Please wait a minute...
Chin. Phys. B, 2021, Vol. 30(1): 017303    DOI: 10.1088/1674-1056/abb65d
CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES Prev   Next  

Optical conductivity of twisted bilayer graphene near the magic angle

Lu Wen(文露), Zhiqiang Li(李志强), and Yan He(贺言)†
College of Physics, Sichuan University, Chengdu 610064, China
Abstract  We theoretically study the band structure and optical conductivity of twisted bilayer graphene (TBG) near the magic angle considering the effects of lattice relaxation. We show that the optical conductivity spectrum is characterized by a series of peaks associated with the van Hove singularities in the band structure, and the peak energies evolve systematically with the twist angle. Lattice relaxation effects in TBG modify its band structure, especially the flat bands, which leads to significant shifts of the peaks in the optical conductivity. These results demonstrate that spectroscopic features in the optical conductivity can serve as fingerprints for exploring the band structure, band gap, and lattice relaxation in magic-angle TBG as well as identifying its rotation angle.
Keywords:  graphene      moir\'e superlattice      magic angle      optical conductivity  
Received:  16 July 2020      Revised:  17 August 2020      Accepted manuscript online:  09 September 2020
PACS:  73.21.Cd (Superlattices)  
  78.67.Wj (Optical properties of graphene)  
  73.22.Pr (Electronic structure of graphene)  
  73.25.+i (Surface conductivity and carrier phenomena)  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11874271 and 11874272).
Corresponding Authors:  Corresponding author. E-mail: heyan_ctp@scu.edu.cn   

Cite this article: 

Lu Wen(文露), Zhiqiang Li(李志强), and Yan He(贺言) Optical conductivity of twisted bilayer graphene near the magic angle 2021 Chin. Phys. B 30 017303

