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石墨烯中选择性增强Kane-Mele型自旋-轨道相互作用

白占斌 王锐 周亚洲 吴天如 葛建雷 李晶 秦宇远 费付聪 曹路 王学锋 王欣然 张帅 孙力玲 宋友 宋凤麒

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石墨烯中选择性增强Kane-Mele型自旋-轨道相互作用

白占斌, 王锐, 周亚洲, 吴天如, 葛建雷, 李晶, 秦宇远, 费付聪, 曹路, 王学锋, 王欣然, 张帅, 孙力玲, 宋友, 宋凤麒

Selective enhancement of Kane Mele-type spin-orbit interaction in graphene

Bai Zhan-Bin, Wang Rui, Zhou Ya-Zhou, Wu Tian-Ru, Ge Jian-Lei, Li Jing, Qin Yu-Yuan, Fei Fu-Cong, Cao Lu, Wang Xue-Feng, Wang Xin-Ran, Zhang Shuai, Sun Li-Ling, Song You, Song Feng-Qi
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  • 增强石墨烯中的自旋-轨道相互作用可能实现无耗散的量子自旋霍尔器件, 这需要在石墨烯样品中引入独特的Kane-Mele型自旋-轨道相互作用, 并保持较高的迁移率. 然而, 对石墨烯的外在修饰往往会引入“外禀型”Rashba自旋-轨道相互作用, 会破坏可能存在的拓扑态, 并带来一定程度的杂质散射, 降低样品迁移率. 在石墨烯表面修饰EDTA-Dy分子后, 载流子迁移率得到了提高, 并且可以看到显著的量子霍尔电导平台. 其弱局域化效应相比被修饰之前得到了抑制, 这意味石墨烯中可能引入了内禀的Kane-Mele型自旋-轨道相互作用, 增强了Elliot-Yafet型电子自旋弛豫机制. 进一步通过矢量磁体磁阻测量, 发现该分子覆盖在石墨烯上后造成了石墨烯微弱的涟漪, 这种涟漪引起的弯曲声子效应模拟了Kane-Mele型自旋-轨道相互作用.
    In order to enhance the spin orbit interaction (SOI) in graphene for seeking the dissipationless quantum spin Hall devices, unique Kane-Mele-type SOI and high mobility samples are desired. However, the common external modification of graphene often introduces “extrinsic” Rashba-type SOI, which will destroy the possible topological state, bring a certain degree of impurity scattering and reduce the sample mobility. Here we show that by the EDTA-Dy molecule dressing, the carrier mobility is even improved, and the quantum Hall plateaus are observed more clearly. The Kane-Mele type SOI is mimicked after dressing, which is evidenced by the suppressed weak localization at equal carrier densities and simultaneous Elliot-Yafet spin relaxation. This is attributed to the spin-flexural phonon coupling induced by the enhanced graphene ripples, as revealed by the in-plane magnetotransport measurement.
      通信作者: 孙力玲, llsun@iphy.ac.cn ; 宋友, yousong@nju.edu.cn ; 宋凤麒, songfengqi@nju.edu.cn
    • 基金项目: 国家重点研发计划(批准号: 2018YFA0306004)和国家自然科学基金 (批准号: U1732273, U1732159, 12025404, 11904166, 11904165, 61822403, 11874203, 11834006, 91622115, 11522432, 11574217, 21571097)资助的课题
      Corresponding author: Sun Li-Ling, llsun@iphy.ac.cn ; Song You, yousong@nju.edu.cn ; Song Feng-Qi, songfengqi@nju.edu.cn
    • Funds: Project supported by the National Key R&D Program of China (Grant No. 2018YFA0306004), the National Natural Science Foundation of China (Grant Nos. U1732273, U1732159, 12025404, 11904166, 11904165, 61822403, 11874203, 11834006, 91622115, 11522432, 11574217, 21571097).
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    Kane C L, Mele E J 2005 Phys. Rev. Lett. 95 146802Google Scholar

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

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    König M, Wiedmann S, Brüne C, Roth A, Buhmann H, Molenkamp Laurens W, Qi X L, Zhang S C 2007 Science 318 766Google Scholar

    [4]

    Knez I, Rettner C T, Yang S H, Parkin S S P, Du L, Du R R, Sullivan G 2014 Phys. Rev. Lett. 112 026602Google Scholar

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    Wang Z F, Zhang H, Liu D, et al. 2016 Nat. Mater. 15 968Google Scholar

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    Fei Z, Palomaki T, Wu S, Zhao W, Cai X, Sun B, Nguyen P, Finney J, Xu X, Cobden D H 2017 Nat. Phys. 13 677Google Scholar

