搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

缀饰格子中时间反演对称破缺的量子自旋霍尔效应

耿虎 计青山 张存喜 王瑞

引用本文:
Citation:

缀饰格子中时间反演对称破缺的量子自旋霍尔效应

耿虎, 计青山, 张存喜, 王瑞

Time-reversal-symmetry broken quantum spin Hall in Lieb lattice

Geng Hu, Ji Qing-Shan, Zhang Cun-Xi, Wang Rui
PDF
导出引用
  • 研究了缀饰格子中的量子自旋霍尔效应,模型中同时考虑了Rashba自旋轨道耦合和交换场的作用.缀饰格子具有简立方对称性,以零能平带和单狄拉克锥结构为主要特点.在缀饰格子中,不论是实现量子自旋霍尔效应还是量子反常霍尔效应,都需要一个不为零的内禀自旋轨道耦合作用来打开一个完全的体能隙,这与石墨烯等六角格子模型有着很大的不同.在交换场破坏了时间反演对称性的情况下,以自旋陈数为标志的量子自旋霍尔效应仍然能够存在,边缘态和极化率的相关结果也证明了这一结论.结果表明自旋陈数比z2拓扑数在表征量子自旋霍尔效应方面有着更广泛的适用范围,相应的结论为利用磁场控制量子自旋霍尔效应提出了一个理论模型和依据.
    In this paper, the time-reversal (TR) symmetry broken quantum spin Hall (QSH) in Lieb lattice is investigated in the presence of both Rashba spin-orbit coupling (SOC) and uniform exchange field. The Lieb lattice has a simple cubic symmetry, and it has three different sites in each unit cell. The most distinctive feature of this model is that it contains only one Dirac-cone in the first Brillouin zone, where the upper dispersive band and the lower dispersive band touch the middle zero-energy band at M point and form a cone-like dispersion. The intrinsic SOC is essentially needed to open the full energy gap in the bulk. When the intrinsic SOC is nonzero, all the band structures are separated everywhere in the Brillouin zone and can be characterized by some topological invariants. The exact QSH first put forward by Kane and Mele in 2005 is characterized by the z2 number. The protection from the TR symmetry ensures the gapless crossing in the surface state in the bulk gap. In our model, the presence of the exchange field breaks the TR symmetry, which results in opening a small gap in the crossing point and the z2 topological order is not suitable for the system. This kind of state is a TR symmetry broken QSH, which is characterized by the spin Chern numbers. The spin Chern numbers have a much wider scope of application than z2 index. It is suitable for both TR symmetry system and the TR symmetry broken system. For Lieb lattice ribbons, the spin polarization and the wave-function distributions are obtained numerically. There exists a weak scattering between the counter-propagating states in the TR symmetry broken QSH, and the spin transport along the boundary with a low dissipation replaces the dissipationless spin current in a TR symmetry system. In experiment, such a system can be realized by the two-dimensional Fermi gases in optical lattice with Lieb symmetry. The above conclusions are expected to give theoretical guidance in the spin device and the quantum information.
      通信作者: 王瑞, wangrui@zjou.edu.cn
    • 基金项目: 国家自然科学基金(批准号:11304281,10547001)和浙江省自然科学基金(批准号:LY13D060002)资助的课题.
      Corresponding author: Wang Rui, wangrui@zjou.edu.cn
    • Funds: Project supported by National Natural Science Foundation of China (Grant Nos. 11304281, 10547001) and the Natural Science Foundation of Zhejiang Province, China (Grant No. LY13D060002).
    [1]

    Klitzing K V, Dorda G, Pepper M 1980 Phys. Rev. Lett. 45 494

    [2]

    Tsui D C, Stormer H L, Gossard A C 1982 Phys. Rev. Lett. 48 1559

    [3]

    Kane C L, Mele E J 2005 Phys. Rev. Lett. 95 226801

    [4]

    Zhang H J, Xu Y, Wang J, Chang K, Zhang S C 2014 Phys. Rev. Lett. 112 216803

    [5]

    Miao M S, Yan Q, van de Wall C G, Lou W K, Li L L, Chang K 2012 Phys. Rev. Lett. 109 186803