1 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 and Geim A K 2013 Nature 497 594
2 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 and Kim P 2013 Nature 497 598
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 and Ashoori R C 2013 Science 340 1427
4 Li G H, Luican A, dos Santos J M B L, Castro Neto A H, Reina A, Kong J and Andrei E Y 2010 Nat. Phys. 6 109
5 Bistritzer R and MacDonald A H 2011 Proc. Natl. Acad. Sci. USA 108 12233
6 dos Santos J M B L, Peres N M R and Castro A H 2007 Phys. Rev. Lett. 99 256802
7 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 and Jarillo-Herrero P 2018 Nature 556 80
8 Cao Y, Fatemi V, Fang S, Watanabe K, Taniguchi T, Kaxiras E and Jarillo-Herrero P 2018 Nature 556 43
9 Yankowitz M, Chen S W, Polshyn H, Zhang Y X, Watanabe K, Taniguchi T, Graf D, Young A F and Dean C R 2019 Science 363 1059
10 Sharpe A L, Fox E J, Barnard A W, Finney J, Watanabe K, Taniguchi T, Kastner M A and Goldhaber-Gordon D 2019 Science 365 605
11 Serlin M, Tschirhart C L, Polshyn H, Zhang Y, Zhu J, Watanabe K, Taniguchi T, Balents L and Young A F 2020 Science 367 900
12 Lu X, Stepanov P, Yang W, Xie M, Aamir M A, Das I, Urgell C, Watanabe K, Taniguchi T, Zhang G, Bachtold A, MacDonald A H and Efetov D K 2019 Nature 574 653
13 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 and Wang F 2020 Nature 579 56
14 Lü X Y and Li Z Q 2019 Acta Phys. Sin. 68 220303 (in Chinese)
15 Basov D N, Fogler M M, Lanzara A, Wang F and Zhang Y B 2014 Rev. Mod. Phys. 86 959
16 Lu X B and Zhang G Y 2015 Acta Phys. Sin. 64 077305 (in Chinese)
17 Sprinkle M, Siegel D, Hu Y, Hicks J, Tejeda A, Taleb-Ibrahimi A, Le Fevre P, Bertran F, Vizzini S, Enriquez H, Chiang S, Soukiassian P, Berger C, de Heer W A, Lanzara A and Conrad E H 2009 Phys. Rev. Lett. 103 226803
18 Zhang Y B, Tang T T, Girit C, Hao Z, Martin M C, Zettl A, Crommie M F, Shen Y R and Wang F 2009 Nature 459 820
19 Brar V W, Wickenburg S, Panlasigui M, Park C H, Wehling T O, Zhang Y B, Decker R, Girit C, Balatsky A V, Louie S G, Zettl A and Crommie M F 2010 Phys. Rev. Lett. 104 036805
20 Siegel D A, Park C H, Hwang C, Deslippe J, Fedorov A V, Louie S G and Lanzara A 2011 Proc. Natl. Acad. Sci. USA 108 11365
21 Zhang Y B, Brar V W, Wang F, Girit C, Yayon Y, Panlasigui M, Zettl A and Crommie M F 2008 Nat. Phys. 4 627
22 Tudorovskiy T and Mikhailov S A 2010 Phys. Rev. B 82 073411
23 Grigorenko A N, Polini M and Novoselov K S 2012 Nat. Photon. 6 749
24 Bonaccorso F, Sun Z, Hasan T and Ferrari A C 2010 Nat. Photon. 4 611
25 Koppens F H L, Mueller T, Avouris P, Ferrari A C, Vitiello M S and Polini M 2014 Nat. Nanotechnol. 9 780
26 Moon P and Koshino M 2013 Phys. Rev. B 87 205404
27 Calderòn M J and Bascones E 2019 arXiv:1912.09935 [cond-mat.str-el]
28 Bi Z, Yuan N F Q and Fu L 2019 Phys. Rev. B 100 035448)
29 Koshino M, Yuan N F Q, Koretsune T, Ochi M, Kuroki K and Fu L 2018 Phys. Rev. X 8 031087
30 Shallcross S, Sharma S, Kandelaki E and Pankratov O A 2010 Phys. Rev. B 81 165105
31 Yoo H, Engelke R, Carr S, Fang S, Zhang K, Cazeaux P, Sung S H, Hovden R, Tsen A W, Taniguchi T, Watanabe K, Yi G C, Kim M, Luskin M, Tadmor E B, Kaxiras E and Kim P 2019 Nat. Mater. 18 448
32 Nam N N T and Koshino M 2017 Phys. Rev. B 96 075311
33 Dai S Y, Xiang Y and Srolovitz D J 2016 Nano Lett. 16 5923
34 Gargiulo F and Yazyev O V2018 2D Mater. 5 01501
35 Kim N Y, Jeong H Y, Kim J H, Kim G, Shin H S and Lee Z 2017 Acs Nano 11 7084
36 van Wijk M M, Schuring A, Katsnelson M I and Fasolino A 2015 2D Mater. 2 034010
37 Woods C R, Britnell L, Eckmann A, Ma R S, Lu J C, Guo H M, Lin X, Yu G L, Cao Y, Gorbachev R V, Kretinin A V, Park J, Ponomarenko L A, Katsnelson M I, Gornostyrev Y N, Watanabe K, Taniguchi T, Casiraghi C, Gao H J, Geim A K and Novoselov K S 2014 Nat. Phys. 10 451
38 Zhang K and Tadmor E B 2018 J. Mech. Phys. Solids 112 225
39 Carr S, Massatt D, Torrisi S B, Cazeaux P, Luskin M and Kaxiras E 2018 Phys. Rev. B 98 224102
