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拓扑半金属的红外光谱研究

许兵 邱子阳 杨润 戴耀民 邱祥冈

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拓扑半金属的红外光谱研究

许兵, 邱子阳, 杨润, 戴耀民, 邱祥冈

Optical properties of topological semimetals

Xu Bing, Qiu Zi-Yang, Yang Run, Dai Yao-Min, Qiu Xiang-Gang
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  • 拓扑半金属是一类全新的拓扑电子态, 展现出丰富而有趣的物理性质. 这类材料不仅在未来电子器件方面具有潜在的应用价值, 同时也是目前量子材料领域研究的热点和前沿. 根据在三维动量空间中能带结构特点的不同, 拓扑半金属可以分为Dirac半金属、Weyl金属和Nodal-line半金属等. 人们已经利用各种实验技术手段对这些材料的物理性质进行了系统的研究. 例如: 角分辨光电子能谱可以直接观测到Weyl半金属表面态上连接两个具有相反手性的Weyl费米子的费米弧; 软X射线的角分辨光电子能谱还可以直接观测到这些拓扑半金属体态中的Dirac点, Weyl点以及Nodal-line; 电输运测量验证了拓扑半金属中由手性反常导致的负磁阻现象; 圆偏振光产生光电流的实验证明了Weyl半金属TaAs中存在相反手性的Weyl费米子; 此外, 人们还发现Weyl半金属具有非常强的非线性效应, 主要表现为很强的二次谐波产生和THz发射效应等. 红外光谱是一种体敏感的实验手段. 该手段不仅覆盖很宽的能量范围(meV到几个eV), 而且具有很高的能量分辨率(最高可达几十个µeV量级), 因此适合研究拓扑半金属体态的电子结构以及晶格振动行为. 研究拓扑半金属材料的红外光谱学性质不仅可以帮助人们更深入理解这类材料的物理性质以及发现新的物理现象, 还可以为拓扑半金属在光学领域的研究和应用奠定基础. 本文介绍了近年来上面提到的几类拓扑半金属材料的红外光谱研究的进展情况.
    Topological semimetal represents a novel quantum phase of matter, which exhibits a variety of fascinating quantum phenomena. This class of materials not only have potential applications in electronic devices, but also represent one of the hottest topics in the field of quantum materials. According to the band structure of these materials in the three-dimensional momentum space, topological semimetals can be classified into Dirac semimetals, Weyl semimetals and nodal-line semimetals. Extensive studies on these materials have been conducted using various techniques. For example, angle-resolved photoemission spectroscopy (ARPES) has directly observed the Fermi arc that connects two Weyl points with opposite chiralities in the surface states of Weyl semimetals; the Dirac points, Weyl points as well as the Dirac nodal line in the bulk states have also been revealed by soft X-ray ARPES; the observation of negative magnetoresistance in transport measurements has been taken as the evidence for the chiral anomaly in Weyl and Dirac semimetals; the chirality of the Weyl fermions have been detected by measuring the photocurrent in response of circularly polarized light; in addition, strong second harmonic generation and THz emission have been observed, indicating strong non-linear effects of Weyl semimetals. Infrared spectroscopy is a bulk-sensitive technique, which not only covers a very broad energy range (meV to several eV), but also has very high energy resolution (dozens of µeV). Investigations into the optical response of these materials not only help understand the physics of the topological phase and explore novel quantum phenomena, but also pave the way for future studies and applications in optics. In this article, we introduce the optical studies on several topological semimetals, including Dirac, Weyl and nodal-line semimetals.
      通信作者: 戴耀民, ymdai@nju.edu.cn ; 邱祥冈, xgqiu@iphy.ac.cn
    • 基金项目: 国家自然科学基金(批准号: 11874206)和中央高校基本科研业务费专项资金(批准号: 020414380095)资助的课题
      Corresponding author: Dai Yao-Min, ymdai@nju.edu.cn ; Qiu Xiang-Gang, xgqiu@iphy.ac.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11874206) and the Fundamental Research Funds for the Central Universities, China (Grant No. 020414380095)
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  • 图 1  固体材料中集体激发模式的特征能量[37]

    Fig. 1.  Characteristic energy scales of collective excitations in solids [37].