    [6]

    Zhang D, Lou W K, Miao M S, Zhang S C, Chang K 2013 Phys. Rev. Lett. 111 156402

    [7]

    Hasan M Z, Kane C L 2010 Rev. Mod. Phys. 82 3045

    [8]

    Qi X L, Zhang S C 2010 Physics Today 63 33

    [9]

    Li Z J, Li Q, Chen Z G, Li H B, Fang Y 2014 Chin. Phys. B 23 028102

    [10]

    Thouless D J, Kohmoto M, Nightingale M P, Den Nijs M 1982 Phys. Rev. Lett. 49 405

    [11]

    Kane C L, Mele E J 2005 Phys. Rev. Lett. 95 146802

    [12]

    Bernevig B A, Hughes T L, Zhang S C 2006 Science 314 1757

    [13]

    Konig M, Wiedmann S, Brune C, Roth A, Buthmann H, Molenkamp L W, Qi X L, Zhang S C 2007 Science 318 766

    [14]

    Sheng D N, Weng Z Y, Sheng L, Haldane F D M 2006 Phys. Rev. Lett. 97 036808

    [15]

    Yang Y Y, Xu Z, Sheng L, Wang B G, Xing D Y, Sheng D N 2011 Phys. Rev. Lett. 107 066602

    [16]

    Pradan E 2009 Phys. Rev. B 80 125327

    [17]

    Qiao Z H, Yang S A, Feng W X, Tse W K, Ding J, Yao Y G, Wang J, Niu Q 2010 Phys. Rev. B 82 161414

    [18]

    Haldane F D M 1988 Phys. Rev. Lett. 61 2015

    [19]

    Onoda M, Nagaosa N 2003 Phys. Rev. Lett. 90 206601

    [20]

    Liu C X, Qi X L, Dai X, Fang Z, Zhang S C 2008 Phys. Rev. Lett. 101 146802

    [21]

    Raghu S, Chung S B, Qi X L, Zhang S C 2010 Phys. Rev. Lett. 104 116401

    [22]

    Yu R, Zhang W, Zhang H J, Zhang S C, Dai X, Fang Z 2010 Science 329 61

    [23]

    Wu C 2008 Phys. Rev. Lett. 101 186807

    [24]

    Guo H M, Franz M 2009 Phys. Rev. B 80 113102

    [25]

    Zhang Z Y 2011 J. Phys. Condens. Matter 23 365801

    [26]

    Ishizuka H, Motome Y 2013 Phys. Rev. B 87 081105

    [27]

    Kargarian M, Fiete G A 2010 Phys. Rev. B 82 085106

    [28]

    Chen W C, Liu R, Wang Y F, Gong C D 2012 Phys. Rev. B 86 085311

    [29]

    Ohgushi K, Murakami S, Nagaosa N 2000 Phys. Rev. B 62 R6065

    [30]

    Wang Z, Zhang P 2008 Phys. Rev. B 77 125119

    [31]

    Shen R, Shao L B, Wang B, Xing D Y 2010 Phys. Rev. B 81 041410

    [32]

    Beugeling W, Everts J C, Morais S C 2012 Phys. Rev. B 86 195129

    [33]

    Zhao A, Shen S Q 2012 Phys. Rev. B 85 085209

    [34]

    Weeks C, Franz M 2010 Phys. Rev. B 82 085310

    [35]

    Sun K, Fradkin E 2008 Phys. Rev. B 78 245122

    [36]

    He Y, Moore J, Varma C M 2012 Phys. Rev. B 85 155106

    [37]

    Stanescu T D, Galitski V, Vaishnav J Y, Clark C W, Das Sarma S 2009 Phys. Rev. A 79 053639

    [38]

    Zhu S L, Fu H, Wu C J, Zhang S C, Duan L M 2006 Phys. Rev. Lett. 97 240401

    [39]

    Bloch I, Dalibard J, Zwerger W 2008 Rev. Mod. Phys. 80 885

    [40]

    Goldman N, Urban D F, Bercioux D 2011 Phys. Rev. A 83 063601

    [41]