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    Tang S, Zhang C, Wong D, et al. 2017 Nat. Phys. 13 683Google Scholar

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    Gmitra M, Konschuh S, Ertler C, Ambrosch-Draxl C, Fabian J 2009 Phys. Rev. B 80 235431Google Scholar

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    Yao Y, Ye F, Qi X L, Zhang S C, Fang Z 2007 Phys. Rev. B 75 041401Google Scholar

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    Balakrishnan J, Kok Wai Koon G, Jaiswal M, Castro Neto A H, Özyilmaz B 2013 Nat. Phys. 9 284Google Scholar

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    Withers F, Dubois M, Savchenko A K 2010 Phys. Rev. B 82 073403Google Scholar

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    Jia Z, Yan B, Niu J, Han Q, Zhu R, Yu D, Wu X 2015 Phys. Rev. B 91 085411Google Scholar

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    Marchenko D, Varykhalov A, Scholz M R, Bihlmayer G, Rashba E I, Rybkin A, Shikin A M, Rader O 2012 Nat. Commun. 3 1232Google Scholar

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    Wang Y, Cai X, Reutt-Robey J, Fuhrer M S 2015 Phys. Rev. B 92 161411Google Scholar

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    Qin Y, Wang S, Wang R, Bu H, Wang X, Wang X, Song F, Wang B, Wang G 2016 Appl. Phys. Lett. 108 203106Google Scholar

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    Weeks C, Hu J, Alicea J, Franz M, Wu R 2011 Phys. Rev. X 1 021001Google Scholar

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    Lee P, Jin K H, Sung S J, et al. 2015 ACS Nano 9 10861Google Scholar

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    Wang Z, Ki D K, Khoo J Y, Mauro D, Berger H, Levitov L S, Morpurgo A F 2016 Phys. Rev. X 6 041020Google Scholar

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    Wakamura T, Reale F, Palczynski P, Gueron S, Mattevi C, Bouchiat H 2018 Phys. Rev. Lett. 120 106802Google Scholar

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    Ochoa H, Castro Neto A H, Guinea F 2012 Phys. Rev. Lett. 108 206808Google Scholar

    [21]

    Zomer P J, Guimarães M H D, Tombros N, van Wees B J 2012 Phys. Rev. B 86 161416Google Scholar

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    Nassimbeni L R, Wright M R W, van Niekerk J C, McCallum P A 1979 Acta Crystallogr. Sec. B 35 1341Google Scholar

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    Li C, Komatsu K, Bertrand S, Clavé G, Campidelli S, Filoramo A, Guéron S, Bouchiat H 2016 Phys. Rev. B 93 045403Google Scholar

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    Bergman G 1982 Phys. Rev. Lett. 48 1046Google Scholar

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    McCann E, Kechedzhi K, Fal'ko V I, Suzuura H, Ando T, Altshuler B L 2006 Phys. Rev. Lett. 97 146805Google Scholar

    [26]

    McCann E, Fal’ko V I 2014 Physics of Graphene (edited by Aoki H, S. Dresselhaus M) (Switzerland: Springer, Cham) pp327-345

    [27]

    McCann E, Fal’ko V I 2012 Phys. Rev. Lett. 108 166606Google Scholar

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    Singh A K, Iqbal M W, Singh V K, Iqbal M Z, Lee J H, Chun S-H, Shin K, Eom J 2012 J. Mater. Chem. 22 15168Google Scholar

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    Ishigami M, Chen J H, Cullen W G, Fuhrer M S, Williams E D 2007 Nano. Lett. 7 1643Google Scholar

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    Du X, Skachko I, Barker A, Andrei E Y 2008 Nat. Nanotechnol. 3 491Google Scholar

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    Lundeberg M B, Folk J A 2010 Phys. Rev. Lett. 105 146804Google Scholar

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    Ochoa H, Castro Neto A H, Fal'ko V I, Guinea F 2012 Phys. Rev. B 86 245411Google Scholar

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    Pruisken A M M, Schäfer L 1981 Phys. Rev. Lett. 46 490Google Scholar

  • 图 1  EDTA-Dy修饰的石墨烯器件及其输运特性 (a)石墨烯介观输运结构图, 用橘色小球代表EDTA-Dy分子修饰在石墨烯上面; (b) EDTA-Dy分子修饰的石墨烯的拉曼光谱; (c)在2, 20和290 K温度下, EDTA-Dy修饰石墨烯的电阻随门电压的变化; (d) 在温度2 K和磁场12 T的条件下, 分子修饰后的石墨烯的纵向电阻$ {\rho }_{xx} $和霍尔电导$ {\mathrm{\sigma }}_{xy} $随门电压的变化