    图 2  迈克耳孙干涉仪的光路示意图

    Fig. 2.  Schematic beam path of a Michelson interferometer.

    图 3  右侧表示光强随动镜位置的变化曲线$I(x)$; 左侧是功率谱$I(\nu)$. 左侧的$I(\nu)$均由右侧对应的$I(x)$傅里叶变换得到[38]

    Fig. 3.  Right panels portray the intensity as a function of the displacement of the moving mirror $I(x)$; Left panels show the power spectra $I(\nu)$, which are calculated from $I(x)$ through a Fourier transform [38].

    图 4  原位镀金技术测量材料绝对反射率的装置示意图

    Fig. 4.  Schematic plot of the in situ gold evaporation system.

    图 5  利用原位镀金技术测量的YbMnSb2的绝对反射率以及原始数据

    Fig. 5.  Reflectivity and raw data of YbMnSb2 measured using the in situ gold evaporation technique.

    图 6  (a) ZrTe5在8 K时的光电导谱. 红色虚线对应为数据的线性拟合. (b)波数和场强平方根标度下的相对反射率. 虚线对应为峰值的线性拟合[31,33]

    Fig. 6.  (a) The optical conductivity of ZrTe5 at 8 K. The red dotted line is the linear fitting of $\sigma_1(\omega)$. (b) The pseudocolor photograph of the and relative reflectivity $R(B)/R(0)$ as functions of wave number and $\sqrt{B}$. The dashed lines are linear fittings of the peak energies dependent on $\sqrt{B}$[31,33].

    图 7  (a) ZrTe5在150 K时的光电导谱以及相应的数据拟合. (b)温度依赖的能隙值[42]

    Fig. 7.  (a) Fit of $\sigma_1(\omega)$ at 150 K. Thin solid lines represent the Drude (blue), phonon modes (orange), and interband (black) terms. (b) Experimentally obtained value of the band gap for ZrTe5 at different temperatures[42].

    图 8  TaAs光电导谱上的Drude分量谱重随温度的变换[32]

    Fig. 8.  Drude weight as a function of temperature for TaAs[32].

    图 9  TaAs在5 K时的光电导谱. 蓝线和红线代表两个不同能量范围内的线性. 插图是对应的频率依赖的谱重, 如蓝色虚线所示, 它遵循频率的平方依赖关系[32]

    Fig. 9.  Optical conductivity for TaAs at 5 K. The blue and black solid lines through the data are linear guides to the eye. The inset shows the spectral weight as a function of frequency at 5 K (red solid curve), which follows an $\omega^2$ behavior (blue dashed line)[32].

    图 10  (a) TaAs (107)面测得的不同温度的反射率. (b) TaAs (107)面的不同温度的光电导谱[45]

    Fig. 10.  (a) Reflectivity of TaAs (107) surface at different temperatures. (b) Optical conductivity of TaAs (107) surface at different temperatures[45].

    图 11  (a)不同温度下的$A_1$声子线型. 黑线是对应的Fano拟合结果. (b) Fano参数$1/q^2$的温度依赖关系. 红线是基于模型的拟合结果. (c) Weyl节点附近的能带结构. 红色箭头代表为声子能量大小的带间跃迁[45]

    Fig. 11.  (a) Line shape of the $A_1$ phonon at different temperatures. The black solid lines through the data denote the Fano fitting results. (b) Temperature dependence of the Fano parameter $1/q^2$. The red solid line through the data represents the modelling result. (c) Band structure near the Weyl points W1 in TaAs. The red arrows represent the electronic transitions at the energy of the $A_1$ mode $\hbar \omega_0$[45].

