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Plasmonics plays an important role in the development of nanophotonics, which allows breaking diffraction limit and controlling light in deep-subwavelength scale due to the strong interaction between light and free carriers. Noble metals and 2-dimensional electron gas have been the main platforms for studying plasmonics over the past decade. The metal-based plasmonic devices have exhibited great potential in various applications, including integrated photonic systems, biological sensing, super-resolution imaging and surface-enhanced Raman scattering, etc. Because of the high carrier density, plasmons of noble metals are realized in the near-infrared to visible frequency range. With the rapid development of new materials, many other plasmonic materials are discovered to exhibit new properties. One example is the graphene plasmons working in the mid-infrared and terahertz spectral range, which exhibit strong field confinement and frequency tunability due to the massless Dirac fermions and other exotic electrical and optical properties. Recently, topological materials, the band structures of which are composed of cones with linear dispersion like in graphene, are discovered, such as the topological insulators, Dirac semimetals, Weyl semimetals and nodal line semimetals, providing another platform to study the Dirac plasmons. Such linear dispersion results in small electron mass and unique carrier density dependence of plasmons. In addition, topological materials possess a tremendous amount of exotic electron properties, such as the ultrahigh mobility, topological surface states and chiral anomaly in Weyl semimetals, etc. Many of these electronic properties can be inherited by the collective oscillation of free electrons, promising new possibility for plasmonics. Here, the experimental observations of plasmons in topological insulators and topological semimetals are reviewed, with special focus on the studies based on electron energy loss spectrum and Fourier transform infrared spectroscopy. At the end, other topological materials with potential for hosting 2D plasmons are discussed. This review provides an overview of plasmons in topological semimetals and may stimulate further quest of more exotic features for plasmons.
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Keywords:
- topological insulators /
- topological semimetals /
- plasmons
[1] Brongersma M L, Shalaev V M 2010 Science 328 440Google Scholar
[2] West P R, Ishii S, Naik G V, Emani N K, Shalaev V M, Boltasseva A 2010 Laser Photonics Rev. 4 795Google Scholar
[3] Huang S, Song C, Zhang G, Yan H 2016 Nanophotonics 6 1191
[4] Low T, Avouris P 2014 ACS Nano 8 1086Google Scholar
[5] Chen J, Badioli M, Alonso-Gonzalez P, Thongrattanasiri S, Huth F, Osmond J, Spasenovic M, Centeno A, Pesquera A, Godignon P, Elorza A Z, Camara N, Garcia de Abajo F J, Hillenbrand R, Koppens F H 2012 Nature 487 77Google Scholar
[6] Fei Z, Rodin A S, Andreev G O, Bao W, McLeod A S, Wagner M, Zhang L M, Zhao Z, Thiemens M, Dominguez G, Fogler M M, Castro Neto A H, Lau C N, Keilmann F, Basov D N 2012 Nature 487 82Google Scholar
[7] Ju L, Geng B, Horng J, Girit C, Martin M, Hao Z, Bechtel H A, Liang X, Zettl A, Shen Y R, Wang F 2011 Nat. Nanotechnol. 6 630Google Scholar
[8] Jia W, Ren P W, Tian Y C, Fan C Z 2019 Chin. Phys. B 28 026102Google Scholar
[9] Ding G W, Liu S B, Zhang H F, Kong X K, Li H M, Li B X, Liu S Y, Li H 2015 Chin. Phys. B 24 118103Google Scholar
[10] Das Sarma S, Hwang E H 2009 Phys. Rev. Lett. 102 206412Google Scholar