    Gibertini M, Singha A, Pellegrini V, Polini M, Vignale G, Pinczuk A, Pfeiffer L N, West K W 2009 Phys. Rev. B 79 241406

    [42]

    Zhang C, Tewari S, Lutchyn R M, Das Sarma S 2008 Phys. Rev. Lett. 101 160401

    [43]

    Chosh P, Sau J D, Tewari S, Das Sarma S 2010 Phys. Rev. B 82 184525

    [44]

    Temari S, Sau J D 2012 Phys. Rev. Lett. 109 150408

  • [1]

    Klitzing K V, Dorda G, Pepper M 1980 Phys. Rev. Lett. 45 494

    [2]

    Tsui D C, Stormer H L, Gossard A C 1982 Phys. Rev. Lett. 48 1559

    [3]

    Kane C L, Mele E J 2005 Phys. Rev. Lett. 95 226801

    [4]

    Zhang H J, Xu Y, Wang J, Chang K, Zhang S C 2014 Phys. Rev. Lett. 112 216803

    [5]

    Miao M S, Yan Q, van de Wall C G, Lou W K, Li L L, Chang K 2012 Phys. Rev. Lett. 109 186803

    [6]

    Zhang D, Lou W K, Miao M S, Zhang S C, Chang K 2013 Phys. Rev. Lett. 111 156402

    [7]

    Hasan M Z, Kane C L 2010 Rev. Mod. Phys. 82 3045

    [8]

    Qi X L, Zhang S C 2010 Physics Today 63 33

    [9]

    Li Z J, Li Q, Chen Z G, Li H B, Fang Y 2014 Chin. Phys. B 23 028102

    [10]

    Thouless D J, Kohmoto M, Nightingale M P, Den Nijs M 1982 Phys. Rev. Lett. 49 405

    [11]

    Kane C L, Mele E J 2005 Phys. Rev. Lett. 95 146802

    [12]

    Bernevig B A, Hughes T L, Zhang S C 2006 Science 314 1757

    [13]

    Konig M, Wiedmann S, Brune C, Roth A, Buthmann H, Molenkamp L W, Qi X L, Zhang S C 2007 Science 318 766

    [14]

    Sheng D N, Weng Z Y, Sheng L, Haldane F D M 2006 Phys. Rev. Lett. 97 036808

    [15]

    Yang Y Y, Xu Z, Sheng L, Wang B G, Xing D Y, Sheng D N 2011 Phys. Rev. Lett. 107 066602

    [16]

    Pradan E 2009 Phys. Rev. B 80 125327

    [17]

    Qiao Z H, Yang S A, Feng W X, Tse W K, Ding J, Yao Y G, Wang J, Niu Q 2010 Phys. Rev. B 82 161414

    [18]

    Haldane F D M 1988 Phys. Rev. Lett. 61 2015

    [19]

    Onoda M, Nagaosa N 2003 Phys. Rev. Lett. 90 206601

    [20]

    Liu C X, Qi X L, Dai X, Fang Z, Zhang S C 2008 Phys. Rev. Lett. 101 146802

    [21]

    Raghu S, Chung S B, Qi X L, Zhang S C 2010 Phys. Rev. Lett. 104 116401

    [22]

    Yu R, Zhang W, Zhang H J, Zhang S C, Dai X, Fang Z 2010 Science 329 61

    [23]

    Wu C 2008 Phys. Rev. Lett. 101 186807

    [24]

    Guo H M, Franz M 2009 Phys. Rev. B 80 113102

    [25]

    Zhang Z Y 2011 J. Phys. Condens. Matter 23 365801

    [26]

    Ishizuka H, Motome Y 2013 Phys. Rev. B 87 081105

    [27]

    Kargarian M, Fiete G A 2010 Phys. Rev. B 82 085106

    [28]

    Chen W C, Liu R, Wang Y F, Gong C D 2012 Phys. Rev. B 86 085311

    [29]

    Ohgushi K, Murakami S, Nagaosa N 2000 Phys. Rev. B 62 R6065

    [30]

