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极化激元—光与物质中的电子、声子、激子或磁振子等发生强耦合而形成的一种新的集体振荡模式, 近年来在纳米光子学领域受到了广泛的关注. 低维材料极化激元拥有的高空间压缩比、低损耗、光电可调控等特点使其在微纳光子学器件中有着极高的潜在应用价值, 比如石墨烯中波长可调的等离极化激元、六方氮化硼中高质量的双曲声子极化激元、三氧化钼中面内各向异性的拓扑声子极化激元、碳纳米管中的一维拉廷格液体等离极化激元等. 这些极化激元相互之间以及极化激元与外场之间还能进一步发生显著的耦合相互作用, 产生各种丰富新奇的物理现象, 极大地拓展了极化激元的应用前景. 本文以几种典型的低维纳米材料中极化激元的耦合特性为例, 从表征纳米极化激元的扫描近场光学显微技术出发, 首先简单介绍几种典型极化激元的基本性质, 然后详细讨论各种极化激元之间以及极化激元与外场的耦合, 最后展望极化激元耦合作用的潜在应用.
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关键词:
- 极化激元 /
- 低维材料 /
- 耦合特性 /
- 扫描近场光学显微技术
Polaritons, i.e. new collective modes formed by the strong coupling between light and electrons, phonons, excitons, or magnons in matter, have recently received extensive attention. Polaritons in low-dimensional materials exhibit strong spatial confinement, high quality factor, and gate-tunability. Typical examples include gate-tunable graphene surface plasmon polaritons, high-quality hyperbolic phonon polaritons in hexagonal boron nitride, topological phonon polaritons in α-MoO3, and one-dimensional Luttinger-liquid plasmon polaritons in carbon nanotubes. These unique properties make polaritons an excellent candidate for future nano-photonics devices. Further, these polaritons can significantly interact with each other, resulting in a variety of polariton-polariton coupling phenomena, greatly expanding their applications. In this review paper, we first introduce scanning near-field optical microscopy, i.e. the technique used to probe polaritons in low-dimensional materials, then give a brief introduction to the basic properties of polaritons. Next, we discuss in detail the coupling behavior between various polaritons. Finally, potential applications of polaritons coupling are proposed.-
Keywords:
- polaritons /
- low-dimensional materials /
- coupling behavior /
- scanning near-field optical spectroscopy
[1] Yankowitz M, Xue J, Cormode D, Sanchez-Yamagishi J D, Watanabe K, Taniguchi T, Jarillo-Herrero P, Jacquod P, LeRoy B J 2012 Nat. Phys. 8 382Google Scholar
[2] Yang W, Chen G, Shi Z, Liu C C, Zhang L, Xie G, Cheng M, Wang D, Yang R, Shi D, Watanabe K, Taniguchi T, Yao Y, Zhang Y, Zhang G 2013 Nat. Mater. 12 792Google Scholar
[3] Hunt B, Sanchez-Yamagishi J D, Young A F, Yankowitz M, LeRoy B J, Watanabe K, Taniguchi T, Moon P, Koshino M, Jarillo-Herrero P, Ashoori R C 2013 Science 340 1427Google Scholar
[4] Dean C R, Wang L, Maher P, Forsythe C, Ghahari F, Gao Y, Katoch J, Ishigami M, Moon P, Koshino M, Taniguchi T, Watanabe K, Shepard K L, Hone J, Kim P 2013 Nature 497 598Google Scholar
[5] Ponomarenko L A, Gorbachev R V, Yu G L, Elias D C, Jalil R, Patel A A, Mishchenko A, Mayorov A S, Woods C R, Wallbank J R, Mucha-Kruczynski M, Piot B A, Potemski M, Grigorieva I V, Novoselov K S, Guinea F, Fal’ko V I, Geim A K 2013 Nature 497 594Google Scholar
[6] Chen Z G, Shi Z, Yang W, Lu X, Lai Y, Yan H, Wang F, Zhang G, Li Z 2014 Nat. Commun. 5 4461Google Scholar
[7] Shi Z, Jin C, Yang W, Ju L, Horng J, Lu X, Bechtel H A, Martin M C, Fu D, Wu J, Watanabe K, Taniguchi T, Zhang Y, Bai X, Wang E, Zhang G, Wang F 2014 Nat. Phys. 10 743Google Scholar
[8] Ni G X, Wang H, Wu J S, Fei Z, Goldflam M D, Keilmann F, Özyilmaz B, Castro Neto A H, Xie X M, Fogler M M, Basov D N 2015 Nat. Mater. 14 1217Google Scholar
[9] Ribeiro-Palau R, Zhang C, Watanabe K, Taniguchi T, Hone J, Dean C R 2018 Science 361 690Google Scholar