[11] Zhang H, Liu C X, Qi X L, Dai X, Fang Z, Zhang S C 2009 Nat. Phys. 5 438Google Scholar
[12] Wang Z H, Gao X P A, Zhang Z D 2018 Chin. Phys. B 27 107901Google Scholar
[13] Liu Z K, Zhou B, Zhang Y, Wang Z J, Weng H M, Prabhakaran D, Mo S K, Shen Z X, Fang Z, Dai X, Hussain Z, Chen Y L 2014 Science 343 864Google Scholar
[14] Borisenko S, Gibson Q, Evtushinsky D, Zabolotnyy V, Büchner B, Cava R J 2014 Phys. Rev. Lett. 113 027603Google Scholar
[15] Neupane M, Xu S Y, Sankar R, Alidoust N, Bian G, Liu C, Belopolski I, Chang T R, Jeng H T, Lin H, Bansil A, Chou F, Hasan M Z 2014 Nat. Commun. 5 3786Google Scholar
[16] Liu Z K, Jiang J, Zhou B, Wang Z J, Zhang Y, Weng H M, Prabhakaran D, Mo S K, Peng H, Dudin P, Kim T, Hoesch M, Fang Z, Dai X, Shen Z X, Feng D L, Hussain Z, Chen Y L 2014 Nat. Mater. 13 677Google Scholar
[17] Li Q, Kharzeev D E, Zhang C, Huang Y, Pletikosić I, Fedorov A V, Zhong R D, Schneeloch J A, Gu G D, Valla T 2016 Nat. Phys. 12 550Google Scholar
[18] Wang Z, Sun Y, Chen X Q, Franchini C, Xu G, Weng H, Dai X, Fang Z 2012 Phys. Rev. B 85 195320Google Scholar
[19] Burkov A A, Balents L 2011 Phys. Rev. Lett. 107 127205Google Scholar
[20] Halász G B, Balents L 2012 Phys. Rev. B 85 035103Google Scholar
[21] Huang S M, Xu S Y, Belopolski I, Lee C C, Chang G, Wang B, Alidoust N, Bian G, Neupane M, Zhang C, Jia S, Bansil A, Lin H, Hasan M Z 2015 Nat. Commun. 6 7373Google Scholar
[22] Weng H, Fang C, Fang Z, Bernevig B A, Dai X 2015 Phys. Rev. X 5 011029
[23] Souma S, Wang Z, Kotaka H, Sato T, Nakayama K, Tanaka Y, Kimizuka H, Takahashi T, Yamauchi K, Oguchi T, Segawa K, Ando Y 2016 Phys. Rev. B 93 161112Google Scholar
[24] Lv B Q, Weng H M, Fu B B, Wang X P, Miao H, Ma J, Richard P, Huang X C, Zhao L X, Chen G F, Fang Z, Dai X, Qian T, Ding H 2015 Phys. Rev. X 5 031013
[25] Xu S Y, Belopolski I, Alidoust N, Neupane M, Bian G, Zhang C, Sankar R, Chang G, Yuan Z, Lee C C, Huang S M, Zheng H, Ma J, Sanchez D S, Wang B, Bansil A, Chou F, Shibayev P P, Lin H, Jia S, Hasan M Z 2015 Science 349 613Google Scholar
[26] Xu S Y, Alidoust N, Belopolski I, Yuan Z, Bian G, Chang T-R, Zheng H, Strocov V N, Sanchez D S, Chang G, Zhang C, Mou D, Wu Y, Huang L, Lee C C, Huang S M, Wang B, Bansil A, Jeng H T, Neupert T, Kaminski A, Lin H, Jia S, Zahid Hasan M 2015 Nat. Phys. 11 748Google Scholar
[27] Xu S Y, Belopolski I, Sanchez D S, Zhang C, Chang G, Guo C, Bian G, Yuan Z, Lu H, Chang T R, Shibayev P P, Prokopovych M L, Alidoust N, Zheng H, Lee C C, Huang S M, Sankar R, Chou F, Hsu C H, Jeng H T, Bansil A, Neupert T, Strocov V N, Lin H, Jia S, Hasan M Z 2015 Sci. Adv. 1 e1501092Google Scholar
[28] Burkov A A, Hook M D, Balents L 2011 Phys. Rev. B 84 235126Google Scholar
[29] Fang C, Weng H, Dai X, Fang Z 2016 Chin. Phys. B 25 117106Google Scholar
[30] Wu Y, Wang L L, Mun E, Johnson D D, Mou D, Huang L, Lee Y, Bud’ko S L, Canfield P C, Kaminski A 2016 Nat. Phys. 12 667Google Scholar
[31] Schoop L M, Ali M N, Strasser C, Topp A, Varykhalov A, Marchenko D, Duppel V, Parkin S S, Lotsch B V, Ast C R 2016 Nat. Commun. 7 11696Google Scholar
[32] Neupane M, Belopolski I, Hosen M M, Sanchez D S, Sankar R, Szlawska M, Xu S Y, Dimitri K, Dhakal N, Maldonado P, Oppeneer P M, Kaczorowski D, Chou F, Hasan M Z, Durakiewicz T 2016 Phys. Rev. B 93 201104Google Scholar
[33] Hu J, Tang Z, Liu J, Liu X, Zhu Y, Graf D, Myhro K, Tran S, Lau C N, Wei J, Mao Z 2016 Phys. Rev. Lett. 117 016602Google Scholar
[34] Bian G, Chang T R, Sankar R, Xu S Y, Zheng H, Neupert T, Chiu C K, Huang S M, Chang G, Belopolski I, Sanchez D S, Neupane M, Alidoust N, Liu C, Wang B, Lee C C, Jeng H T, Zhang C, Yuan Z, Jia S, Bansil A, Chou F, Lin H, Hasan M Z 2016 Nat. Commun. 7 10556Google Scholar