    Wang Z, Zhang P 2008 Phys. Rev. B 77 125119

    [31]

    Shen R, Shao L B, Wang B, Xing D Y 2010 Phys. Rev. B 81 041410

    [32]

    Beugeling W, Everts J C, Morais S C 2012 Phys. Rev. B 86 195129

    [33]

    Zhao A, Shen S Q 2012 Phys. Rev. B 85 085209

    [34]

    Weeks C, Franz M 2010 Phys. Rev. B 82 085310

    [35]

    Sun K, Fradkin E 2008 Phys. Rev. B 78 245122

    [36]

    He Y, Moore J, Varma C M 2012 Phys. Rev. B 85 155106

    [37]

    Stanescu T D, Galitski V, Vaishnav J Y, Clark C W, Das Sarma S 2009 Phys. Rev. A 79 053639

    [38]

    Zhu S L, Fu H, Wu C J, Zhang S C, Duan L M 2006 Phys. Rev. Lett. 97 240401

    [39]

    Bloch I, Dalibard J, Zwerger W 2008 Rev. Mod. Phys. 80 885

    [40]

    Goldman N, Urban D F, Bercioux D 2011 Phys. Rev. A 83 063601

    [41]

    Gibertini M, Singha A, Pellegrini V, Polini M, Vignale G, Pinczuk A, Pfeiffer L N, West K W 2009 Phys. Rev. B 79 241406

    [42]

    Zhang C, Tewari S, Lutchyn R M, Das Sarma S 2008 Phys. Rev. Lett. 101 160401

    [43]

    Chosh P, Sau J D, Tewari S, Das Sarma S 2010 Phys. Rev. B 82 184525

    [44]