[10] Cao Y, Fatemi V, Demir A, Fang S, Tomarken S L, Luo J Y, Sanchez-Yamagishi J D, Watanabe K, Taniguchi T, Kaxiras E, Ashoori R C, Jarillo-Herrero P 2018 Nature 556 80Google Scholar
[11] Cao Y, Fatemi V, Fang S, Watanabe K, Taniguchi T, Kaxiras E, Jarillo-Herrero P 2018 Nature 556 43Google Scholar
[12] Chen G, Jiang L, Wu S, Lyu B, Li H, Chittari B L, Watanabe K, Taniguchi T, Shi Z, Jung J, Zhang Y, Wang F 2019 Nat. Phys. 15 237Google Scholar
[13] Chen G, Sharpe A L, Gallagher P, Rosen I T, Fox E J, Jiang L, Lyu B, Li H, Watanabe K, Taniguchi T, Jung J, Shi Z, Goldhaber-Gordon D, Zhang Y, Wang F 2019 Nature 572 215Google Scholar
[14] Yankowitz M, Chen S, Polshyn H, Zhang Y, Watanabe K, Taniguchi T, Graf D, Young A F, Dean C R 2019 Science 363 1059Google Scholar
[15] Chen G, Sharpe A L, Fox E J, Zhang Y H, Wang S, Jiang L, Lyu B, Li H, Watanabe K, Taniguchi T, Shi Z, Senthil T, Goldhaber-Gordon D, Zhang Y, Wang F 2020 Nature 579 56Google Scholar
[16] Deng A, Hu C, Shen P, Chen J, Luo X, Lyu B, Watanabe K, Taniguchi T, Wang R, Liang Q, Ma J, Shi Z 2022 Small 18 e2105687Google Scholar
[17] HillenbRand R, Knoll B, Keilmann F 2001 J. Microsc. 202 77Google Scholar
[18] Basov D N, Fogler M M, García de Abajo F J 2016 Science 354 1992Google Scholar
[19] Low T, Chaves A, Caldwell J D, Kumar A, Fang N X, Avouris P, Heinz T F, Guinea F, Martin-Moreno L, Koppens F 2017 Nat. Mater. 16 182Google Scholar
[20] Zhang Q, Hu G, Ma W, Li P, Krasnok A, Hillenbrand R, Alù A, Qiu C W 2021 Nature 597 187Google Scholar
[21] 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
[22] Chen J, Badioli M, Alonso-González P, Thongrattanasiri S, Huth F, Osmond J, Spasenović M, Centeno A, Pesquera A, Godignon P, Zurutuza Elorza A, Camara N, de Abajo F J G, Hillenbrand R, Koppens F H L 2012 Nature 487 77Google Scholar
[23] 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
[24] Zhao W, Zhao S, Li H, Wang S, Wang S, Utama M I B, Kahn S, Jiang Y, Xiao X, Yoo S, Watanabe K, Taniguchi T, Zettl A, Wang F 2021 Nature 594 517Google Scholar
[25] Dong Y, Xiong L, Phinney I Y, Sun Z, Jing R, McLeod A S, Zhang S, Liu S, Ruta F L, Gao H, Dong Z, Pan R, Edgar J H, Jarillo-Herrero P, Levitov L S, Millis A J, Fogler M M, Bandurin D A, Basov D N 2021 Nature 594 513Google Scholar
[26] Luttinger J M 1963 J. Math. Phys. 4 1154Google Scholar
[27] Voit J 1995 Rep. Prog. Phys. 58 977Google Scholar
[28] Kane C L, Fisher M P A 1992 Phys. Rev. Lett. 68 1220Google Scholar
[29] Bockrath M, Cobden D H, Lu J, Rinzler A G, Smalley R E, Balents L, McEuen P L 1999 Nature 397 598Google Scholar
[30] Shi Z, Hong X, Bechtel H A, Zeng B, Martin M C, Watanabe K, Taniguchi T, Shen Y R, Wang F 2015 Nat. Photonics 9 515Google Scholar
[31] Kane C, Balents L, Fisher M P A 1997 Phys. Rev. Lett. 79 5086Google Scholar
[32] Egger R, Gogolin A O 1997 Phys. Rev. Lett. 79 5082Google Scholar
[33] Wang S, Zhao S, Shi Z, Wu F, Zhao Z, Jiang L, Watanabe K, Taniguchi T, Zettl A, Zhou C, Wang F 2020 Nat. Mater. 19 986Google Scholar
[34] Wang L, Lyu B, Gao Q, Chen J, Ying Z, Deng A, Shi Z 2020 Chin. Phys. Lett. 37 028101Google Scholar
[35] Dai S, Fei Z, Ma Q, Rodin A S, Wagner M, McLeod A S, Liu M K, Gannett W, Regan W, Watanabe K, Taniguchi T, Thiemens M, Dominguez G, Neto A H C, Zettl A, Keilmann F, Jarillo-Herrero P, Fogler M M, Basov D N 2014 Science 343 1125Google Scholar
[36] Shi Z, Bechtel H A, Berweger S, Sun Y, Zeng B, Jin C, Chang H, Martin M C, Raschke M B, Wang F 2015 ACS Photonics 2 790Google Scholar
