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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.
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Keywords:
- graphene /
- spin-orbit interaction /
- flexural phonon /
- weak localization
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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
${{\varepsilon }_{\mathrm{F}}^2}{\tau }_{\mathrm{p}}{\tau }_{\phi }^{-1}$ 与${{\varepsilon }_{\mathrm{F}}^2}{\tau }_{\mathrm{p}}$ 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 146802
Google Scholar
[2] Kane C L, Mele E J 2005 Phys. Rev. Lett. 95 226801
Google Scholar
[3] König M, Wiedmann S, Brüne C, Roth A, Buhmann H, Molenkamp Laurens W, Qi X L, Zhang S C 2007 Science 318 766
Google 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 026602
Google Scholar
[5] Wang Z F, Zhang H, Liu D, et al. 2016 Nat. Mater. 15 968
Google 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. 13 677
Google Scholar
[7] Tang S, Zhang C, Wong D, et al. 2017 Nat. Phys. 13 683
Google Scholar
[8] Gmitra M, Konschuh S, Ertler C, Ambrosch-Draxl C, Fabian J 2009 Phys. Rev. B 80 235431
Google Scholar
[9] Yao Y, Ye F, Qi X L, Zhang S C, Fang Z 2007 Phys. Rev. B 75 041401
Google Scholar
[10] Balakrishnan J, Kok Wai Koon G, Jaiswal M, Castro Neto A H, Özyilmaz B 2013 Nat. Phys. 9 284
Google Scholar
[11] Withers F, Dubois M, Savchenko A K 2010 Phys. Rev. B 82 073403
Google Scholar
[12] Jia Z, Yan B, Niu J, Han Q, Zhu R, Yu D, Wu X 2015 Phys. Rev. B 91 085411
Google 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 1232
Google Scholar
[14] Wang Y, Cai X, Reutt-Robey J, Fuhrer M S 2015 Phys. Rev. B 92 161411
Google 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 203106
Google Scholar
[16] Weeks C, Hu J, Alicea J, Franz M, Wu R 2011 Phys. Rev. X 1 021001
Google Scholar
[17] Lee P, Jin K H, Sung S J, et al. 2015 ACS Nano 9 10861
Google 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 041020
Google Scholar
[19] Wakamura T, Reale F, Palczynski P, Gueron S, Mattevi C, Bouchiat H 2018 Phys. Rev. Lett. 120 106802
Google Scholar
[20] Ochoa H, Castro Neto A H, Guinea F 2012 Phys. Rev. Lett. 108 206808
Google Scholar
[21] Zomer P J, Guimarães M H D, Tombros N, van Wees B J 2012 Phys. Rev. B 86 161416
Google Scholar
[22] Nassimbeni L R, Wright M R W, van Niekerk J C, McCallum P A 1979 Acta Crystallogr. Sec. B 35 1341
Google Scholar
[23] Li C, Komatsu K, Bertrand S, Clavé G, Campidelli S, Filoramo A, Guéron S, Bouchiat H 2016 Phys. Rev. B 93 045403
Google Scholar
[24] Bergman G 1982 Phys. Rev. Lett. 48 1046
Google Scholar
[25] McCann E, Kechedzhi K, Fal'ko V I, Suzuura H, Ando T, Altshuler B L 2006 Phys. Rev. Lett. 97 146805
Google 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 166606
Google 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 15168
Google Scholar
[29] Ishigami M, Chen J H, Cullen W G, Fuhrer M S, Williams E D 2007 Nano. Lett. 7 1643
Google Scholar
[30] Du X, Skachko I, Barker A, Andrei E Y 2008 Nat. Nanotechnol. 3 491
Google Scholar
[31] Lundeberg M B, Folk J A 2010 Phys. Rev. Lett. 105 146804
Google Scholar
[32] Ochoa H, Castro Neto A H, Fal'ko V I, Guinea F 2012 Phys. Rev. B 86 245411
Google Scholar
[33] Pruisken A M M, Schäfer L 1981 Phys. Rev. Lett. 46 490
Google Scholar
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