    图 12  YbMnSb2在7 K时的光电导谱. 红色实线示意了恒定光电导. 插图为随频率变化的光电导谱重, 其中红色虚线表明谱重在200—500 cm–1范围内随$\omega$线性增加[64]

    Fig. 12.  $\sigma_{1}(\omega)$ for YbMnSb2 at 7 K. The red dashed line through the data is constant guide to the eye. The blue solid curve in the inset displays the spectral weight as a function of frequency at 7 K, which follows an $\omega$ behavior (red dashed line)[64]

    图 13  (a)为考虑G型反铁磁序和自旋轨道耦合的作用下计算得出的YbMnSb2能带分布图. 红色部分主要是Sb1原子的$p_{x/y}$轨道电子. (b)和(c)分别为从$\Gamma$到任意两个点$X_1$$X_2$($M$-$X$上)的电子态分布. (d)为YbMnSb2在Dirac nodal line部分的三维能带分布示意图[64]

    Fig. 13.  (a) Calculated band structure of YbMnSb2 with spin-orbital coupling in the G-type antiferromagnetic order. The red color denotes the $p_{x/y}$ orbitals of Sb1 atom. The electronic structure from $\Gamma$ to the two representative points $X_{1}$ (b) and $X_{2}$ (c) along $M\sim X$. (d) The sketch shows three-dimensional band structures of YbMnSb2 for the Dirac nodal-line[64]

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

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    Qi X L, Zhang S C 2011 Rev. Mod. Phys. 83 1057Google Scholar

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    Armitage N P, Mele E J, Vishwanath A 2018 Rev. Mod. Phys. 90 015001Google Scholar

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    Young S M, Zaheer S, Teo J C Y, Kane C L, Mele E J, Rappe A M 2012 Phys. Rev. Lett. 108 140405Google Scholar

    [5]

    Wang Z J, Sun Y, Chen X Q, Franchini C, Xu G, Weng H M, Dai X, Fang Z 2012 Phys. Rev. B 85 195320Google Scholar

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    Wang Z J, Weng H M, Fang Z 2013 Phys. Rev. B 88 125427Google Scholar

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    Weng H M, Dai X, Fang Z 2014 Phys. Rev. X 4 011002

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    Xu, S Y, Belopolski I, Alidous N 2015 Science 349 613Google Scholar

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    Lv B Q, Weng H M, Fu B B, et al. 2015 Phys. Rev. X 5 031013

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    Martin D, George G. Electrodynamics of Solids. Cambridge University press, 2002.

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    Christopher C H, Reedyk M, Crandles D A, Timusk T 1993 Applied Optics 32 2976Google Scholar

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    Homes C C, Ali M N, Cava R J 2015 Phys. Rev. B 92 161109Google Scholar

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    Li X B, Huang W K, Lv Y Y, et al. 2016 Phys. Rev. Lett. 116 176803Google Scholar

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    Moreschini L, Johannsen J C, Berger H, et al. 2016 Phys. Rev. B 94 081101Google Scholar

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    Parameswaran S A, T Grover, D A. Abanin, D A. Pesin, and A Vishwanath 2014 Phys. Rev. X 4 031035

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    Weng H M, Fang C, Fang Z, B. Andrei Bernevig, and Xi Dai 2015 Phys. Rev. X 5 011029

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    Phillip E C A, Carbotte J P 2014 Phys. Rev. B 89 245121Google Scholar

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    Kuzmenko A B, Benfatto L, E. Cappelluti, I. Crassee, D. van der Marel, P. Blake, K. S. Novoselov, and A. K. Geim 2009 Phys. Rev. Lett. 103 116804Google Scholar

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出版历程
  • 收稿日期:  2019-10-07
  • 修回日期:  2019-11-11
  • 上网日期:  2019-11-19
  • 刊出日期:  2019-11-20

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