[37] Li P, Dolado I, Alfaro-Mozaz F J, Casanova F, Hueso L E, Liu S, Edgar J H, Nikitin A Y, Vélez S, Hillenbrand R 2018 Science 359 892Google Scholar
[38] Ni G, McLeod A S, Sun Z, Matson J R, Lo C F B, Rhodes D A, Ruta F L, Moore S L, Vitalone R A, Cusco R, Artús L, Xiong L, Dean C R, Hone J C, Millis A J, Fogler M M, Edgar J H, Caldwell J D, Basov D N 2021 Nano Lett. 21 5767Google Scholar
[39] Zheng Z, Chen J, Wang Y, Wang X, Chen X, Liu P, Xu J, Xie W, Chen H, Deng S, Xu N 2018 Adv. Mater. 30 1705318Google Scholar
[40] Ma W, Alonso-González P, Li S, Nikitin A Y, Yuan J, Martín-Sánchez J, Taboada-Gutiérrez J, Amenabar I, Li P, Vélez S, Tollan C, Dai Z, Zhang Y, Sriram S, Kalantar-Zadeh K, Lee S T, Hillenbrand R, Bao Q 2018 Nature 562 557Google Scholar
[41] Low T, Roldán R, Wang H, Xia F, Avouris P, Moreno L M, Guinea F 2014 Phys. Rev. Lett. 113 106802Google Scholar
[42] Wang C, Huang S, Xing Q, Xie Y, Song C, Wang F, Yan H 2020 Nat. Commun. 11 1158Google Scholar
[43] Lu H, Dai S, Yue Z, Fan Y, Cheng H, Di J, Mao D, Li E, Mei T, Zhao J 2019 Nanoscale 11 4759Google Scholar
[44] Lu H, Yue Z, Li Y, Zhang Y, Zhang M, Zeng W, Gan X, Mao D, Xiao F, Mei T, Zhao W, Wang X, Gu M, Zhao J 2020 Light:Science & Applications 9 191Google Scholar
[45] Yue Z, Ren H, Wei S, Lin J, Gu M 2018 Nat. Commun. 9 4413Google Scholar
[46] Dubrovkin A M, Qiang B, Krishnamoorthy H N S, Zheludev N I, Wang Q J 2018 Nat. Commun. 9 1762Google Scholar
[47] Fei Z, Scott M E, Gosztola D J, Foley J J, Yan J, Mandrus D G, Wen H, Zhou P, Zhang D W, Sun Y, Guest J R, Gray S K, Bao W, Wiederrecht G P, Xu X 2016 Phys. Rev. B 94 081402Google Scholar
[48] Wang B, Zhang X, Yuan X, Teng J 2012 Appl. Phys. Lett. 100 131111Google Scholar
[49] Hu C, Deng A, Shen P, Luo X, Zhou X, Wu T, Huang X, Dong Y, Watanabe K, Taniguchi T, Xie G B, Li X J, Liang Q, Shi Z W 2021 Nanoscale 13 14628Google Scholar
[50] Wang S, Yoo S, Zhao S, Zhao W, Kahn S, Cui D, Wu F, Jiang L, Utama M I B, Li H, Li S, Zibrov A, Regan E, Wang D, Zhang Z, Watanabe K, Taniguchi T, Zhou C, Wang F 2021 Nat. Commun. 12 5039Google Scholar
[51] Wang Y, Xue C, Zhang Z, Zheng H, Zhang W, Yan S 2016 Sci. Rep. 6 38891Google Scholar
[52] Yan X, Wang T, Xiao S, Liu T, Hou H, Cheng L, Jiang X 2017 Sci. Rep. 7 13917Google Scholar
[53] Sun C, Dong Z, Si J, Deng X 2017 Opt. Express 25 1242Google Scholar
[54] Emani N K, Chung T F, Kildishev A V, Shalaev V M, Chen Y P, Boltasseva A 2014 Nano Lett. 14 78Google Scholar
[55] Chen Z X, Chen J H, Wu Z J, Hu W, Zhang X J, Lu Y Q 2014 Appl. Phys. Lett. 104 161114Google Scholar
[56] Brar V W, Jang M S, Sherrott M, Kim S, Lopez J J, Kim L B, Choi M, Atwater H 2014 Nano Lett. 14 3876Google Scholar
[57] Yang X, Zhai F, Hu H, Hu D, Liu R, Zhang S, Sun M, Sun Z, Chen J, Dai Q 2016 Adv. Mater. 28 2931Google Scholar
[58] Dai S, Ma Q, Liu M K, Andersen T, Fei Z, Goldflam M D, Wagner M, Watanabe K, Taniguchi T, Thiemens M, Keilmann F, Janssen G C, Zhu S E, Jarillo-Herrero P, Fogler M M, Basov D N 2015 Nat. Nanotechnol. 10 682Google Scholar
[59] Zhang Y, Hu C, Lyu B, Li H, Ying Z, Wang L, Deng A, Luo X, Gao Q, Chen J, Du J, Shen P, Watanabe K, Taniguchi T, Kang J H, Wang F, Zhang Y, Shi Z W 2020 Nano Lett. 20 2770Google Scholar
[60] Hu G, Ou Q, Si G, Wu Y, Wu J, Dai Z, Krasnok A, Mazor Y, Zhang Q, Bao Q, Qiu C-W, Alù A 2020 Nature 582 209Google Scholar
[61] Zheng Z, Sun F, Huang W, Jiang J, Zhan R, Ke Y, Chen H, Deng S 2020 Nano Lett. 20 5301Google Scholar
