Optical properties of topological semimetals

Xu Bing; Qiu Zi-Yang; Yang Run; Dai Yao-Min; Qiu Xiang-Gang

doi:10.7498/aps.68.20191510

Abstract

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.

Keywords:

Authors and contacts

1.
Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
2.
National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China

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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References

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Cited By

图 1 固体材料中集体激发模式的特征能量^[37]

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

DownLoad: Full-Size Img PowerPoint

图 2 迈克耳孙干涉仪的光路示意图

Figure 2. Schematic beam path of a Michelson interferometer.

DownLoad: Full-Size Img PowerPoint

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]

Figure 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].

DownLoad: Full-Size Img PowerPoint

图 4 原位镀金技术测量材料绝对反射率的装置示意图

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

DownLoad: Full-Size Img PowerPoint

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

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

DownLoad: Full-Size Img PowerPoint

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]

Figure 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].

DownLoad: Full-Size Img PowerPoint

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]

Figure 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].

DownLoad: Full-Size Img PowerPoint

图 8 TaAs光电导谱上的Drude分量谱重随温度的变换^[32]

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

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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]

Figure 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].

DownLoad: Full-Size Img PowerPoint

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]

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

DownLoad: Full-Size Img PowerPoint

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]

Figure 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].

DownLoad: Full-Size Img PowerPoint

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]

Figure 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]

DownLoad: Full-Size Img PowerPoint

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$X_1$和$X_2$($M$-$X$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]

Figure 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]

