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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.
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关键词:
- 红外光谱 /
- Dirac半金属 /
- Weyl半金属 /
- Nodal-line半金属
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:
- Infrared spectroscopy /
- Dirac semimetal /
- Weyl semimetal /
- Nodal-Line semimetal
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Google Scholar
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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 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 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$X_1$ 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]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] -
[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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