[62] Chen M, Lin X, Dinh T H, Zheng Z, Shen J, Ma Q, Chen H, Jarillo-Herrero P, Dai S 2020 Nat. Mater. 19 1307Google Scholar
[63] Duan J, Capote-Robayna N, Taboada-Gutiérrez J, Álvarez-Pérez G, Prieto I, Martín-Sánchez J, Nikitin A Y, Alonso-González P 2020 Nano Lett. 20 5323Google Scholar
[64] Zhao X Y, Huang J H, Zhuo Z Y, Xue Y Z, Ding K, Dou X M, Liu J, Sun B Q 2020 Chin. Phys. Lett. 37 044204Google Scholar
[65] Lyu B, Li H, Jiang L, Shan W, Hu C, Deng A, Ying Z, Wang L, Zhang Y, Bechtel H A, Martin M C, Taniguchi T, Watanabe K, Luo W, Wang F, Shi Z W 2019 Nano Lett. 19 1982Google Scholar
[66] Du J, Lyu B, Shan W, Chen J, Zhou X, Xie J, Deng A, Hu C, Liang Q, Xie G, Li X J, Luo W D, Shi Z W 2021 Chin. Phys. Lett. 38 056301Google Scholar
[67] Zhou Y, Scuri G, Wild D S, High A A, Dibos A, Jauregui L A, Shu C, De Greve K, Pistunova K, Joe A Y, Taniguchi T, Watanabe K, Kim P, Lukin M D, Park H 2017 Nat. Nanotechnol. 12 856Google Scholar
[68] Gelly R J, Renaud D, Liao X, Pingault B, Bogdanovic S, Scuri G, Watanabe K, Taniguchi T, Urbaszek B, Park H, Lončar M 2022 Nat. Commun. 13 232Google Scholar
[69] Ni G X, Wang L, Goldflam M D, Wagner M, Fei Z, McLeod A S, Liu M K, Keilmann F, Özyilmaz B, Castro Neto A H, Hone J, Fogler M M, Basov D N 2016 Nat. Photonics 10 244Google Scholar
[70] Huber M A, Mooshammer F, Plankl M, Viti L, Sandner F, Kastner L Z, Frank T, Fabian J, Vitiello M S, Cocker T L, Huber R 2017 Nat. Nanotechnol. 12 207Google Scholar
[71] Liu M, Yin X, Ulin-Avila E, Geng B, Zentgraf T, Ju L, Wang F, Zhang X 2011 Nature 474 64Google Scholar
[72] Phare C T, Daniel Lee Y H, Cardenas J, Lipson M 2015 Nat. Photonics 9 511Google Scholar
[73] Ansell D, Radko I P, Han Z, Rodriguez F J, Bozhevolnyi S I, Grigorenko A N 2015 Nat. Commun. 6 8846Google Scholar
[74] Wong L J, Kaminer I, Ilic O, Joannopoulos J D, Soljačić M 2016 Nat. Photonics 10 46Google Scholar
[75] Rodrigo D, Limaj O, Janner D, Etezadi D, García de Abajo F J, Pruneri V, Altug H 2015 Science 349 165Google Scholar
[76] Chand S B, Woods J M, Mejia E, Taniguchi T, Watanabe K, Grosso G 2022 Nano Lett. 22 3087Google Scholar
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图 2 一维碳纳米管中的等离激元 (a) 金属性碳纳米管中的等离激元[30]; (b) 金属性碳纳米管中的等离激元波长与碳管数量的关系[30]; (c) 金属性与半导体性碳纳米管中拉廷格液体等离激元随栅压的变化[33] (出自文献[30, 33], 已获得授权)
Fig. 2. Plasmons in one-dimensional carbon nanotube: (a) Plasmons in metallic carbon nanotube[30]; (b) quantized Luttinger liquid plasmon in metallic carbon nanotube[30]; (c) variation of Luttinger liquid plasmons in metallic and semiconducting carbon nanotubes with gate voltage[33] (Reproduced with permission from Ref. [30, 33]).
图 3 六方氮化硼中的声子极化激元[38] (a), (b) 声子极化激元的近场红外成像; (c) 不同温度下声子极化激元的空间衰减分布(出自文献[38], 已获得授权)
Fig. 3. Phonon polaritons in hexagonal boron nitride[38]: (a), (b) Nanoscale infrared images of phonon polaritons; (c) line profiles of the temperature-dependent phonon polaritons (Reproduced with permission from Ref. [38]).
图 4 石墨烯中表面等离激元的耦合 (a) 表面等离激元耦合的示意图及电场分布[48]; (b) 耦合器件的结构示意图; (c) 等离激元耦合模式的近场成像; (d) 不同区域的等离激元的振动曲线; (e) 等离激元耦合模式的傅里叶变换[49] (出自文献[48, 49], 已获得授权)
Fig. 4. Surface plasmon coupling in graphene: (a) Schematic of plasmon coupling and the electric field distribution[48]; (b) device structure of the two graphene layers; (c) near-field infrared imaging of the interlayer-coupled plasmons; (d) plasmon line profiles extracted from different regions; (e) Fourier transform of the coupling modes[49] (Reproduced with permission from Ref. [48, 49]).