[35] Feng B, Fu B, Kasamatsu S, Ito S, Cheng P, Liu C C, Feng Y, Wu S, Mahatha S K, Sheverdyaeva P, Moras P, Arita M, Sugino O, Chiang T C, Shimada K, Miyamoto K, Okuda T, Wu K, Chen L, Yao Y, Matsuda I 2017 Nat. Commun. 8 1007Google Scholar
[36] Song H D, Sheng D, Wang A Q, Li J G, Yu D P, Liao Z M 2017 Chin. Phys. B 26 037301Google Scholar
[37] Wang H, Wang J 2018 Chin. Phys. B 27 107402Google Scholar
[38] 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
[39] Huang X, Zhao L, Long Y, Wang P, Chen D, Yang Z, Liang H, Xue M, Weng H, Fang Z, Dai X, Chen G 2015 Phys. Rev. X 5 031023
[40] Xu X T, Jia S 2016 Chin. Phys. B 25 117204Google Scholar
[41] Liang T, Lin J, Gibson Q, Kushwaha S, Liu M, Wang W, Xiong H, Sobota J A, Hashimoto M, Kirchmann P S, Shen Z X, Cava R J, Ong N P 2018 Nat. Phys. 14 451Google Scholar
[42] Burkov A A 2014 Phys. Rev. Lett. 113 187202Google Scholar
[43] Stauber T, Gómez-Santos G, Brey L 2013 Phys. Rev. B 88 205427Google Scholar
[44] Stauber T, Gómez-Santos G, Brey L 2017 ACS Photonics 4 2978Google Scholar
[45] Stauber T 2014 J. Phys. Condens. Matter 26 123201Google Scholar
[46] Di Pietro P, Ortolani M, Limaj O, Di Gaspare A, Giliberti V, Giorgianni F, Brahlek M, Bansal N, Koirala N, Oh S, Calvani P, Lupi S 2013 Nat. Nanotechnol. 8 556Google Scholar
[47] Autore M, Engelkamp H, D’Apuzzo F, Gaspare A D, Pietro P D, Vecchio I L, Brahlek M, Koirala N, Oh S, Lupi S 2015 ACS Photonics 2 1231Google Scholar
[48] Autore M, D’Apuzzo F, Di Gaspare A, Giliberti V, Limaj O, Roy P, Brahlek M, Koirala N, Oh S, García de Abajo F J, Lupi S 2015 Adv. Opt. Mater. 3 1257Google Scholar
[49] Ou J Y, So J K, Adamo G, Sulaev A, Wang L, Zheludev N I 2014 Nat. Commun. 5 5139Google Scholar
[50] Ginley T P, Law S 2018 Adv. Opt. Mater. 6 1800113Google Scholar
[51] Autore M, Giorgianni F, D’Apuzzo F, Di Gaspare A, Lo Vecchio I, Brahlek M, Koirala N, Oh S, Schade U, Ortolani M, Lupi S 2016 Nanoscale 8 4667Google Scholar
[52] Nascimento V B, de Carvalho V E, Paniago R, Soares E A, Ladeira L O, Pfannes H D 1999 J. Electron. Spectrosc. Relat. Phenom. 104 99Google Scholar
[53] Liou S C, Chu M W, Sankar R, Huang F T, Shu G J, Chou F C, Chen C H 2013 Phys. Rev. B 87 085126Google Scholar
[54] Politano A, Silkin V M, Nechaev I A, Vitiello M S, Viti L, Aliev Z S, Babanly M B, Chiarello G, Echenique P M, Chulkov E V 2015 Phys. Rev. Lett. 115 216802Google Scholar
[55] Kogar A, Vig S, Thaler A, Wong M H, Xiao Y, Reig-i-Plessis D, Cho G Y, Valla T, Pan Z, Schneeloch J, Zhong R, Gu G D, Hughes T L, MacDougall G J, Chiang T C, Abbamonte P 2015 Phys. Rev. Lett. 115 257402Google Scholar
[56] Jia X, Zhang S, Sankar R, Chou F C, Wang W, Kempa K, Plummer E W, Zhang J, Zhu X, Guo J 2017 Phys. Rev. Lett. 119 136805Google Scholar
[57] Zhu X, Cao Y, Zhang S, Jia X, Guo Q, Yang F, Zhu L, Zhang J, Plummer E W, Guo J 2015 Rev. Sci. Instrum. 86 083902Google Scholar
[58] Hofmann J, Das Sarma S 2016 Phys. Rev. B 93 241402Google Scholar
[59] Zhou J, Chang H R, Xiao D 2015 Phys. Rev. B 91 035114Google Scholar
[60] Politano A, Chiarello G, Ghosh B, Sadhukhan K, Kuo C N, Lue C S, Pellegrini V, Agarwal A 2018 Phys. Rev. Lett. 121 086804Google Scholar
[61] Chiarello G, Hofmann J, Li Z, Fabio V, Guo L, Chen X, Das Sarma S, Politano A 2019 Phys. Rev. B 99 121401Google Scholar
[62] Ashish Chanana N L, Hugo O, Condori Quispe, Prashanth Gopalan, Joshua R, Winger S B, Ajay Nahata, Vikram Deshpande, Michael A Scarpulla, Berardi, Sensale-Rodriguez 2018 arXiv:1811.04306