DownLoad: Full-Size Img PowerPoint

[1]	Hasan M Z, Kane C L 2010 Rev. Mod. Phys. 82 3045 Google Scholar
[2]	Qi X L, Zhang S C 2011 Rev. Mod. Phys. 83 1057 Google Scholar
[3]	Armitage N P, Mele E J, Vishwanath A 2018 Rev. Mod. Phys. 90 015001 Google Scholar
[4]	Young S M, Zaheer S, Teo J C Y, Kane C L, Mele E J, Rappe A M 2012 Phys. Rev. Lett. 108 140405 Google 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 195320 Google Scholar
[6]	Wang Z J, Weng H M, Fang Z 2013 Phys. Rev. B 88 125427 Google Scholar
[7]	Wan X G, Turner A M, Vishwanath A, Savrasov S Y 2011 Phys. Rev. B 83 205101 Google Scholar
[8]	Weng H M, Dai X, Fang Z 2014 Phys. Rev. X 4 011002
[9]	Xu, S Y, Belopolski I, Alidous N 2015 Science 349 613 Google Scholar
[10]	Lv B Q, Weng H M, Fu B B, et al. 2015 Phys. Rev. X 5 031013
[11]	Lv B Q, Xu N, Weng H M et al. 2015 Nat Phys 11 724 Google Scholar
[12]	Xu S Y, Alidoust N, Belopolski I, et al. 2015 Nat Phys 11 748 Google Scholar
[13]	Soluyanov A A, Gresch D, Wang Z J, et al. 2015 Nature 527 495
[14]	Burkov A A, Hook M D, Balents L 2011 Phys. Rev. B 84 235126 Google Scholar
[15]	Fang C, Chen Y G, Kee H Y, Fu L 2015 Phys. Rev. B 92 081201 Google Scholar
[16]	Bian G, Chang T R, Sankar R, et al. 2016 Nat Commun 7 10556 Google Scholar
[17]	Neupane M, Belopolski I, Mofazzel M, et al. 2016 Phys. Rev. B 93 201104 Google Scholar
[18]	Hu J, Tang Z J, Liu J Y, et al. 2016 Phys. Rev. Lett. 117 016602 Google Scholar
[19]	Liu Z K, Zhou B, Zhang Y, et al. 2014 Science 343 864 Google Scholar
[20]	Borisenko S, Gibson Q, Evtushinsky D, et al. 2014 Phys. Rev. Lett. 113 027603 Google Scholar
[21]	Son D T, Spivak B Z 2013 Phys. Rev. B 88 104412 Google Scholar
[22]	Huang X C, Zhao L X, Long Y J, et al. 2015 Phys. Rev. X 5 031023
[23]	Zhang C L, Xu S Y, Belopolski I, et al. 2016 Nat. Commun. 7 10735 Google Scholar
[24]	Yang L X, Liu Z K, Sun Y et al. 2015 Nat Phys 11 728 Google Scholar
[25]	Shao Y M, Sun Z Y, Wang Y, et al. 2019 Proceedings of the National Academy of Sciences 116 1168 Google Scholar
[26]	Li Q, Kharzeev D E, Zhang C, et al. 2016 Nat Phys 12 550 Google Scholar
[27]	Xiong J, Kushwaha S K, Liang T, et al. 2015 Science
[28]	Qiong M, Xu S Y, Chan C K, et al. Direct optical detection of Weyl fermion chirality in a topological semimetal. Nature Physics, 13: 842-, May 2017.
[29]	Wu L, Patankar S, Morimoto T, et al. 2017 Nat Phys 13 350 Google Scholar
[30]	Sirica N, Tobey R I, Zhao L X, et al. 2019 Phys. Rev. Lett. 122 197401 Google Scholar
[31]	Chen R Y, Zhang S J, Schneeloch J A, Zhang C, Li Q, Gu G D, Wang N L 2015 Phys. Rev. B 92 075107 Google Scholar
[32]	Xu B, Dai Y M, Zhao L X, et al. 2016 Phys. Rev. B 93 121110 Google Scholar
[33]	Chen R Y, Chen Z G, Song X Y, et al. 2015 Phys. Rev. Lett. 115 176404 Google Scholar
[34]	Akrap A, Hakl M, Tchoumakov S, et al. 2016 Phys. Rev. Lett. 117 136401 Google Scholar
[35]	Yuan X, Zhong B Y, Song C Y, et al. 2018 Nature Communications 9 1854
[36]	Schilling M B, Schoop L M, Lotsch B V, Dressel M, Pronin A V 2017 Phys. Rev. Lett. 119 187401 Google Scholar
[37]	Basov D N, Richard D A , Dirk M, Martin D 2011 Rev. Mod. Phys. 83 471 Google Scholar
[38]	Martin D, George G. Electrodynamics of Solids. Cambridge University press, 2002.
[39]	Christopher C H, Reedyk M, Crandles D A, Timusk T 1993 Applied Optics 32 2976 Google Scholar
[40]	Basov D N, Timusk T 2005 Rev. Mod. Phys. 77 721 Google Scholar
[41]	Jenkins G S, Lane C, Barbiellini B, et al. 2016 Phys. Rev. B 94 085121 Google Scholar
[42]	Xu B, Zhao L X, Marsik P, et al. 2018 Phys. Rev. Lett. 121 187401 Google Scholar
[43]	Martino E, Crassee I, Eguchi G, et al. 2019 Phys. Rev. Lett. 122 217402 Google Scholar
[44]	Xu B, Dai Y M, Shen B, et al. 2015 Phys. Rev. B 91 104510 Google Scholar
[45]	Xu B, Dai Y M, Zhao L X, et al. 2017 Nat. Commun. 8 14933
[46]	Homes C C, Ali M N, Cava R J 2015 Phys. Rev. B 92 161109 Google Scholar
[47]	Li X B, Huang W K, Lv Y Y, et al. 2016 Phys. Rev. Lett. 116 176803 Google Scholar
[48]	Moreschini L, Johannsen J C, Berger H, et al. 2016 Phys. Rev. B 94 081101 Google Scholar
[49]	Xu G, Hongming Weng, Zhijun Wang, Xi Dai, and Zhong Fang 2011 Phys. Rev. Lett. 107 186806 Google Scholar
[50]	Nielsen H B, Masao Ninomiya 1983 Physics Letters B 130 389 Google Scholar
[51]	Parameswaran S A, T Grover, D A. Abanin, D A. Pesin, and A Vishwanath 2014 Phys. Rev. X 4 031035
[52]	Weng H M, Fang C, Fang Z, B. Andrei Bernevig, and Xi Dai 2015 Phys. Rev. X 5 011029
[53]	Phillip E C A, Carbotte J P 2014 Phys. Rev. B 89 245121 Google Scholar
[54]	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 116804 Google Scholar
[55]	Tang T T, Zhang Y B, Cheol-Hwan Park, Baisong Geng, Caglar Girit, Zhao Hao, Michael C. Martin, Alex Zettl, Michael F. Crommie, Steven G. Louie, Y. Ron Shen, and Feng Wang 2010 Nat Nano 5 32 Google Scholar
[56]	Li Z Q, Lui C H, Emmanuele Cappelluti, Lara Benfatto, Kin Fai Mak, G. L. Carr, Jie Shan, and Tony F. Heinz 2012 Phys. Rev. Lett. 108 156801 Google Scholar
[57]	LaForge A D, Frenzel A, Pursley B C, et al. 2010 Phys. Rev. B 81 125120 Google Scholar
[58]	Sim S W, Koirala N, Matthew Brahlek, Ji Ho Sung, Jun Park, Soonyoung Cha, Moon-Ho Jo, Seongshik Oh, and Hyunyong Choi 2015 Phys. Rev. B 91 235438 Google Scholar
[59]	Homes C C, Dai Y M, J. Schneeloch, R. D. Zhong, and G. D. Gu 2016 Phys. Rev. B 93 125135 Google Scholar
[60]	Sergey B, Daniil E, Quinn G, Alexander Y, Klaus K, Timur Kim, Mazhar Ali, Jeroen van den Brink, Moritz Hoesch, Alexander Fedorov, Erik Haubold, Yevhen Kushnirenko, Ivan Soldatov, Rudolf Schäfer, and Robert J. Cava. Time-reversal symmetry breaking type-II Weyl state in YbMnBi2. Nature Communications, 10(1): 3424-, 2019.
[61]	Chinotti M, Pal A, Ren W J, Petrovic C, Degiorgi L 2016 Phys. Rev. B 94 245101 Google Scholar
[62]	Dipanjan C, Bing C, Alexander Y, Quinn D G 2017 Phys. Rev. B 96 075151 Google Scholar
[63]	Wang Y Y, Xu S, Sun L L, Xia T L 2018 Phys. Rev. Materials 2 021201 Google Scholar
[64]	Qiu Z Y, Le C C, Liao Z Y, et al. 2019 Phys. Rev. B 100 125136 Google Scholar
[65]	Ádám B, Attila V 2013 Phys. Rev. B 87 125425 Google Scholar
[66]	Mak K F, Matthew Y S, Yang W, et al. 2008 Phys. Rev. Lett. 101 196405 Google Scholar
[67]	Mukherjee S P, Carbotte J P 2017 Phys. Rev. B 95 214203 Google Scholar

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Vol. 68, Issue 22 - 2019-11-20

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