    Fig. 1.  The EDTA-Dy dressed graphene and its device transport: (a) Schematic configuration of the device, where the EDTA-Dy (orange balls) coats the graphene sheet; (b) Raman spectrum of EDTA-Dy dressed graphene, indicating that the sample is a single layer graphene sheet; (c) resistance as a function of back gate voltage (Vg) for EDTA-Dy dressed graphene at 2, 20 and 290 K; (d) Vg dependence of the longitudinal resistivity $ {\rho }_{xx} $ and the Hall conductivity $ {\mathrm{\sigma }}_{xy} $ measured in a magnetic field of 12 T at a temperature of 2 K, where the Hall conductivity goes quantized and the longitudinal resistivity approaches zero.

    图 2  EDTA-Dy修饰石墨烯引起的被抑制的弱局域化现象及EY机制拟合 (a), (b) 2 K时石墨烯被修饰前后的弱局域化随门电压的调控; (c)修饰前后石墨烯中${{\varepsilon }_{\mathrm{F}}^2}{\tau }_{\mathrm{p}}{\tau }_{\phi }^{-1}$${{\varepsilon }_{\mathrm{F}}^2}{\tau }_{\mathrm{p}}$的关系, 实线和虚线是各自的二项式拟合

    Fig. 2.  Suppressed weak-localization in the EDTA-Dy decorated graphene device and EY plot: (a), (b) Weak localization of pristine and EDTA-Dy dressed graphene at different $ {V}_{\mathrm{g}} $ while fixing the temperature of 2 K; (c) ${{\varepsilon }_{\mathrm{F}}^2}{\tau }_{\mathrm{p}}{\tau }_{\phi }^{-1}$ as a function of ${{\varepsilon }_{\mathrm{F}}^2}{\tau }_{\mathrm{p}}$ for the pristine and EDTA-Dy dressed graphene, where solid and dashed line are the fit for them, respectively.

    图 3  原子力显微镜表征和矢量磁体测量的石墨烯涟漪结构 (a)未修饰的的本征石墨烯(上)和分子修饰石墨烯(下)的原子力显微镜形貌图, 图中比例尺为100 nm; (b)在水平磁场下, 分子修饰前后石墨烯的磁电阻随磁场强度的变化, 其中实线由(2)式拟合得到, 拟合参数分别为n = 6.44 × 1012 cm–2 和4.27 × 1012 cm–2, 插图是矢量磁体测量示意图; (c), (d)在一系列特定平行磁场B//下, 修饰前后石墨烯的磁电阻对垂直磁场(B<0.04 T)的弱局域化响应; (e)拟合得到修饰前后石墨烯的退相干速率$ {\tau }_{\phi }^{-1} $与平行磁场${B}_{/ / }^{2}$的关系, 其斜率与$ {Z}^{2}R $相关

    Fig. 3.  Atomic force microscope characterization and ripple configuration revealed by the vector magnet measurement. (a) Atomic force microscope images of pristine graphene (upper) and EDTA-Dy dressed graphene (down). The scale bar is 100 nm. (b) Resistivity of pristine graphene and EDTA-Dy dressed graphene dependent on $ {B}_{/ /}^{2} $. The solid lines are the fitting according to Eq. (2) using n = 6.44 × 1012 cm–2 and 4.27 × 1012 cm–2. The inset is the measurement configuration. (c), (d) B–dependent magnetoconductivity (B<0.04 T), at a series of fixed B//. Dashed lines are the fitting according to Eq. (3). Panel (c) and (d) correspond to the graphene before and after EDTA-Dy dressing, respectively. (e) Extracted values of $ {\tau }_{\phi }^{-1} $ plotted against ${B}_{// }^{2}$ , the slope is related to $ {Z}^{2}R $.