[63] Frenzel A J, Homes C C, Gibson Q D, Shao Y M, Post K W, Charnukha A, Cava R J, Basov D N 2017 Phys. Rev. B 95 245140Google Scholar
[64] Basov D N, Fogler M M, García de Abajo F J 2016 Science 354 aag1992Google Scholar
[65] Soluyanov A A, Gresch D, Wang Z, Wu Q, Troyer M, Dai X, Bernevig B A 2015 Nature 527 495Google Scholar
[66] Deng K, Wan G, Deng P, Zhang K, Ding S, Wang E, Yan M, Huang H, Zhang H, Xu Z, Denlinger J, Fedorov A, Yang H, Duan W, Yao H, Wu Y, Fan S, Zhang H, Chen X, Zhou S 2016 Nat. Phys. 12 1105Google Scholar
[67] Haubold E, Koepernik K, Efremov D, Khim S, Fedorov A, Kushnirenko Y, van den Brink J, Wurmehl S, Büchner B, Kim T K, Hoesch M, Sumida K, Taguchi K, Yoshikawa T, Kimura A, Okuda T, Borisenko S V 2017 Phys. Rev. B 95 241108Google Scholar
[68] Yankowitz M, Ma Q, Jarillo-Herrero P, LeRoy B J 2019 Nat. Rev. Phys. 1 112Google Scholar
[69] 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
[70] Ni G X, McLeod A S, Sun Z, Wang L, Xiong L, Post K W, Sunku S S, Jiang B Y, Hone J, Dean C R, Fogler M M, Basov D N 2018 Nature 557 530Google Scholar
[71] Yan Z, Huang P W, Wang Z 2016 Phys. Rev. B 93 085138Google Scholar
[72] Long Z, Wang Y, Erukhimova M, Tokman M, Belyanin A 2018 Phys. Rev. Lett. 120 037403Google Scholar
[73] Song J C W, Rudner M S 2017 Phys. Rev. B 96 205443Google Scholar
[74] Hofmann J, Das Sarma S 2015 Phys. Rev. B 91 241108Google Scholar
[75] Lai J, Liu X, Ma J, Wang Q, Zhang K, Ren X, Liu Y, Gu Q, Zhuo X, Lu W, Wu Y, Li Y, Feng J, Zhou S, Chen J H, Sun D 2018 Adv. Mater. 30 e1707152Google Scholar
[76] Ma J, Gu Q, Liu Y, Lai J, Yu P, Zhuo X, Liu Z, Chen J H, Feng J, Sun D 2019 Nat. Mater. 18 476Google Scholar
[77] Nemilentsau A, Low T, Hanson G 2016 Phys. Rev. Lett. 116 066804Google Scholar
[78] Zhou J, Liu F, Lin J, Huang X, Xia J, Zhang B, Zeng Q, Wang H, Zhu C, Niu L, Wang X, Fu W, Yu P, Chang T R, Hsu C H, Wu D, Jeng H T, Huang Y, Lin H, Shen Z, Yang C, Lu L, Suenaga K, Zhou W, Pantelides S T, Liu G, Liu Z 2016 Adv. Mater. 29 1603471
[79] Zhou L, Zubair A, Wang Z, Zhang X, Ouyang F, Xu K, Fang W, Ueno K, Li J, Palacios T, Kong J, Dresselhaus M S 2016 Adv. Mater. 28 9526Google Scholar
[80] Li J, Cheng S, Liu Z, Zhang W, Chang H 2018 J. Phys. Chem. C 122 7005Google Scholar
[81] Naylor C H, Parkin W M, Gao Z, Kang H, Noyan M, Wexler R B, Tan L Z, Kim Y, Kehayias C E, Streller F, Zhou Y R, Carpick R, Luo Z, Park Y W, Rappe A M, Drndić M, Kikkawa J M, Johnson A T C 2017 2D Mater. 4 021008
[82] Chen K, Chen Z, Wan X, Zheng Z, Xie F, Chen W, Gui X, Chen H, Xie W, Xu J 2017 Adv. Mater. 29 1700704Google Scholar
[83] Yang L, Zhang W, Li J, Cheng S, Xie Z, Chang H 2017 ACS Nano 11 1964Google Scholar
[84] Xu X, Chen S, Liu S, Cheng X, Xu W, Li P, Wan Y, Yang S, Gong W, Yuan K, Gao P, Ye Y, Dai L 2019 J. Am. Chem. Soc. 141 2128Google Scholar
[85] Zhou L, Xu K, Zubair A, Liao A D, Fang W, Ouyang F, Lee Y H, Ueno K, Saito R, Palacios T, Kong J, Dresselhaus M S 2015 J. Am. Chem. Soc. 137 11892Google Scholar
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图 1 石墨烯等离激元的电学调控[7] (a)器件示意图(上图)和石墨烯光栅结构AFM轮廓图(下图); (b)石墨烯光栅在不同门电压下的透射光谱图. 主图为入射光偏振垂直于光栅方向, 插图为偏振平行于光栅方向; (c)不同宽度光栅的等离激元频率随载流子浓度(费米面能量)的依赖关系
Figure 1. Tunable plasmon resonance in gated plasmon ribbon array[7]: (a) Schematic of the device (upper panel) and AFM image of a typical ribbon array (lower panel); (b) gate dependent plasmon resonance with light polarization perpendicular to the ribbon array. Inset shows the spectra with parallel light polarization; (c) normalized plasmon frequency as a function of Fermi energy and carrier density for different ribbon width.
