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二维WTe2晶格对称性的光学研究

何宽鱼 邱天宇 奚啸翔

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二维WTe2晶格对称性的光学研究

何宽鱼, 邱天宇, 奚啸翔

Optical study on crystal symmetry of two-dimensional WTe2

He Kuan-Yu, Qiu Tian-Yu, Xi Xiao-Xiang
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  • 二维WTe2由于特殊的晶格对称性而衍生出量子自旋霍尔效应、非线性霍尔效应等奇异性质. 确定其晶体结构的细节, 是理解这些性质的重要出发点. 本文利用温度、偏振依赖的拉曼光谱与光学二次谐波产生, 详细研究了一至三层WTe2的晶格对称性. 实验发现, 单层样品具有可观的二次谐波产生信号, 表明其晶格中心对称性破缺, 且偏振依赖符合$ {C}_{s} $点群, 与此前普遍认为的中心对称的$ 1{T}' $结构不同. 双层样品具有更为显著的二次谐波产生信号, 且信号强度的温度依赖与铁电相变一致, 表明层间堆叠产生了更强的中心对称性破缺, 提供了该体系中存在层间滑移铁电的证据. 三层样品的二次谐波产生信号约为单层样品的五倍, 但比双层样品弱一个数量级, 表明层间堆叠导致其具有较弱的中心对称性破缺. 仅单层与双层样品中出现了多个显著的二阶拉曼散射峰, 其温度依赖反映出电子结构对层间耦合高度敏感. 这些结果将有助于完善对原子级厚度WTe2物理性质的理解.
    Two-dimensional WTe2 possesses a special crystal symmetry, leading to novel properties such as quantum spin Hall effect and nonlinear Hall effect. Determining the details of its crystal structure is essential for understanding these interesting properties. Here, we report an optical study on the crystal symmetry of monolayer, bilayer, and trilayer WTe2, using temperature and polarization dependent Raman spectroscopy and optical second harmonic generation (SHG). We find that monolayer WTe2 is noncentrosymmetric as indicated by its sizable SHG, in contrast to the commonly believed centrosymmetric 1T' structure. The polarization dependence of the SHG is consistent with the Cs point group. Bilayer WTe2 exhibits SHG signal more than one order of magnitude higher than in the monolayer and trilayer samples, with its temperature dependence reflecting the ferroelectric phase transition, evidencing strong inversion symmetry breaking induced by layer stacking and interlayer-sliding ferroelectricity. We also observe prominent second-order resonant Raman scattering peaks only in monolayer and bilayer WTe2, but not in thicker samples, and their temperature dependence indicates an electronic structure highly sensitive to interlayer coupling. These results will be useful for further exploring the properties of atomically thin WTe2.
      通信作者: 奚啸翔, xxi@nju.edu.cn
    • 基金项目: 国家自然科学基金(批准号: 11774151)和国家重点基础研究发展计划 (批准号: 2018YFA0307000)资助的课题.
      Corresponding author: Xi Xiao-Xiang, xxi@nju.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11774151) and the National Key Research and Development Program of China (Grant No. 2018YFA0307000).
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    Wu S, Fatemi V, Gibson Q D, Watanabe K, Taniguchi T, Cava R J, Jarillo-Herrero P 2018 Science 359 76Google Scholar

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    Qian X, Liu J, Fu L, Li J 2014 Science 346 1344Google Scholar

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    Sajadi E, Palomaki T, Fei Z, Zhao W, Bement P, Olsen C, Luescher S, Xu X, Folk J A, Cobden D H 2018 Science 362 922Google Scholar

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    Fei Z, Zhao W, Palomaki T A, Sun B, Miller M K, Zhao Z, Yan J, Xu X, Cobden D H 2018 Nature 560 336Google Scholar

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    Kim Y, Jhon Y I, Park J, Kim J H, Lee S, Jhon Y M 2016 Nanoscale 8 2309Google Scholar

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    Jiang Y C, Gao J, Wang L 2016 Sci. Rep. 6 19624Google Scholar

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    Chen Y, Deng C, Wei Y, Liu J, Su Y, Xie S, Cai W, Peng G, Huang H, Dai M, Zheng X, Zhang X 2021 Appl. Phys. Lett. 119 063104Google Scholar

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    Yip S 2014 Annu. Rev. Condens. Matter Phys. 5 15Google Scholar

