搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

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

引用本文:
Citation:

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
PDF
HTML
导出引用
  • 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)
    [1]

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

    [2]

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

    [3]

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

    [6]

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

    [7]

    Wan X G, Turner A M, Vishwanath A, Savrasov S Y 2011 Phys. Rev. B 83 205101Google 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 613Google 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 724Google Scholar

    [12]

    Xu S Y, Alidoust N, Belopolski I, et al. 2015 Nat Phys 11 748Google 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 235126Google Scholar

    [15]

    Fang C, Chen Y G, Kee H Y, Fu L 2015 Phys. Rev. B 92 081201Google Scholar

    [16]

    Bian G, Chang T R, Sankar R, et al. 2016 Nat Commun 7 10556Google Scholar

    [17]

    Neupane M, Belopolski I, Mofazzel M, et al. 2016 Phys. Rev. B 93 201104Google Scholar

    [18]

    Hu J, Tang Z J, Liu J Y, et al. 2016 Phys. Rev. Lett. 117 016602Google Scholar

    [19]

    Liu Z K, Zhou B, Zhang Y, et al. 2014 Science 343 864Google Scholar

    [20]

    Borisenko S, Gibson Q, Evtushinsky D, et al. 2014 Phys. Rev. Lett. 113 027603Google Scholar

    [21]

    Son D T, Spivak B Z 2013 Phys. Rev. B 88 104412Google 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 10735Google Scholar

    [24]

    Yang L X, Liu Z K, Sun Y et al. 2015 Nat Phys 11 728Google Scholar

    [25]

    Shao Y M, Sun Z Y, Wang Y, et al. 2019 Proceedings of the National Academy of Sciences 116 1168Google Scholar

    [26]

    Li Q, Kharzeev D E, Zhang C, et al. 2016 Nat Phys 12 550Google 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 350Google Scholar

    [30]

    Sirica N, Tobey R I, Zhao L X, et al. 2019 Phys. Rev. Lett. 122 197401Google 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 075107Google Scholar

    [32]

    Xu B, Dai Y M, Zhao L X, et al. 2016 Phys. Rev. B 93 121110Google Scholar

    [33]

    Chen R Y, Chen Z G, Song X Y, et al. 2015 Phys. Rev. Lett. 115 176404Google Scholar

    [34]

    Akrap A, Hakl M, Tchoumakov S, et al. 2016 Phys. Rev. Lett. 117 136401Google 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 187401Google Scholar

    [37]

    Basov D N, Richard D A , Dirk M, Martin D 2011 Rev. Mod. Phys. 83 471Google 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 2976Google Scholar

    [40]

    Basov D N, Timusk T 2005 Rev. Mod. Phys. 77 721Google Scholar

    [41]

    Jenkins G S, Lane C, Barbiellini B, et al. 2016 Phys. Rev. B 94 085121Google Scholar

    [42]

    Xu B, Zhao L X, Marsik P, et al. 2018 Phys. Rev. Lett. 121 187401Google Scholar

    [43]

    Martino E, Crassee I, Eguchi G, et al. 2019 Phys. Rev. Lett. 122 217402Google Scholar

    [44]

    Xu B, Dai Y M, Shen B, et al. 2015 Phys. Rev. B 91 104510Google 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 161109Google Scholar

    [47]

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

    [48]

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

    [49]

    Xu G, Hongming Weng, Zhijun Wang, Xi Dai, and Zhong Fang 2011 Phys. Rev. Lett. 107 186806Google Scholar

    [50]

    Nielsen H B, Masao Ninomiya 1983 Physics Letters B 130 389Google 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 245121Google 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 116804Google 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 32Google 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 156801Google Scholar

    [57]

    LaForge A D, Frenzel A, Pursley B C, et al. 2010 Phys. Rev. B 81 125120Google 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 235438Google Scholar

    [59]

    Homes C C, Dai Y M, J. Schneeloch, R. D. Zhong, and G. D. Gu 2016 Phys. Rev. B 93 125135Google 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 245101Google Scholar

    [62]

    Dipanjan C, Bing C, Alexander Y, Quinn D G 2017 Phys. Rev. B 96 075151Google Scholar

    [63]

    Wang Y Y, Xu S, Sun L L, Xia T L 2018 Phys. Rev. Materials 2 021201Google Scholar

    [64]

    Qiu Z Y, Le C C, Liao Z Y, et al. 2019 Phys. Rev. B 100 125136Google Scholar

    [65]

    Ádám B, Attila V 2013 Phys. Rev. B 87 125425Google Scholar

    [66]

    Mak K F, Matthew Y S, Yang W, et al. 2008 Phys. Rev. Lett. 101 196405Google Scholar

    [67]

    Mukherjee S P, Carbotte J P 2017 Phys. Rev. B 95 214203Google Scholar

  • 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]

  • [1]

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

    [2]

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

    [3]

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

    [6]

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

    [7]