图 4 拓扑绝缘体等离激元的远红外和可见光远场光谱研究 (a)不同光栅宽度下拓扑绝缘体薄膜等离激元共振模式远红外吸收谱[46]; (b)由(a)中实验得到的等离激元色散关系[46]. 虚线和点线分别为考虑表面态电子和体载流子后计算的等离激元色散; (c)外加垂直于面的磁场后, 拓扑绝缘体薄膜光栅结构中磁性等离激元和回旋共振模式随磁场的变化关系[47]; (d)圆环阵列结构下, 拓扑绝缘体薄膜等离激元色散关系[48]; (e)可见到紫外波段拓扑绝缘体等离激元共振模式[49]; (f)拓扑绝缘体薄膜光栅结构中等离激元共振模式随着薄膜厚度的依赖关系[50]
Figure 4. Far filed spectroscopic study of the plasmon modes in topological insulator films: (a) Extinction spectra of plasmon resonance modes in topological insulator ribbon arrays with different width; (b) plasmon dispersion extracted from Fig. (a). Fig. (a) and Fig. (b) from Ref. [46]; (c) magnetoplasmon mode and cyclotron resonance in topological insulator ribbon array as a function of external magnetic field[47]; (d) plasmon dispersion in topological insulator microring array[48]; (e) plasmon resonance modes of topological insulator ribbon array from visible to ultraviolet frequency range[49]; (f) plasmon dispersion as a function of film thickness in topological insulator ribbon arrays[50].
图 5 拓扑绝缘体等离激元电子能量损失谱研究 (a)距离晶体边界不同位置处的能量损失谱(上图)和由上图黑线导出的介电常数(下图)[53]; (b)高能量分辨EELS测量到的拓扑绝缘体等离激元色散模式[54]; (c)高能量分辨EELS测量到的具有线性色散的声学支等离激元模式[57]
Figure 5. EELS study of plasmon modes in topological insulator: (a) EELS spectra at different spots from the edge (upper panel). Calculated permittivity from the black line (lower panel)[53]; (b) plasmon dispersion derived from the EELS spectra with high energy resolution[54]; (c) unusual acoustic plasmon modes with linear dispersion measured with high energy resolution EELS[57].
图 6 拓扑半金属等离激元研究 (a)利用EELS测量PtTe2中体等离激元色散模式[60]; (b)超高分辨EELS下测到的NbAs和TaAs表面等离激元模式[61]; (c)太赫兹波段Cd2As3薄膜的光栅结构中等离激元的远场透射谱[62]; (d)和(e)由WTe2体材料单晶的反射谱得到的各向异性体等离激元频率(d)和有效质量比(e)随温度的变化[63]
Figure 6. Experiments of plasmons in topological semimetals: (a) Bulk plasmon dispersion in PtTe2 measured by EELS[60]; (b) energy loss spectra of plasmon modes in NbAs and TaAs measured by EELS[61]; (c) transmission spectra of plasmon modes of Cd2As3 in THz range[62]. (d) and (e) temperature dependence of the anisotropic bulk plasmon and effective mass ratio in WTe2[63].
图 7 大面积高质量拓扑材料薄膜CVD生长 (a)—(c) CVD方法生长大面积WTe2和MoTe2单晶薄膜[78]; (d), (e)利用Te化金属薄膜的方法生长大面积多晶MoTe2薄膜[79]
Figure 7. Synthesis of topological material films with large area and high quality by CVD method: (a) to (c) CVD growth of large area single crystal films of WTe2 and MoTe2[78]; (d) and (e) large area MoTe2 film grown from Mo[79].
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[1] Brongersma M L, Shalaev V M 2010 Science 328 440Google Scholar
[2] West P R, Ishii S, Naik G V, Emani N K, Shalaev V M, Boltasseva A 2010 Laser Photonics Rev. 4 795Google Scholar
[3] Huang S, Song C, Zhang G, Yan H 2016 Nanophotonics 6 1191
[4] Low T, Avouris P 2014 ACS Nano 8 1086Google Scholar
[5] Chen J, Badioli M, Alonso-Gonzalez P, Thongrattanasiri S, Huth F, Osmond J, Spasenovic M, Centeno A, Pesquera A, Godignon P, Elorza A Z, Camara N, Garcia de Abajo F J, Hillenbrand R, Koppens F H 2012 Nature 487 77Google Scholar
[6] Fei Z, Rodin A S, Andreev G O, Bao W, McLeod A S, Wagner M, Zhang L M, Zhao Z, Thiemens M, Dominguez G, Fogler M M, Castro Neto A H, Lau C N, Keilmann F, Basov D N 2012 Nature 487 82Google Scholar
[7] Ju L, Geng B, Horng J, Girit C, Martin M, Hao Z, Bechtel H A, Liang X, Zettl A, Shen Y R, Wang F 2011 Nat. Nanotechnol. 6 630Google Scholar
[8] Jia W, Ren P W, Tian Y C, Fan C Z 2019 Chin. Phys. B 28 026102Google Scholar