图 5 碳纳米管与石墨烯等离激元的耦合[50] (a) 耦合结构的示意图; (b) 碳纳米管等离激元的波长随石墨烯栅极电压变化的近场图像; (c) 这种不同维度的体系中等离激元耦合模式的理论计算与实验结果的对比(出自文献[50], 已获得授权)
Fig. 5. Plasmon coupling in a mixed-dimensional system between carbon nanotube (CNT) and graphene[50]: (a) Schematic of CNT/hBN/graphene heterostructure; (b) near-field images of the plasmon wavelength in carbon nanotube varying with gate voltage applied to the graphene; (c) comparison between experimentally extracted gate-dependent plasmon wavelengths and theoretical calculation of the hybrid plasmon modes (Reproduced with permission from Ref. [50]).
图 6 银纳米线/六方氮化硼中的等离激元与声子极化激元的耦合[59] (a) 银纳米线和六方氮化硼异质结构形成切伦科夫辐射的近场红外成像(标尺: 2 μm); (b) 辐射角度随激发光波长而变化的理论计算与实验结果的对比; (c) 等离激元的阻力系数以及等离激元与声子极化激元的相对动量失配随激发光波长的变化 (出自文献[59], 已获得授权)
Fig. 6. Coupling between plasmon and phonon polariton in silver nanowire/boron nitride heterostructure[59]: (a) Infrared nanoimaging of Cherenkov phonon polaritons in a silver nanowire and hexagonal boron nitride heterostructure (scale bar: 2 μm); (b) comparison between theoretical calculation and experimental results of radiation angle varying with excitation wavelength; (c) extracted plasmon damping ratio and the relative momentum mismatch between the plasmon and phonon polariton with the excitation wavelength (Reproduced with permission from Ref. [59]).
图 7 声子极化激元之间的耦合[61] (a) 不同转角时声子极化激元耦合传播的近场成像; (b) 不同转角时的电场分布计算结果; (c) 声子极化激元的色散关系(出自文献[61], 已获得授权)
Fig. 7. Coupling between phonon polaritons[61]: (a) Near field imaging of the propagation of the coupled phonon polariton at different angles; (b) calculation results of electric field distribution at different angles; (c) phonon polariton dispersion relations (Reproduced with permission from Ref. [61]).
图 8 六方氮化硼声子极化激元与应力场的耦合[65] (a) 近场探测六方氮化硼中局域应力的示意图; (b) 六方氮化硼中局域应力分布的近场成像; (c) 声子极化激元与局域应力场耦合导致应力区域的红外响应随探测频率而改变; (d) 六方氮化硼的声子共振频率随应力场强度的变化; (e) 沿不同方向的应力分布与褶皱半径的关系(出自文献[65], 已获得授权)
Fig. 8. Coupling between phonon polaritons and local strain in hexagonal boron nitride: (a) Schematic of the near-field detection of local strain in boron nitride[65]; (b) near field imaging of the local strain distribution in boron nitride; (c) different infrared response of the local strain with frequency resulted by the coupling between phonon polaritons and local strain; (d) first-principles calculation results for the TO phonon frequency shift under an isotropic biaxial strain; (e) theoretical results of local strain distribution in radial and tangential directions with the winkle radius (Reproduced with permission from Ref. [65]).
图 9 双层石墨烯声子极化激元与应力场的耦合[66] (a) 通过外加电场激活双层石墨烯的声子红外活性的示意图; (b) 声子极化激元与局域应力场耦合导致应力区域的红外响应随频率而变化; (c) 60 V栅压下具有法诺线形的石墨烯声子响应; (d), (e) 声子与局域应力场耦合导致的声子共振频率的偏移(出自文献[66], 已获得授权)
Fig. 9. Coupling between phonon polaritons and local strain in bilayer graphene[66]: (a) Schematic of the activation of phonon polariton in bilayer graphene by means of an external electric field; (b) different infrared response of the local strain with frequency resulted by the coupling between phonon polaritons and local strain; (c) graphene phonon response with Fano line shape at 60 V gate voltage; (d), (e) shift of phonon resonance frequency caused by the coupling of phonon polariton and local strain (Reproduced with permission from Ref. [66]).