    Wan X G, Turner A M, Vishwanath A, Savrasov S Y 2011 Phys. Rev. B 83 205101Google 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 613Google 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 724Google Scholar

    [12]

    Xu S Y, Alidoust N, Belopolski I, et al. 2015 Nat Phys 11 748Google 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 235126Google Scholar

    [15]

    Fang C, Chen Y G, Kee H Y, Fu L 2015 Phys. Rev. B 92 081201Google Scholar

    [16]

    Bian G, Chang T R, Sankar R, et al. 2016 Nat Commun 7 10556Google Scholar

    [17]

    Neupane M, Belopolski I, Mofazzel M, et al. 2016 Phys. Rev. B 93 201104Google Scholar

    [18]

    Hu J, Tang Z J, Liu J Y, et al. 2016 Phys. Rev. Lett. 117 016602Google Scholar

    [19]

    Liu Z K, Zhou B, Zhang Y, et al. 2014 Science 343 864Google Scholar

    [20]

    Borisenko S, Gibson Q, Evtushinsky D, et al. 2014 Phys. Rev. Lett. 113 027603Google Scholar

    [21]

    Son D T, Spivak B Z 2013 Phys. Rev. B 88 104412Google 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 10735Google Scholar

    [24]

    Yang L X, Liu Z K, Sun Y et al. 2015 Nat Phys 11 728Google Scholar

    [25]

    Shao Y M, Sun Z Y, Wang Y, et al. 2019 Proceedings of the National Academy of Sciences 116 1168Google Scholar

    [26]

    Li Q, Kharzeev D E, Zhang C, et al. 2016 Nat Phys 12 550Google 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 350Google Scholar

    [30]

    Sirica N, Tobey R I, Zhao L X, et al. 2019 Phys. Rev. Lett. 122 197401Google 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 075107Google Scholar

    [32]

    Xu B, Dai Y M, Zhao L X, et al. 2016 Phys. Rev. B 93 121110Google Scholar

    [33]

    Chen R Y, Chen Z G, Song X Y, et al. 2015 Phys. Rev. Lett. 115 176404Google Scholar

    [34]

    Akrap A, Hakl M, Tchoumakov S, et al. 2016 Phys. Rev. Lett. 117 136401Google 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 187401Google Scholar

    [37]

    Basov D N, Richard D A , Dirk M, Martin D 2011 Rev. Mod. Phys. 83 471Google 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 2976Google Scholar

    [40]

    Basov D N, Timusk T 2005 Rev. Mod. Phys. 77 721Google Scholar

    [41]

    Jenkins G S, Lane C, Barbiellini B, et al. 2016 Phys. Rev. B 94 085121Google Scholar

    [42]

    Xu B, Zhao L X, Marsik P, et al. 2018 Phys. Rev. Lett. 121 187401Google Scholar

    [43]

    Martino E, Crassee I, Eguchi G, et al. 2019 Phys. Rev. Lett. 122 217402Google Scholar

    [44]

    Xu B, Dai Y M, Shen B, et al. 2015 Phys. Rev. B 91 104510Google 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 161109Google Scholar

    [47]

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

    [48]

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

    [49]

    Xu G, Hongming Weng, Zhijun Wang, Xi Dai, and Zhong Fang 2011 Phys. Rev. Lett. 107 186806Google Scholar

    [50]

    Nielsen H B, Masao Ninomiya 1983 Physics Letters B 130 389Google 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 245121Google 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 116804Google 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 32Google 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 156801Google Scholar

    [57]

    LaForge A D, Frenzel A, Pursley B C, et al. 2010 Phys. Rev. B 81 125120Google 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 235438Google Scholar

    [59]

    Homes C C, Dai Y M, J. Schneeloch, R. D. Zhong, and G. D. Gu 2016 Phys. Rev. B 93 125135Google 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 245101Google Scholar

    [62]

    Dipanjan C, Bing C, Alexander Y, Quinn D G 2017 Phys. Rev. B 96 075151Google Scholar

    [63]

    Wang Y Y, Xu S, Sun L L, Xia T L 2018 Phys. Rev. Materials 2 021201Google Scholar

    [64]

    Qiu Z Y, Le C C, Liao Z Y, et al. 2019 Phys. Rev. B 100 125136Google Scholar

    [65]

    Ádám B, Attila V 2013 Phys. Rev. B 87 125425Google Scholar

    [66]

    Mak K F, Matthew Y S, Yang W, et al. 2008 Phys. Rev. Lett. 101 196405Google Scholar

    [67]