[9] Ding G W, Liu S B, Zhang H F, Kong X K, Li H M, Li B X, Liu S Y, Li H 2015 Chin. Phys. B 24 118103Google Scholar
[10] Das Sarma S, Hwang E H 2009 Phys. Rev. Lett. 102 206412Google Scholar
[11] Zhang H, Liu C X, Qi X L, Dai X, Fang Z, Zhang S C 2009 Nat. Phys. 5 438Google Scholar
[12] Wang Z H, Gao X P A, Zhang Z D 2018 Chin. Phys. B 27 107901Google Scholar
[13] Liu Z K, Zhou B, Zhang Y, Wang Z J, Weng H M, Prabhakaran D, Mo S K, Shen Z X, Fang Z, Dai X, Hussain Z, Chen Y L 2014 Science 343 864Google Scholar
[14] Borisenko S, Gibson Q, Evtushinsky D, Zabolotnyy V, Büchner B, Cava R J 2014 Phys. Rev. Lett. 113 027603Google Scholar
[15] Neupane M, Xu S Y, Sankar R, Alidoust N, Bian G, Liu C, Belopolski I, Chang T R, Jeng H T, Lin H, Bansil A, Chou F, Hasan M Z 2014 Nat. Commun. 5 3786Google Scholar
[16] Liu Z K, Jiang J, Zhou B, Wang Z J, Zhang Y, Weng H M, Prabhakaran D, Mo S K, Peng H, Dudin P, Kim T, Hoesch M, Fang Z, Dai X, Shen Z X, Feng D L, Hussain Z, Chen Y L 2014 Nat. Mater. 13 677Google Scholar
[17] Li Q, Kharzeev D E, Zhang C, Huang Y, Pletikosić I, Fedorov A V, Zhong R D, Schneeloch J A, Gu G D, Valla T 2016 Nat. Phys. 12 550Google Scholar
[18] Wang Z, Sun Y, Chen X Q, Franchini C, Xu G, Weng H, Dai X, Fang Z 2012 Phys. Rev. B 85 195320Google Scholar
[19] Burkov A A, Balents L 2011 Phys. Rev. Lett. 107 127205Google Scholar
[20] Halász G B, Balents L 2012 Phys. Rev. B 85 035103Google Scholar
[21] Huang S M, Xu S Y, Belopolski I, Lee C C, Chang G, Wang B, Alidoust N, Bian G, Neupane M, Zhang C, Jia S, Bansil A, Lin H, Hasan M Z 2015 Nat. Commun. 6 7373Google Scholar
[22] Weng H, Fang C, Fang Z, Bernevig B A, Dai X 2015 Phys. Rev. X 5 011029
[23] Souma S, Wang Z, Kotaka H, Sato T, Nakayama K, Tanaka Y, Kimizuka H, Takahashi T, Yamauchi K, Oguchi T, Segawa K, Ando Y 2016 Phys. Rev. B 93 161112Google Scholar
[24] Lv B Q, Weng H M, Fu B B, Wang X P, Miao H, Ma J, Richard P, Huang X C, Zhao L X, Chen G F, Fang Z, Dai X, Qian T, Ding H 2015 Phys. Rev. X 5 031013
[25] Xu S Y, Belopolski I, Alidoust N, Neupane M, Bian G, Zhang C, Sankar R, Chang G, Yuan Z, Lee C C, Huang S M, Zheng H, Ma J, Sanchez D S, Wang B, Bansil A, Chou F, Shibayev P P, Lin H, Jia S, Hasan M Z 2015 Science 349 613Google Scholar
[26] Xu S Y, Alidoust N, Belopolski I, Yuan Z, Bian G, Chang T-R, Zheng H, Strocov V N, Sanchez D S, Chang G, Zhang C, Mou D, Wu Y, Huang L, Lee C C, Huang S M, Wang B, Bansil A, Jeng H T, Neupert T, Kaminski A, Lin H, Jia S, Zahid Hasan M 2015 Nat. Phys. 11 748Google Scholar
[27] Xu S Y, Belopolski I, Sanchez D S, Zhang C, Chang G, Guo C, Bian G, Yuan Z, Lu H, Chang T R, Shibayev P P, Prokopovych M L, Alidoust N, Zheng H, Lee C C, Huang S M, Sankar R, Chou F, Hsu C H, Jeng H T, Bansil A, Neupert T, Strocov V N, Lin H, Jia S, Hasan M Z 2015 Sci. Adv. 1 e1501092Google Scholar
[28] Burkov A A, Hook M D, Balents L 2011 Phys. Rev. B 84 235126Google Scholar
[29] Fang C, Weng H, Dai X, Fang Z 2016 Chin. Phys. B 25 117106Google Scholar
[30] Wu Y, Wang L L, Mun E, Johnson D D, Mou D, Huang L, Lee Y, Bud’ko S L, Canfield P C, Kaminski A 2016 Nat. Phys. 12 667Google Scholar
[31] Schoop L M, Ali M N, Strasser C, Topp A, Varykhalov A, Marchenko D, Duppel V, Parkin S S, Lotsch B V, Ast C R 2016 Nat. Commun. 7 11696Google Scholar
[32] Neupane M, Belopolski I, Hosen M M, Sanchez D S, Sankar R, Szlawska M, Xu S Y, Dimitri K, Dhakal N, Maldonado P, Oppeneer P M, Kaczorowski D, Chou F, Hasan M Z, Durakiewicz T 2016 Phys. Rev. B 93 201104Google Scholar