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[1] Yankowitz M, Xue J, Cormode D, Sanchez-Yamagishi J D, Watanabe K, Taniguchi T, Jarillo-Herrero P, Jacquod P, LeRoy B J 2012 Nat. Phys. 8 382Google Scholar
[2] Yang W, Chen G, Shi Z, Liu C C, Zhang L, Xie G, Cheng M, Wang D, Yang R, Shi D, Watanabe K, Taniguchi T, Yao Y, Zhang Y, Zhang G 2013 Nat. Mater. 12 792Google Scholar
[3] Hunt B, Sanchez-Yamagishi J D, Young A F, Yankowitz M, LeRoy B J, Watanabe K, Taniguchi T, Moon P, Koshino M, Jarillo-Herrero P, Ashoori R C 2013 Science 340 1427Google Scholar
[4] Dean C R, Wang L, Maher P, Forsythe C, Ghahari F, Gao Y, Katoch J, Ishigami M, Moon P, Koshino M, Taniguchi T, Watanabe K, Shepard K L, Hone J, Kim P 2013 Nature 497 598Google Scholar
[5] Ponomarenko L A, Gorbachev R V, Yu G L, Elias D C, Jalil R, Patel A A, Mishchenko A, Mayorov A S, Woods C R, Wallbank J R, Mucha-Kruczynski M, Piot B A, Potemski M, Grigorieva I V, Novoselov K S, Guinea F, Fal’ko V I, Geim A K 2013 Nature 497 594Google Scholar
[6] Chen Z G, Shi Z, Yang W, Lu X, Lai Y, Yan H, Wang F, Zhang G, Li Z 2014 Nat. Commun. 5 4461Google Scholar
[7] Shi Z, Jin C, Yang W, Ju L, Horng J, Lu X, Bechtel H A, Martin M C, Fu D, Wu J, Watanabe K, Taniguchi T, Zhang Y, Bai X, Wang E, Zhang G, Wang F 2014 Nat. Phys. 10 743Google Scholar
[8] Ni G X, Wang H, Wu J S, Fei Z, Goldflam M D, Keilmann F, Özyilmaz B, Castro Neto A H, Xie X M, Fogler M M, Basov D N 2015 Nat. Mater. 14 1217Google Scholar
[9] Ribeiro-Palau R, Zhang C, Watanabe K, Taniguchi T, Hone J, Dean C R 2018 Science 361 690Google Scholar
[10] Cao Y, Fatemi V, Demir A, Fang S, Tomarken S L, Luo J Y, Sanchez-Yamagishi J D, Watanabe K, Taniguchi T, Kaxiras E, Ashoori R C, Jarillo-Herrero P 2018 Nature 556 80Google Scholar
[11] Cao Y, Fatemi V, Fang S, Watanabe K, Taniguchi T, Kaxiras E, Jarillo-Herrero P 2018 Nature 556 43Google Scholar
[12] Chen G, Jiang L, Wu S, Lyu B, Li H, Chittari B L, Watanabe K, Taniguchi T, Shi Z, Jung J, Zhang Y, Wang F 2019 Nat. Phys. 15 237Google Scholar
[13] Chen G, Sharpe A L, Gallagher P, Rosen I T, Fox E J, Jiang L, Lyu B, Li H, Watanabe K, Taniguchi T, Jung J, Shi Z, Goldhaber-Gordon D, Zhang Y, Wang F 2019 Nature 572 215Google Scholar
[14] Yankowitz M, Chen S, Polshyn H, Zhang Y, Watanabe K, Taniguchi T, Graf D, Young A F, Dean C R 2019 Science 363 1059Google Scholar
[15] Chen G, Sharpe A L, Fox E J, Zhang Y H, Wang S, Jiang L, Lyu B, Li H, Watanabe K, Taniguchi T, Shi Z, Senthil T, Goldhaber-Gordon D, Zhang Y, Wang F 2020 Nature 579 56Google Scholar
[16] Deng A, Hu C, Shen P, Chen J, Luo X, Lyu B, Watanabe K, Taniguchi T, Wang R, Liang Q, Ma J, Shi Z 2022 Small 18 e2105687Google Scholar
[17] HillenbRand R, Knoll B, Keilmann F 2001 J. Microsc. 202 77Google Scholar
[18] Basov D N, Fogler M M, García de Abajo F J 2016 Science 354 1992Google Scholar
[19] Low T, Chaves A, Caldwell J D, Kumar A, Fang N X, Avouris P, Heinz T F, Guinea F, Martin-Moreno L, Koppens F 2017 Nat. Mater. 16 182Google Scholar
[20] Zhang Q, Hu G, Ma W, Li P, Krasnok A, Hillenbrand R, Alù A, Qiu C W 2021 Nature 597 187Google Scholar
[21] 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
[22] Chen J, Badioli M, Alonso-González P, Thongrattanasiri S, Huth F, Osmond J, Spasenović M, Centeno A, Pesquera A, Godignon P, Zurutuza Elorza A, Camara N, de Abajo F J G, Hillenbrand R, Koppens F H L 2012 Nature 487 77Google Scholar
[23] 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
[24] Zhao W, Zhao S, Li H, Wang S, Wang S, Utama M I B, Kahn S, Jiang Y, Xiao X, Yoo S, Watanabe K, Taniguchi T, Zettl A, Wang F 2021 Nature 594 517Google Scholar