    Mukherjee S P, Carbotte J P 2017 Phys. Rev. B 95 214203Google Scholar

  • [1] 李绍民, 孙利群. 基于改进波长调制光谱技术的高吸收度甲烷气体测量. 物理学报, 2023, 72(1): 010701. doi: 10.7498/aps.72.20221725
    [2] 陈书刚, 李学思, 韩宇. 第二类Weyl半金属的金属-超导-金属结中的Andreev反射. 物理学报, 2022, 71(12): 127201. doi: 10.7498/aps.71.20211962
    [3] 李绍民, 孙利群. 基于改进波长调制光谱技术的高吸收度甲烷气体测量. 物理学报, 2022, 0(0): 0-0. doi: 10.7498/aps.71.20221725
    [4] 邱子阳, 陈岩, 邱祥冈. 拓扑材料BaMnSb2的红外光谱学研究. 物理学报, 2022, 71(10): 107201. doi: 10.7498/aps.71.20220011
    [5] 邱梓恒, AhmedYousif Ghazal, 龙金友, 张嵩. 三乙胺分子构象与红外光谱的理论研究. 物理学报, 2022, 71(10): 103601. doi: 10.7498/aps.71.20220123
    [6] 施斌, 袁荔, 唐天宇, 陆利敏, 赵先豪, 魏晓楠, 唐延林. 特丁基对苯二酚的光谱及密度泛函研究. 物理学报, 2021, 70(5): 053102. doi: 10.7498/aps.70.20201555
    [7] 吴晨晨, 郭相东, 胡海, 杨晓霞, 戴庆. 石墨烯等离激元增强红外光谱. 物理学报, 2019, 68(14): 148103. doi: 10.7498/aps.68.20190903
    [8] 林桐, 胡蝶, 时立宇, 张思捷, 刘妍琦, 吕佳林, 董涛, 赵俊, 王楠林. 铁基超导体Li0.8Fe0.2ODFeSe的红外光谱研究. 物理学报, 2018, 67(20): 207102. doi: 10.7498/aps.67.20181401
    [9] 王安静, 方勇华, 李大成, 崔方晓, 吴军, 刘家祥, 李扬裕, 赵彦东. 面阵探测下的污染云团红外光谱仿真. 物理学报, 2017, 66(11): 114203. doi: 10.7498/aps.66.114203
    [10] 杜永平, 刘慧美, 万贤纲. 5d过渡金属氧化物中的奇异量子物性研究. 物理学报, 2015, 64(18): 187201. doi: 10.7498/aps.64.187201
    [11] 颜丙敏, 贾晓鹏, 秦杰明, 孙士帅, 周振翔, 房超, 马红安. 氮氢共掺杂金刚石中氢的典型红外特征峰的表征. 物理学报, 2014, 63(4): 048101. doi: 10.7498/aps.63.048101
    [12] 刘江平, 黎军, 刘元琼, 雷海乐, 韦建军. 低温下氘分子红外吸收特性研究. 物理学报, 2014, 63(2): 023301. doi: 10.7498/aps.63.023301
    [13] 孙友文, 谢品华, 徐晋, 周海金, 刘诚, 王杨, 刘文清, 司福祺, 曾议. 采用加权函数修正的差分光学吸收光谱反演环境大气中的CO2垂直柱浓度. 物理学报, 2013, 62(13): 130703. doi: 10.7498/aps.62.130703
    [14] 刘江平, 毕鹏, 雷海乐, 黎军, 韦建军. 近三相点温度低温固体氘的红外吸收谱. 物理学报, 2013, 62(16): 163301. doi: 10.7498/aps.62.163301
    [15] 李鑫, 羊梦诗, 叶志鹏, 陈亮, 徐灿, 储修祥. 甘氨酸色氨酸寡肽链的红外光谱的密度泛函研究. 物理学报, 2013, 62(15): 156103. doi: 10.7498/aps.62.156103
    [16] 孙杰, 聂秋华, 王国祥, 王训四, 戴世勋, 张巍, 宋宝安, 沈祥, 徐铁峰. PbI2对远红外Te基硫系玻璃光学性能的影响. 物理学报, 2011, 60(11): 114212. doi: 10.7498/aps.60.114212
    [17] 刘晓东, 陶万军, 郑旭光, 萩原雅人, 孟冬冬, 张森林, 郭其新. 磁几何阻挫材料羟基氯化钴的中红外光谱特征. 物理学报, 2011, 60(3): 037803. doi: 10.7498/aps.60.037803
    [18] 聂秋华, 王国祥, 王训四, 徐铁峰, 戴世勋, 沈祥. Ga对新型远红外Te基硫系玻璃光学性能的影响. 物理学报, 2010, 59(11): 7949-7955. doi: 10.7498/aps.59.7949
    [19] 毕鹏, 刘元琼, 唐永建, 杨向东, 雷海乐. 液氢平面低温冷冻靶的红外吸收谱. 物理学报, 2010, 59(11): 7531-7534. doi: 10.7498/aps.59.7531
    [20] 凌志华. 垂直排列液晶盒中反铁电液晶TFMHxPOCBC-D2偏振红外光谱研究. 物理学报, 2001, 50(2): 227-232. doi: 10.7498/aps.50.227
计量
  • 文章访问数:  9156
  • PDF下载量:  453
  • 被引次数: 0
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

/

返回文章
返回