[33] Hu J, Tang Z, Liu J, Liu X, Zhu Y, Graf D, Myhro K, Tran S, Lau C N, Wei J, Mao Z 2016 Phys. Rev. Lett. 117 016602Google Scholar
[34] Bian G, Chang T R, Sankar R, Xu S Y, Zheng H, Neupert T, Chiu C K, Huang S M, Chang G, Belopolski I, Sanchez D S, Neupane M, Alidoust N, Liu C, Wang B, Lee C C, Jeng H T, Zhang C, Yuan Z, Jia S, Bansil A, Chou F, Lin H, Hasan M Z 2016 Nat. Commun. 7 10556Google Scholar
[35] Feng B, Fu B, Kasamatsu S, Ito S, Cheng P, Liu C C, Feng Y, Wu S, Mahatha S K, Sheverdyaeva P, Moras P, Arita M, Sugino O, Chiang T C, Shimada K, Miyamoto K, Okuda T, Wu K, Chen L, Yao Y, Matsuda I 2017 Nat. Commun. 8 1007Google Scholar
[36] Song H D, Sheng D, Wang A Q, Li J G, Yu D P, Liao Z M 2017 Chin. Phys. B 26 037301Google Scholar
[37] Wang H, Wang J 2018 Chin. Phys. B 27 107402Google Scholar
[38] 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
[39] Huang X, Zhao L, Long Y, Wang P, Chen D, Yang Z, Liang H, Xue M, Weng H, Fang Z, Dai X, Chen G 2015 Phys. Rev. X 5 031023
[40] Xu X T, Jia S 2016 Chin. Phys. B 25 117204Google Scholar
[41] Liang T, Lin J, Gibson Q, Kushwaha S, Liu M, Wang W, Xiong H, Sobota J A, Hashimoto M, Kirchmann P S, Shen Z X, Cava R J, Ong N P 2018 Nat. Phys. 14 451Google Scholar
[42] Burkov A A 2014 Phys. Rev. Lett. 113 187202Google Scholar
[43] Stauber T, Gómez-Santos G, Brey L 2013 Phys. Rev. B 88 205427Google Scholar
[44] Stauber T, Gómez-Santos G, Brey L 2017 ACS Photonics 4 2978Google Scholar
[45] Stauber T 2014 J. Phys. Condens. Matter 26 123201Google Scholar
[46] Di Pietro P, Ortolani M, Limaj O, Di Gaspare A, Giliberti V, Giorgianni F, Brahlek M, Bansal N, Koirala N, Oh S, Calvani P, Lupi S 2013 Nat. Nanotechnol. 8 556Google Scholar
[47] Autore M, Engelkamp H, D’Apuzzo F, Gaspare A D, Pietro P D, Vecchio I L, Brahlek M, Koirala N, Oh S, Lupi S 2015 ACS Photonics 2 1231Google Scholar
[48] Autore M, D’Apuzzo F, Di Gaspare A, Giliberti V, Limaj O, Roy P, Brahlek M, Koirala N, Oh S, García de Abajo F J, Lupi S 2015 Adv. Opt. Mater. 3 1257Google Scholar
[49] Ou J Y, So J K, Adamo G, Sulaev A, Wang L, Zheludev N I 2014 Nat. Commun. 5 5139Google Scholar
[50] Ginley T P, Law S 2018 Adv. Opt. Mater. 6 1800113Google Scholar
[51] Autore M, Giorgianni F, D’Apuzzo F, Di Gaspare A, Lo Vecchio I, Brahlek M, Koirala N, Oh S, Schade U, Ortolani M, Lupi S 2016 Nanoscale 8 4667Google Scholar
[52] Nascimento V B, de Carvalho V E, Paniago R, Soares E A, Ladeira L O, Pfannes H D 1999 J. Electron. Spectrosc. Relat. Phenom. 104 99Google Scholar
[53] Liou S C, Chu M W, Sankar R, Huang F T, Shu G J, Chou F C, Chen C H 2013 Phys. Rev. B 87 085126Google Scholar
[54] Politano A, Silkin V M, Nechaev I A, Vitiello M S, Viti L, Aliev Z S, Babanly M B, Chiarello G, Echenique P M, Chulkov E V 2015 Phys. Rev. Lett. 115 216802Google Scholar
[55] Kogar A, Vig S, Thaler A, Wong M H, Xiao Y, Reig-i-Plessis D, Cho G Y, Valla T, Pan Z, Schneeloch J, Zhong R, Gu G D, Hughes T L, MacDougall G J, Chiang T C, Abbamonte P 2015 Phys. Rev. Lett. 115 257402Google Scholar
[56] Jia X, Zhang S, Sankar R, Chou F C, Wang W, Kempa K, Plummer E W, Zhang J, Zhu X, Guo J 2017 Phys. Rev. Lett. 119 136805Google Scholar
[57] Zhu X, Cao Y, Zhang S, Jia X, Guo Q, Yang F, Zhu L, Zhang J, Plummer E W, Guo J 2015 Rev. Sci. Instrum. 86 083902Google Scholar
[58] Hofmann J, Das Sarma S 2016 Phys. Rev. B 93 241402Google Scholar
[59] Zhou J, Chang H R, Xiao D 2015 Phys. Rev. B 91 035114Google Scholar