[25] Dong Y, Xiong L, Phinney I Y, Sun Z, Jing R, McLeod A S, Zhang S, Liu S, Ruta F L, Gao H, Dong Z, Pan R, Edgar J H, Jarillo-Herrero P, Levitov L S, Millis A J, Fogler M M, Bandurin D A, Basov D N 2021 Nature 594 513Google Scholar
[26] Luttinger J M 1963 J. Math. Phys. 4 1154Google Scholar
[27] Voit J 1995 Rep. Prog. Phys. 58 977Google Scholar
[28] Kane C L, Fisher M P A 1992 Phys. Rev. Lett. 68 1220Google Scholar
[29] Bockrath M, Cobden D H, Lu J, Rinzler A G, Smalley R E, Balents L, McEuen P L 1999 Nature 397 598Google Scholar
[30] Shi Z, Hong X, Bechtel H A, Zeng B, Martin M C, Watanabe K, Taniguchi T, Shen Y R, Wang F 2015 Nat. Photonics 9 515Google Scholar
[31] Kane C, Balents L, Fisher M P A 1997 Phys. Rev. Lett. 79 5086Google Scholar
[32] Egger R, Gogolin A O 1997 Phys. Rev. Lett. 79 5082Google Scholar
[33] Wang S, Zhao S, Shi Z, Wu F, Zhao Z, Jiang L, Watanabe K, Taniguchi T, Zettl A, Zhou C, Wang F 2020 Nat. Mater. 19 986Google Scholar
[34] Wang L, Lyu B, Gao Q, Chen J, Ying Z, Deng A, Shi Z 2020 Chin. Phys. Lett. 37 028101Google Scholar
[35] Dai S, Fei Z, Ma Q, Rodin A S, Wagner M, McLeod A S, Liu M K, Gannett W, Regan W, Watanabe K, Taniguchi T, Thiemens M, Dominguez G, Neto A H C, Zettl A, Keilmann F, Jarillo-Herrero P, Fogler M M, Basov D N 2014 Science 343 1125Google Scholar
[36] Shi Z, Bechtel H A, Berweger S, Sun Y, Zeng B, Jin C, Chang H, Martin M C, Raschke M B, Wang F 2015 ACS Photonics 2 790Google Scholar
[37] Li P, Dolado I, Alfaro-Mozaz F J, Casanova F, Hueso L E, Liu S, Edgar J H, Nikitin A Y, Vélez S, Hillenbrand R 2018 Science 359 892Google Scholar
[38] Ni G, McLeod A S, Sun Z, Matson J R, Lo C F B, Rhodes D A, Ruta F L, Moore S L, Vitalone R A, Cusco R, Artús L, Xiong L, Dean C R, Hone J C, Millis A J, Fogler M M, Edgar J H, Caldwell J D, Basov D N 2021 Nano Lett. 21 5767Google Scholar
[39] Zheng Z, Chen J, Wang Y, Wang X, Chen X, Liu P, Xu J, Xie W, Chen H, Deng S, Xu N 2018 Adv. Mater. 30 1705318Google Scholar
[40] Ma W, Alonso-González P, Li S, Nikitin A Y, Yuan J, Martín-Sánchez J, Taboada-Gutiérrez J, Amenabar I, Li P, Vélez S, Tollan C, Dai Z, Zhang Y, Sriram S, Kalantar-Zadeh K, Lee S T, Hillenbrand R, Bao Q 2018 Nature 562 557Google Scholar
[41] Low T, Roldán R, Wang H, Xia F, Avouris P, Moreno L M, Guinea F 2014 Phys. Rev. Lett. 113 106802Google Scholar
[42] Wang C, Huang S, Xing Q, Xie Y, Song C, Wang F, Yan H 2020 Nat. Commun. 11 1158Google Scholar
[43] Lu H, Dai S, Yue Z, Fan Y, Cheng H, Di J, Mao D, Li E, Mei T, Zhao J 2019 Nanoscale 11 4759Google Scholar
[44] Lu H, Yue Z, Li Y, Zhang Y, Zhang M, Zeng W, Gan X, Mao D, Xiao F, Mei T, Zhao W, Wang X, Gu M, Zhao J 2020 Light:Science & Applications 9 191Google Scholar
[45] Yue Z, Ren H, Wei S, Lin J, Gu M 2018 Nat. Commun. 9 4413Google Scholar
[46] Dubrovkin A M, Qiang B, Krishnamoorthy H N S, Zheludev N I, Wang Q J 2018 Nat. Commun. 9 1762Google Scholar
[47] Fei Z, Scott M E, Gosztola D J, Foley J J, Yan J, Mandrus D G, Wen H, Zhou P, Zhang D W, Sun Y, Guest J R, Gray S K, Bao W, Wiederrecht G P, Xu X 2016 Phys. Rev. B 94 081402Google Scholar
[48] Wang B, Zhang X, Yuan X, Teng J 2012 Appl. Phys. Lett. 100 131111Google Scholar
[49] Hu C, Deng A, Shen P, Luo X, Zhou X, Wu T, Huang X, Dong Y, Watanabe K, Taniguchi T, Xie G B, Li X J, Liang Q, Shi Z W 2021 Nanoscale 13 14628Google Scholar
[50] Wang S, Yoo S, Zhao S, Zhao W, Kahn S, Cui D, Wu F, Jiang L, Utama M I B, Li H, Li S, Zibrov A, Regan E, Wang D, Zhang Z, Watanabe K, Taniguchi T, Zhou C, Wang F 2021 Nat. Commun. 12 5039Google Scholar