    Temari S, Sau J D 2012 Phys. Rev. Lett. 109 150408

  • [1] 陈西浩, 夏继宏, 李孟辉, 翟福强, 朱广宇. 自旋-1/2量子罗盘链的量子相与相变. 物理学报, 2022, 71(3): 030302. doi: 10.7498/aps.71.20211433
    [2] 王志梅, 王虹, 薛乃涛, 成高艳. 自旋轨道耦合量子点系统中的量子相干. 物理学报, 2022, 71(7): 078502. doi: 10.7498/aps.71.20212111
    [3] 贾亮广, 刘猛, 陈瑶瑶, 张钰, 王业亮. 单层二维量子自旋霍尔绝缘体1T'-WTe2研究进展. 物理学报, 2022, (): . doi: 10.7498/aps.71.20220100
    [4] 陈西浩, 夏继宏, 李孟辉, 翟福强, 朱广宇. 自旋-1/2量子罗盘链的量子相与相变. 物理学报, 2021, (): . doi: 10.7498/aps.70.20211433
    [5] 张爱霞, 姜艳芳, 薛具奎. 光晶格中自旋轨道耦合玻色-爱因斯坦凝聚体的非线性能谱特性. 物理学报, 2021, 70(20): 200302. doi: 10.7498/aps.70.20210705
    [6] 薛海斌, 段志磊, 陈彬, 陈建宾, 邢丽丽. 自旋轨道耦合Su-Schrieffer-Heeger原子链系统的电子输运特性. 物理学报, 2021, 70(8): 087301. doi: 10.7498/aps.70.20201742
    [7] 施婷婷, 汪六九, 王璟琨, 张威. 自旋轨道耦合量子气体中的一些新进展. 物理学报, 2020, 69(1): 016701. doi: 10.7498/aps.69.20191241
    [8] 陈爱民, 刘东昌, 段佳, 王洪雷, 相春环, 苏耀恒. 含有Dzyaloshinskii-Moriya相互作用的自旋1键交替海森伯模型的量子相变和拓扑序标度. 物理学报, 2020, 69(9): 090302. doi: 10.7498/aps.69.20191773
    [9] 李志强, 王月明. 一维谐振子束缚的自旋轨道耦合玻色气体. 物理学报, 2019, 68(17): 173201. doi: 10.7498/aps.68.20190143
    [10] 梁滔, 李铭. 自旋轨道耦合系统中的整数量子霍尔效应. 物理学报, 2019, 68(11): 117101. doi: 10.7498/aps.68.20190037
    [11] 陈西浩, 王秀娟. 一维扩展量子罗盘模型的拓扑序和量子相变. 物理学报, 2018, 67(19): 190301. doi: 10.7498/aps.67.20180855
    [12] 杨圆, 陈帅, 李小兵. Rashba自旋轨道耦合下square-octagon晶格的拓扑相变. 物理学报, 2018, 67(23): 237101. doi: 10.7498/aps.67.20180624
    [13] 龙洋, 任捷, 江海涛, 孙勇, 陈鸿. 超构材料中的光学量子自旋霍尔效应. 物理学报, 2017, 66(22): 227803. doi: 10.7498/aps.66.227803
    [14] 刘胜利, 厉建峥, 程杰, 王海云, 李永涛, 张红光, 李兴鳌. 强自旋轨道耦合化合物Sr2-xLaxIrO4的掺杂和拉曼谱学. 物理学报, 2015, 64(20): 207103. doi: 10.7498/aps.64.207103
    [15] 陈东海, 杨谋, 段后建, 王瑞强. 自旋轨道耦合作用下石墨烯pn结的电子输运性质. 物理学报, 2015, 64(9): 097201. doi: 10.7498/aps.64.097201
    [16] 陈光平. 简谐+四次势中自旋轨道耦合旋转玻色-爱因斯坦凝聚体的基态结构. 物理学报, 2015, 64(3): 030302. doi: 10.7498/aps.64.030302
    [17] 龚士静, 段纯刚. 金属表面Rashba自旋轨道耦合作用研究进展. 物理学报, 2015, 64(18): 187103. doi: 10.7498/aps.64.187103
    [18] 张磊, 李辉武, 胡梁宾. 二维自旋轨道耦合电子气中持续自旋螺旋态的稳定性的研究. 物理学报, 2012, 61(17): 177203. doi: 10.7498/aps.61.177203
    [19] 杨杰, 董全力, 江兆潭, 张杰. 自旋轨道耦合作用对碳纳米管电子能带结构的影响. 物理学报, 2011, 60(7): 075202. doi: 10.7498/aps.60.075202
    [20] 余志强, 谢泉, 肖清泉. 狭义相对论下电子自旋轨道耦合对X射线光谱的影响. 物理学报, 2010, 59(2): 925-931. doi: 10.7498/aps.59.925
计量
  • 文章访问数:  3648
  • PDF下载量:  270
  • 被引次数: 0
出版历程
  • 收稿日期:  2016-12-08
  • 修回日期:  2017-04-17
  • 刊出日期:  2017-06-05

缀饰格子中时间反演对称破缺的量子自旋霍尔效应

  • 1. 浙江海洋大学电子信息科学与工程系, 舟山 316022;
  • 2. 浙江海洋大学东海科学与技术学院, 舟山 316000
  • 通信作者: 王瑞, wangrui@zjou.edu.cn
    基金项目: 国家自然科学基金(批准号:11304281,10547001)和浙江省自然科学基金(批准号:LY13D060002)资助的课题.

摘要: 研究了缀饰格子中的量子自旋霍尔效应,模型中同时考虑了Rashba自旋轨道耦合和交换场的作用.缀饰格子具有简立方对称性,以零能平带和单狄拉克锥结构为主要特点.在缀饰格子中,不论是实现量子自旋霍尔效应还是量子反常霍尔效应,都需要一个不为零的内禀自旋轨道耦合作用来打开一个完全的体能隙,这与石墨烯等六角格子模型有着很大的不同.在交换场破坏了时间反演对称性的情况下,以自旋陈数为标志的量子自旋霍尔效应仍然能够存在,边缘态和极化率的相关结果也证明了这一结论.结果表明自旋陈数比z2拓扑数在表征量子自旋霍尔效应方面有着更广泛的适用范围,相应的结论为利用磁场控制量子自旋霍尔效应提出了一个理论模型和依据.

English Abstract

参考文献 (44)

目录

    /

    返回文章
    返回