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  • 图 1  (a) 单层(左图)和三层(右图)WTe2的晶体结构. 单层中的黑点表示$ {C}_{2 a} $螺旋轴. 右图对比了将三层WTe2进行$ {C}_{2 a} $操作之后的结构(阴影部分), 在第二层中无法与原结构重合, 因此双层与三层WTe2均不具有中心对称性; (b) 不同厚度WTe2的300 K拉曼光谱. 50 cm–1以下和以上的光谱分别在垂直($ \perp $)和平行(//)偏振条件下获得. P0—P9为拉曼声子; (c), (d) P0, P1和P8峰位的厚度依赖, 由拟合图(b)中数据获得; (c)中实线为根据$\sqrt{1-\mathrm{cos}(\mathrm{\pi }/N)}$拟合的结果, N为层数

    Fig. 1.  (a) Crystal structures of monolayer (left) and trilayer (right) WTe2. The black dots in the monolayer structure indicate $ {C}_{2 a} $ screw rotation axes. The trilayer structure does not overlap with its counterpart after $ {C}_{2 a} $operation (shaded) in the second layer, meaning that bilayer and trilayer WTe2 do not possess inversion symmetry. (b) Raman spectra of WTe2 with thickness ranging from 1 to 4 layers, collected at 300 K. The spectral ranges below and above 50 cm–1 are measured in the cross ($ \perp $) and parallel (//) polarization configurations, respectively. P0–P9 denote the observed Raman modes. (c), (d) Thickness dependence of the peak frequencies for P0, P1, and P8, obtained by fitting analysis of the data in Figure (b). The solid line in Figure (c) is a fit to $\sqrt{1-\mathrm{cos}(\mathrm{\pi }/N)}$, where N is the layer number.

    图 2  (a)—(c) 1—3层 (1L—3L) WTe2在平行偏振条件下的温度依赖拉曼散射强度图; (d)—(f) 分别为图(a)—(c)中300—460 cm–1范围内在若干温度点的拉曼谱. 星号(*)标注的峰来自于蓝宝石衬底

    Fig. 2.  (a)–(c) Temperature dependent Raman scattering intensity maps for monolayer, bilayer, and trilayer (1L–3L) WTe2, measured in the parallel polarization configuration. (d)–(f) The corresponding spectra between 300 and 460 cm–1 at selected temperatures. The peaks marked by the asterisks are from the sapphire substrate.

    图 3  (a), (b) 双层 WTe2样品在 4 K 的偏振角度依赖拉曼散射强度图, 分别在平行与垂直偏振条件下测得; (c) 各个拉曼峰的峰强随偏振角度的依赖. 实心与空心符号为实验数据, 实线为根据文中模型拟合的结果

    Fig. 3.  (a), (b) Polarization angle dependent Raman scattering intensity maps for bilayer WTe2, measured in the parallel and cross polarization configurations, respectively, at 4 K. (c) Polarization angle dependent intensity for each Raman mode. The filled and empty symbols are experimental data, and the solid lines are fits as described in the text.

    图 4  (a) 机械剥离获得的WTe2样品的光学照片. 数字和虚线分别代表样品的层数和不同厚度区域之间的分界线. 比例尺: 5 μm; (b), (c) 对图(a)中方框区域进行SHG扫描的成像图, 均在垂直偏振条件下获得, 入射光偏振方向分别对应于图(e)中的${30}^{\circ}$${90}^{\circ}$; (d), (e) 单层WTe2的偏振角度依赖SHG, 分别在平行($//$)和垂直($ \perp $)偏振条件下获得. 实线为根据正文中模型拟合的结果. 所有数据在4 K获得; (f) 上图为单层WTe2在文献中普遍认为所具有的中心对称的$1{T}{'}$结构, 同图1(a). 下图为单层WTe2中心对称性破缺的一种可能结构[9], 称作${1{T}}_{{d}}$

    Fig. 4.  (a) Optical image of mechanically exfoliated WTe2, with layer numbers marked for the thin regions. The dashed lines represent the boundaries between regions of different thickness. Scale bar: 5 μm. (b)–(c) SHG intensity maps for the region marked by the square in (a), obtained in the cross polarization configuration, with the incident polarization angle set to ${30}^{\circ}$ and ${90}^{\circ}$ in (e), respectively. (d)–(e) Polarization angle dependent SHG for monolayer WTe2, measured in the parallel ($//$) and cross ($ \perp $) polarization configurations, respectively. The solid lines are fits as discussed in the text. All data were obtained at 4 K. (f) The upper part is a schematic of the commonly adopted $1{T}{'}$ structure for monolayer WTe2 (same as in Fig. 1(a)), which is centrosymmetric. The lower part shows a possible structure with broken inversion symmetry[9], referred to as $ {1 T}_{d} $.