[51] Wang Y, Xue C, Zhang Z, Zheng H, Zhang W, Yan S 2016 Sci. Rep. 6 38891Google Scholar
[52] Yan X, Wang T, Xiao S, Liu T, Hou H, Cheng L, Jiang X 2017 Sci. Rep. 7 13917Google Scholar
[53] Sun C, Dong Z, Si J, Deng X 2017 Opt. Express 25 1242Google Scholar
[54] Emani N K, Chung T F, Kildishev A V, Shalaev V M, Chen Y P, Boltasseva A 2014 Nano Lett. 14 78Google Scholar
[55] Chen Z X, Chen J H, Wu Z J, Hu W, Zhang X J, Lu Y Q 2014 Appl. Phys. Lett. 104 161114Google Scholar
[56] Brar V W, Jang M S, Sherrott M, Kim S, Lopez J J, Kim L B, Choi M, Atwater H 2014 Nano Lett. 14 3876Google Scholar
[57] Yang X, Zhai F, Hu H, Hu D, Liu R, Zhang S, Sun M, Sun Z, Chen J, Dai Q 2016 Adv. Mater. 28 2931Google Scholar
[58] Dai S, Ma Q, Liu M K, Andersen T, Fei Z, Goldflam M D, Wagner M, Watanabe K, Taniguchi T, Thiemens M, Keilmann F, Janssen G C, Zhu S E, Jarillo-Herrero P, Fogler M M, Basov D N 2015 Nat. Nanotechnol. 10 682Google Scholar
[59] Zhang Y, Hu C, Lyu B, Li H, Ying Z, Wang L, Deng A, Luo X, Gao Q, Chen J, Du J, Shen P, Watanabe K, Taniguchi T, Kang J H, Wang F, Zhang Y, Shi Z W 2020 Nano Lett. 20 2770Google Scholar
[60] Hu G, Ou Q, Si G, Wu Y, Wu J, Dai Z, Krasnok A, Mazor Y, Zhang Q, Bao Q, Qiu C-W, Alù A 2020 Nature 582 209Google Scholar
[61] Zheng Z, Sun F, Huang W, Jiang J, Zhan R, Ke Y, Chen H, Deng S 2020 Nano Lett. 20 5301Google Scholar
[62] Chen M, Lin X, Dinh T H, Zheng Z, Shen J, Ma Q, Chen H, Jarillo-Herrero P, Dai S 2020 Nat. Mater. 19 1307Google Scholar
[63] Duan J, Capote-Robayna N, Taboada-Gutiérrez J, Álvarez-Pérez G, Prieto I, Martín-Sánchez J, Nikitin A Y, Alonso-González P 2020 Nano Lett. 20 5323Google Scholar
[64] Zhao X Y, Huang J H, Zhuo Z Y, Xue Y Z, Ding K, Dou X M, Liu J, Sun B Q 2020 Chin. Phys. Lett. 37 044204Google Scholar
[65] Lyu B, Li H, Jiang L, Shan W, Hu C, Deng A, Ying Z, Wang L, Zhang Y, Bechtel H A, Martin M C, Taniguchi T, Watanabe K, Luo W, Wang F, Shi Z W 2019 Nano Lett. 19 1982Google Scholar
[66] Du J, Lyu B, Shan W, Chen J, Zhou X, Xie J, Deng A, Hu C, Liang Q, Xie G, Li X J, Luo W D, Shi Z W 2021 Chin. Phys. Lett. 38 056301Google Scholar
[67] Zhou Y, Scuri G, Wild D S, High A A, Dibos A, Jauregui L A, Shu C, De Greve K, Pistunova K, Joe A Y, Taniguchi T, Watanabe K, Kim P, Lukin M D, Park H 2017 Nat. Nanotechnol. 12 856Google Scholar
[68] Gelly R J, Renaud D, Liao X, Pingault B, Bogdanovic S, Scuri G, Watanabe K, Taniguchi T, Urbaszek B, Park H, Lončar M 2022 Nat. Commun. 13 232Google Scholar
[69] Ni G X, Wang L, Goldflam M D, Wagner M, Fei Z, McLeod A S, Liu M K, Keilmann F, Özyilmaz B, Castro Neto A H, Hone J, Fogler M M, Basov D N 2016 Nat. Photonics 10 244Google Scholar
[70] Huber M A, Mooshammer F, Plankl M, Viti L, Sandner F, Kastner L Z, Frank T, Fabian J, Vitiello M S, Cocker T L, Huber R 2017 Nat. Nanotechnol. 12 207Google Scholar
[71] Liu M, Yin X, Ulin-Avila E, Geng B, Zentgraf T, Ju L, Wang F, Zhang X 2011 Nature 474 64Google Scholar
[72] Phare C T, Daniel Lee Y H, Cardenas J, Lipson M 2015 Nat. Photonics 9 511Google Scholar
[73] Ansell D, Radko I P, Han Z, Rodriguez F J, Bozhevolnyi S I, Grigorenko A N 2015 Nat. Commun. 6 8846Google Scholar
[74] Wong L J, Kaminer I, Ilic O, Joannopoulos J D, Soljačić M 2016 Nat. Photonics 10 46Google Scholar
[75] Rodrigo D, Limaj O, Janner D, Etezadi D, García de Abajo F J, Pruneri V, Altug H 2015 Science 349 165Google Scholar
[76] Chand S B, Woods J M, Mejia E, Taniguchi T, Watanabe K, Grosso G 2022 Nano Lett. 22 3087Google Scholar
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