  • [1]

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

    [2]

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

    [3]

    König M, Wiedmann S, Brüne C, Roth A, Buhmann H, Molenkamp Laurens W, Qi X L, Zhang S C 2007 Science 318 766Google Scholar

    [4]

    Knez I, Rettner C T, Yang S H, Parkin S S P, Du L, Du R R, Sullivan G 2014 Phys. Rev. Lett. 112 026602Google Scholar

    [5]

    Wang Z F, Zhang H, Liu D, et al. 2016 Nat. Mater. 15 968Google Scholar

    [6]

    Fei Z, Palomaki T, Wu S, Zhao W, Cai X, Sun B, Nguyen P, Finney J, Xu X, Cobden D H 2017 Nat. Phys. 13 677Google Scholar

    [7]

    Tang S, Zhang C, Wong D, et al. 2017 Nat. Phys. 13 683Google Scholar

    [8]

    Gmitra M, Konschuh S, Ertler C, Ambrosch-Draxl C, Fabian J 2009 Phys. Rev. B 80 235431Google Scholar

    [9]

    Yao Y, Ye F, Qi X L, Zhang S C, Fang Z 2007 Phys. Rev. B 75 041401Google Scholar

    [10]

    Balakrishnan J, Kok Wai Koon G, Jaiswal M, Castro Neto A H, Özyilmaz B 2013 Nat. Phys. 9 284Google Scholar

    [11]

    Withers F, Dubois M, Savchenko A K 2010 Phys. Rev. B 82 073403Google Scholar

    [12]

    Jia Z, Yan B, Niu J, Han Q, Zhu R, Yu D, Wu X 2015 Phys. Rev. B 91 085411Google Scholar

    [13]

    Marchenko D, Varykhalov A, Scholz M R, Bihlmayer G, Rashba E I, Rybkin A, Shikin A M, Rader O 2012 Nat. Commun. 3 1232Google Scholar

    [14]

    Wang Y, Cai X, Reutt-Robey J, Fuhrer M S 2015 Phys. Rev. B 92 161411Google Scholar

    [15]

    Qin Y, Wang S, Wang R, Bu H, Wang X, Wang X, Song F, Wang B, Wang G 2016 Appl. Phys. Lett. 108 203106Google Scholar

    [16]

    Weeks C, Hu J, Alicea J, Franz M, Wu R 2011 Phys. Rev. X 1 021001Google Scholar

    [17]

    Lee P, Jin K H, Sung S J, et al. 2015 ACS Nano 9 10861Google Scholar

    [18]

    Wang Z, Ki D K, Khoo J Y, Mauro D, Berger H, Levitov L S, Morpurgo A F 2016 Phys. Rev. X 6 041020Google Scholar

    [19]

    Wakamura T, Reale F, Palczynski P, Gueron S, Mattevi C, Bouchiat H 2018 Phys. Rev. Lett. 120 106802Google Scholar

    [20]

    Ochoa H, Castro Neto A H, Guinea F 2012 Phys. Rev. Lett. 108 206808Google Scholar

    [21]

    Zomer P J, Guimarães M H D, Tombros N, van Wees B J 2012 Phys. Rev. B 86 161416Google Scholar

    [22]

    Nassimbeni L R, Wright M R W, van Niekerk J C, McCallum P A 1979 Acta Crystallogr. Sec. B 35 1341Google Scholar

    [23]

    Li C, Komatsu K, Bertrand S, Clavé G, Campidelli S, Filoramo A, Guéron S, Bouchiat H 2016 Phys. Rev. B 93 045403Google Scholar

    [24]

    Bergman G 1982 Phys. Rev. Lett. 48 1046Google Scholar

    [25]

    McCann E, Kechedzhi K, Fal'ko V I, Suzuura H, Ando T, Altshuler B L 2006 Phys. Rev. Lett. 97 146805Google Scholar

    [26]

    McCann E, Fal’ko V I 2014 Physics of Graphene (edited by Aoki H, S. Dresselhaus M) (Switzerland: Springer, Cham) pp327-345

    [27]

    McCann E, Fal’ko V I 2012 Phys. Rev. Lett. 108 166606Google Scholar

    [28]

    Singh A K, Iqbal M W, Singh V K, Iqbal M Z, Lee J H, Chun S-H, Shin K, Eom J 2012 J. Mater. Chem. 22 15168Google Scholar

    [29]

    Ishigami M, Chen J H, Cullen W G, Fuhrer M S, Williams E D 2007 Nano. Lett. 7 1643Google Scholar

    [30]

    Du X, Skachko I, Barker A, Andrei E Y 2008 Nat. Nanotechnol. 3 491Google Scholar

    [31]

    Lundeberg M B, Folk J A 2010 Phys. Rev. Lett. 105 146804Google Scholar

    [32]

    Ochoa H, Castro Neto A H, Fal'ko V I, Guinea F 2012 Phys. Rev. B 86 245411Google Scholar

    [33]

    Pruisken A M M, Schäfer L 1981 Phys. Rev. Lett. 46 490Google Scholar

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出版历程
  • 收稿日期:  2021-09-29
  • 修回日期:  2021-11-06
  • 上网日期:  2022-03-12
  • 刊出日期:  2022-03-20

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