信息

备注

引言

1 石墨烯及其特性

2 石墨烯中量子反常霍尔效应的理想

3 实验原型设计

4 结 语

期刊信息

4 结语