    图 5  (a)—(d) 不同厚度WTe2在4 K的偏振角度依赖SHG. 实心与空心符号对应的数据分别在平行($//$)与垂直($ \perp $)偏振条件下测得, 实线为根据正文中的模型拟合的结果; (e) 由图(a)—(d)中垂直偏振下的数据在0°—360°范围内积分得到的SHG强度的厚度依赖(双层2H-MoS2的原始数据未给出)

    Fig. 5.  (a)–(d) Polarization angle dependent SHG at 4 K for WTe2 samples of various thickness. The filled and empty symbols represent data collected in the parallel ($//$) and cross ($ \perp $) polarization configurations, respectively. The solid lines are fits as described in the text. (e) Thickness dependence of the SHG, obtained by integrating the cross polarization data in Figure (a)–(d) from 0° to ${360}^{\circ}$. The raw data for bilayer 2H-MoS2 are not shown.

    图 6  实心符号为1—3层样品的SHG在垂直偏振下的温度依赖, 对应于左侧y轴. 空心符号为图2(b)中双层样品P11拉曼峰积分强度的温度依赖, 对应于右侧y

    Fig. 6.  Left axis: temperature dependent SHG intensity for monolayer, bilayer, and trilayer WTe2 in the cross polarization configuration, shown as filled circles. Right axis: temperature dependent integrated intensity for the P11 peak in the Raman spectra in Fig. 2(b) for bilayer WTe2, shown as empty squares.

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    Wang Q H, Kalantar-Zadeh K, Kis A, Coleman J N, Strano M S 2012 Nat. Nanotechnol. 7 699Google Scholar

    [2]

    Ali M N, Xiong J, Flynn S, Tao J, Gibson Q D, Schoop L M, Liang T, Haldolaarachchige N, Hirschberger M, Ong N P, Cava R J 2014 Nature 514 205Google Scholar

    [3]

    Kang D, Zhou Y, Yi W, Yang C, Guo J, Shi Y, Zhang S, Wang Z, Zhang C, Jiang S, Li A, Yang K, Wu Q, Zhang G, Sun L, Zhao Z 2015 Nat. Commun. 6 7804Google Scholar

    [4]

    Pan X C, Chen X, Liu H, Feng Y, Wei Z, Zhou Y, Chi Z, Pi L, Yen F, Song F, Wan X, Yang Z, Wang B, Wang G, Zhang Y 2015 Nat. Commun. 6 7805Google Scholar

    [5]

    Soluyanov A A, Gresch D, Wang Z, Wu Q, Troyer M, Dai X, Bernevig B A 2015 Nature 527 495Google Scholar

    [6]

    Sodemann I, Fu L 2015 Phys. Rev. Lett. 115 216806Google Scholar

    [7]

    Kang K, Li T, Sohn E, Shan J, Mak K F 2019 Nat. Mater. 18 324Google Scholar

    [8]

    Ma Q, Xu S Y, Shen H, MacNeill D, Fatemi V, Chang T R, Valdivia A M M, Wu S, Du Z, Hsu C H, Fang S, Gibson Q D, Watanabe K, Taniguchi T, Cava R J, Kaxiras E, Lu H Z, Lin H, Fu L, Gedik N, Jarillo-Herrero P 2019 Nature 565 337Google Scholar

    [9]

    Xu S Y, Ma Q, Shen H, Fatemi V, Wu S, Chang T R, Chang G, Valdivia A M M, Chan C K, Gibson Q D, Zhou J, Liu Z, Watanabe K, Taniguchi T, Lin H, Cava R J, Fu L, Gedik N, Jarillo-Herrero P 2018 Nat. Phys. 14 900Google Scholar

    [10]

    Xiao J, Wang Y, Wang H, Pemmaraju C D, Wang S, Muscher P, Sie E J, Nyby C M, Devereaux T P, Qian X, Zhang X, Lindenberg A M 2020 Nat. Phys. 16 1028Google Scholar

    [11]

    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

    [12]

    Jing R, Shao Y, Fei Z, Lo C F B, Vitalone R A, Ruta F L, Staunton J, Zheng W J C, McLeod A S, Sun Z, Jiang B Y, Chen X, Fogler M M, Millis A J, Liu M, Cobden D H, Xu X, Basov D N 2021 Nat. Commun. 12 5594Google Scholar

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    Shi Y, Kahn J, Niu B, Fei Z, Sun B, Cai X, Francisco B A, Wu D, Shen Z X, Xu X, Cobden D H, Cui Y T 2019 Sci. Adv. 5 eaat8799Google Scholar

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    Wu S, Fatemi V, Gibson Q D, Watanabe K, Taniguchi T, Cava R J, Jarillo-Herrero P 2018 Science 359 76Google Scholar

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    Qian X, Liu J, Fu L, Li J 2014 Science 346 1344Google Scholar