40 Gusynin V P, Sharapov S G and Carbotte J P 2007 Phys. Rev. Lett. 98 157402
41 Gusynin V P and Sharapov S G 2006 Phys. Rev. B 73 245411
[1] Polarization Raman spectra of graphene nanoribbons
Wangwei Xu(许望伟), Shijie Sun(孙诗杰), Muzi Yang(杨慕紫), Zhenliang Hao(郝振亮), Lei Gao(高蕾), Jianchen Lu(卢建臣), Jiasen Zhu(朱嘉森), Jian Chen(陈建), and Jinming Cai(蔡金明). Chin. Phys. B, 2023, 32(4): 046803.
[2] Spin- and valley-polarized Goos-Hänchen-like shift in ferromagnetic mass graphene junction with circularly polarized light
Mei-Rong Liu(刘美荣), Zheng-Fang Liu(刘正方), Ruo-Long Zhang(张若龙), Xian-Bo Xiao(肖贤波), and Qing-Ping Wu(伍清萍). Chin. Phys. B, 2023, 32(3): 037301.
[3] Graphene metasurface-based switchable terahertz half-/quarter-wave plate with a broad bandwidth
Xiaoqing Luo(罗小青), Juan Luo(罗娟), Fangrong Hu(胡放荣), and Guangyuan Li(李光元). Chin. Phys. B, 2023, 32(2): 027801.
[4] Correlated states in alternating twisted bilayer-monolayer-monolayer graphene heterostructure
Ruirui Niu(牛锐锐), Xiangyan Han(韩香岩), Zhuangzhuang Qu(曲壮壮), Zhiyu Wang(王知雨), Zhuoxian Li(李卓贤), Qianling Liu(刘倩伶), Chunrui Han(韩春蕊), and Jianming Lu(路建明). Chin. Phys. B, 2023, 32(1): 017202.
[5] Adsorption dynamics of double-stranded DNA on a graphene oxide surface with both large unoxidized and oxidized regions
Mengjiao Wu(吴梦娇), Huishu Ma(马慧姝), Haiping Fang(方海平), Li Yang(阳丽), and Xiaoling Lei(雷晓玲). Chin. Phys. B, 2023, 32(1): 018701.
[6] Precisely controlling the twist angle of epitaxial MoS2/graphene heterostructure by AFM tip manipulation
Jiahao Yuan(袁嘉浩), Mengzhou Liao(廖梦舟), Zhiheng Huang(黄智恒), Jinpeng Tian(田金朋), Yanbang Chu(褚衍邦), Luojun Du(杜罗军), Wei Yang(杨威), Dongxia Shi(时东霞), Rong Yang(杨蓉), and Guangyu Zhang(张广宇). Chin. Phys. B, 2022, 31(8): 087302.
[7] Longitudinal conductivity in ABC-stacked trilayer graphene under irradiating of linearly polarized light
Guo-Bao Zhu(朱国宝), Hui-Min Yang(杨慧敏), and Jie Yang(杨杰). Chin. Phys. B, 2022, 31(8): 088102.
[8] Dual-channel tunable near-infrared absorption enhancement with graphene induced by coupled modes of topological interface states
Zeng-Ping Su(苏增平), Tong-Tong Wei(魏彤彤), and Yue-Ke Wang(王跃科). Chin. Phys. B, 2022, 31(8): 087804.
[9] Recent advances of defect-induced spin and valley polarized states in graphene
Yu Zhang(张钰), Liangguang Jia(贾亮广), Yaoyao Chen(陈瑶瑶), Lin He(何林), and Yeliang Wang(王业亮). Chin. Phys. B, 2022, 31(8): 087301.
[10] Dynamically tunable multiband plasmon-induced transparency effect based on graphene nanoribbon waveguide coupled with rectangle cavities system
Zi-Hao Zhu(朱子豪), Bo-Yun Wang(王波云), Xiang Yan(闫香), Yang Liu(刘洋), Qing-Dong Zeng(曾庆栋), Tao Wang(王涛), and Hua-Qing Yu(余华清). Chin. Phys. B, 2022, 31(8): 084210.
[11] Valley-dependent transport in strain engineering graphene heterojunctions
Fei Wan(万飞), X R Wang(王新茹), L H Liao(廖烈鸿), J Y Zhang(张嘉颜),M N Chen(陈梦南), G H Zhou(周光辉), Z B Siu(萧卓彬), Mansoor B. A. Jalil, and Yuan Li(李源). Chin. Phys. B, 2022, 31(7): 077302.
[12] Thermionic electron emission in the 1D edge-to-edge limit
Tongyao Zhang(张桐耀), Hanwen Wang(王汉文), Xiuxin Xia(夏秀鑫), Chengbing Qin(秦成兵), and Xiaoxi Li(李小茜). Chin. Phys. B, 2022, 31(5): 058504.
[13] Photoelectrochemical activity of ZnO:Ag/rGO photo-anodes synthesized by two-steps sol-gel method
D Ben Jemia, M Karyaoui, M A Wederni, A Bardaoui, M V Martinez-Huerta, M Amlouk, and R Chtourou. Chin. Phys. B, 2022, 31(5): 058201.
[14] TiS2-graphene heterostructures enabling polysulfide anchoring and fast electrocatalyst for lithium-sulfur batteries: A first-principles calculation
Wenyang Zhao(赵文阳), Li-Chun Xu(徐利春), Yuhong Guo(郭宇宏), Zhi Yang(杨致), Ruiping Liu(刘瑞萍), and Xiuyan Li(李秀燕). Chin. Phys. B, 2022, 31(4): 047101.
[15] Light-modulated electron retroreflection and Klein tunneling in a graphene-based n-p-n junction
Xingfei Zhou(周兴飞), Ziying Wu(吴子瀛), Yuchen Bai(白宇晨), Qicheng Wang(王起程), Zhentao Zhu(朱震涛), Wei Yan(闫巍), and Yafang Xu(许亚芳). Chin. Phys. B, 2022, 31(4): 047301.
No Suggested Reading articles found!