[60] Politano A, Chiarello G, Ghosh B, Sadhukhan K, Kuo C N, Lue C S, Pellegrini V, Agarwal A 2018 Phys. Rev. Lett. 121 086804Google Scholar
[61] Chiarello G, Hofmann J, Li Z, Fabio V, Guo L, Chen X, Das Sarma S, Politano A 2019 Phys. Rev. B 99 121401Google Scholar
[62] Ashish Chanana N L, Hugo O, Condori Quispe, Prashanth Gopalan, Joshua R, Winger S B, Ajay Nahata, Vikram Deshpande, Michael A Scarpulla, Berardi, Sensale-Rodriguez 2018 arXiv:1811.04306
[63] Frenzel A J, Homes C C, Gibson Q D, Shao Y M, Post K W, Charnukha A, Cava R J, Basov D N 2017 Phys. Rev. B 95 245140Google Scholar
[64] Basov D N, Fogler M M, García de Abajo F J 2016 Science 354 aag1992Google Scholar
[65] Soluyanov A A, Gresch D, Wang Z, Wu Q, Troyer M, Dai X, Bernevig B A 2015 Nature 527 495Google Scholar
[66] Deng K, Wan G, Deng P, Zhang K, Ding S, Wang E, Yan M, Huang H, Zhang H, Xu Z, Denlinger J, Fedorov A, Yang H, Duan W, Yao H, Wu Y, Fan S, Zhang H, Chen X, Zhou S 2016 Nat. Phys. 12 1105Google Scholar
[67] Haubold E, Koepernik K, Efremov D, Khim S, Fedorov A, Kushnirenko Y, van den Brink J, Wurmehl S, Büchner B, Kim T K, Hoesch M, Sumida K, Taguchi K, Yoshikawa T, Kimura A, Okuda T, Borisenko S V 2017 Phys. Rev. B 95 241108Google Scholar
[68] Yankowitz M, Ma Q, Jarillo-Herrero P, LeRoy B J 2019 Nat. Rev. Phys. 1 112Google Scholar
[69] 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
[70] Ni G X, McLeod A S, Sun Z, Wang L, Xiong L, Post K W, Sunku S S, Jiang B Y, Hone J, Dean C R, Fogler M M, Basov D N 2018 Nature 557 530Google Scholar
[71] Yan Z, Huang P W, Wang Z 2016 Phys. Rev. B 93 085138Google Scholar
[72] Long Z, Wang Y, Erukhimova M, Tokman M, Belyanin A 2018 Phys. Rev. Lett. 120 037403Google Scholar
[73] Song J C W, Rudner M S 2017 Phys. Rev. B 96 205443Google Scholar
[74] Hofmann J, Das Sarma S 2015 Phys. Rev. B 91 241108Google Scholar
[75] Lai J, Liu X, Ma J, Wang Q, Zhang K, Ren X, Liu Y, Gu Q, Zhuo X, Lu W, Wu Y, Li Y, Feng J, Zhou S, Chen J H, Sun D 2018 Adv. Mater. 30 e1707152Google Scholar
[76] Ma J, Gu Q, Liu Y, Lai J, Yu P, Zhuo X, Liu Z, Chen J H, Feng J, Sun D 2019 Nat. Mater. 18 476Google Scholar
[77] Nemilentsau A, Low T, Hanson G 2016 Phys. Rev. Lett. 116 066804Google Scholar
[78] Zhou J, Liu F, Lin J, Huang X, Xia J, Zhang B, Zeng Q, Wang H, Zhu C, Niu L, Wang X, Fu W, Yu P, Chang T R, Hsu C H, Wu D, Jeng H T, Huang Y, Lin H, Shen Z, Yang C, Lu L, Suenaga K, Zhou W, Pantelides S T, Liu G, Liu Z 2016 Adv. Mater. 29 1603471
[79] Zhou L, Zubair A, Wang Z, Zhang X, Ouyang F, Xu K, Fang W, Ueno K, Li J, Palacios T, Kong J, Dresselhaus M S 2016 Adv. Mater. 28 9526Google Scholar
[80] Li J, Cheng S, Liu Z, Zhang W, Chang H 2018 J. Phys. Chem. C 122 7005Google Scholar
[81] Naylor C H, Parkin W M, Gao Z, Kang H, Noyan M, Wexler R B, Tan L Z, Kim Y, Kehayias C E, Streller F, Zhou Y R, Carpick R, Luo Z, Park Y W, Rappe A M, Drndić M, Kikkawa J M, Johnson A T C 2017 2D Mater. 4 021008
[82] Chen K, Chen Z, Wan X, Zheng Z, Xie F, Chen W, Gui X, Chen H, Xie W, Xu J 2017 Adv. Mater. 29 1700704Google Scholar
[83] Yang L, Zhang W, Li J, Cheng S, Xie Z, Chang H 2017 ACS Nano 11 1964Google Scholar
[84] Xu X, Chen S, Liu S, Cheng X, Xu W, Li P, Wan Y, Yang S, Gong W, Yuan K, Gao P, Ye Y, Dai L 2019 J. Am. Chem. Soc. 141 2128Google Scholar
[85] Zhou L, Xu K, Zubair A, Liao A D, Fang W, Ouyang F, Lee Y H, Ueno K, Saito R, Palacios T, Kong J, Dresselhaus M S 2015 J. Am. Chem. Soc. 137 11892Google Scholar
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