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    Tang S, Zhang C, Wong D, Pedramrazi Z, Tsai H Z, Jia C, Moritz B, Claassen M, Ryu H, Kahn S, Jiang J, Yan H, Hashimoto M, Lu D, Moore R G, Hwang C C, Hwang C, Hussain Z, Chen Y, Ugeda M M, Liu Z, Xie X, Devereaux T P, Crommie M F, Mo S K, Shen Z X 2017 Nat. Phys. 13 683Google Scholar

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    Sajadi E, Palomaki T, Fei Z, Zhao W, Bement P, Olsen C, Luescher S, Xu X, Folk J A, Cobden D H 2018 Science 362 922Google Scholar

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    Fatemi V, Wu S, Cao Y, Bretheau L, Gibson Q D, Watanabe K, Taniguchi T, Cava R J, Jarillo-Herrero P 2018 Science 362 926Google Scholar

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    Fei Z, Zhao W, Palomaki T A, Sun B, Miller M K, Zhao Z, Yan J, Xu X, Cobden D H 2018 Nature 560 336Google Scholar

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    Wang H, Qian X 2019 npj Comput. Mater. 5 119Google Scholar

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    Yang Q, Wu M, Li J 2018 J. Phys. Chem. Lett. 9 7160Google Scholar

    [22]

    钟婷婷, 吴梦昊 2020 物理学报 69 217707Google Scholar

    Zhong T T, Wu M H 2020 Acta Phys. Sin. 69 217707Google Scholar

    [23]

    Kong W D, Wu S F, Richard P, Lian C-S, Wang J T, Yang C L, Shi Y G, Ding H 2015 Appl. Phys. Lett. 106 081906Google Scholar

    [24]

    Ma X, Guo P, Yi C, Yu Q, Zhang A, Ji J, Tian Y, Jin F, Wang Y, Liu K, Xia T, Shi Y, Zhang Q 2016 Phys. Rev. B 94 214105Google Scholar

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    Song Q, Pan X, Wang H, Zhang K, Tan Q, Li P, Wan Y, Wang Y, Xu X, Lin M, Wan X, Song F, Dai L 2016 Sci. Rep. 6 29254Google Scholar

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    Kim M, Han S, Kim J H, Lee J U, Lee Z, Cheong H 2016 2D Mater. 3 034004

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    Jana M K, Singh A, Late D J, Rajamathi C R, Biswas K, Felser C, Waghmare U V, Rao C N R 2015 J. Phys. Condens. Matter 27 285401Google Scholar

    [28]

    Kim Y, Jhon Y I, Park J, Kim J H, Lee S, Jhon Y M 2016 Nanoscale 8 2309Google Scholar

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    Lee J, Ye F, Wang Z, Yang R, Hu J, Mao Z, Wei J, Feng P X L 2016 Nanoscale 8 7854Google Scholar

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    Jiang Y C, Gao J, Wang L 2016 Sci. Rep. 6 19624Google Scholar

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    Chen Y, Deng C, Wei Y, Liu J, Su Y, Xie S, Cai W, Peng G, Huang H, Dai M, Zheng X, Zhang X 2021 Appl. Phys. Lett. 119 063104Google Scholar

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    Yip S 2014 Annu. Rev. Condens. Matter Phys. 5 15Google Scholar

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    Castellanos-Gomez A, Buscema M, Molenaar R, Singh V, Janssen L, van der Zant H S J, Steele G A 2014 2D Mater. 1 011002

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    Wang L, Meric I, Huang P Y, Gao Q, Gao Y, Tran H, Taniguchi T, Watanabe K, Campos L M, Muller D A, Guo J, Kim P, Hone J, Shepard K L, Dean C R 2013 Science 342 614Google Scholar

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    Ye F, Lee J, Hu J, Mao Z, Wei J, Feng P X L 2016 Small 12 5802Google Scholar

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    Song Q, Wang H, Xu X, Pan X, Wang Y, Song F, Wan X, Dai L 2016 RSC Adv. 6 103830Google Scholar

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    Yang W, Yuan Z Y, Luo Y Q, Yang Y, Zheng F W, Hu Z H, Wang X H, Liu Y A, Zhang P 2019 Phy. Rev. B 99 235401Google Scholar

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    Lin Z, Liu W, Tian S, Zhu K, Huang Y, Yang Y 2021 Sci. Rep. 11 7037Google Scholar

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    Yoon D, Son Y W, Cheong H 2011 Nano Lett. 11 3227Google Scholar

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    Beams R, Cançado L G, Krylyuk S, Kalish I, Kalanyan B, Singh A K, Choudhary K, Bruma A, Vora P M, Tavazza F, Davydov A V, Stranick S J 2016 ACS Nano 10 9626Google Scholar

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出版历程
  • 收稿日期:  2022-04-24
  • 修回日期:  2022-05-14
  • 上网日期:  2022-08-25
  • 刊出日期:  2022-09-05

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