Please wait a minute...
Chin. Phys. B, 2023, Vol. 32(10): 107302    DOI: 10.1088/1674-1056/acb2c1
CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES Prev   Next  

Effects of strain on the flat band in twisted bilayer graphene

Zhen Zhang(张镇), Lu Wen(文露), Youkai Qiao(乔友凯), and Zhiqiang Li(李志强)
College of Physics, Sichuan University, Chengdu 610064, China
Abstract  Based on the effective continuum model, we systematically study the electronic band structures and density of states of twisted bilayer graphene near the magic angle under the influence of different types of strain, including shear strain, volume-preserving strain and biaxial strain. We find that the flat bands behave very differently under various types of strain. Volume-preserving strain generically leads to broader van Hove singularities associated with the flat bands compared with those under shear strain, with dissimilar strain direction dependence. The band structures and density of states under shear and volume-preserving strains change with the strain direction, while those under biaxial strain are independent of the direction of strain. In particular, the effect of biaxial strain on twisted bilayer graphene is geometrically and electronically similar to the influence of the twisted angle. Our results reveal the characteristic structures in the band structures and density of states under various types of strain, which can serve as fingerprints for exploring the effects of strain on the novel physics of this system.
Keywords:  graphene      moiré superlattice      magic angle and strain  
Received:  16 September 2022      Revised:  10 January 2023      Accepted manuscript online:  13 January 2023
PACS:  73.22.Pr (Electronic structure of graphene)  
  73.21.Cd (Superlattices)  
  81.05.ue (Graphene)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11874271). We thank Yan He for theoretical support and discussions.
Corresponding Authors:  Zhiqiang Li     E-mail:  zhiqiangli@scu.edu.cn

Cite this article: 

Zhen Zhang(张镇), Lu Wen(文露), Youkai Qiao(乔友凯), and Zhiqiang Li(李志强) Effects of strain on the flat band in twisted bilayer graphene 2023 Chin. Phys. B 32 107302

[1] 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
[2] Cao Y, Fatemi V, Fang S, Watanabe K, Taniguchi T, Kaxiras E and Jarillo-Herrero P 2018 Nature 556 43
[3] Arora H S, Polski R, Zhang Y R, Thomson A, Choi Y, Kim H, Lin Z, Wilson I Z, Xu X D, Chu J H, Watanabe K, Taniguchi T, Alicea J and Nadj-Perge S 2020 Nature 583 379
[4] Cao Y, Chowdhury D, Rodan-Legrain D, Rubies-Bigorda O, Watanabe K, Taniguchi T, Senthil T and Jarillo-Herrero P 2020 Phys. Rev. Lett. 124 076801
[5] Chen G R, Sharpe A L, Fox E J, Zhang Y H, Wang S X, Jiang L L, Lyu B S, Li H Y, Watanabe K, Taniguchi T, Shi Z W, Senthil T, Goldhaber-Gordon D, Zhang Y B and Wang F 2020 Nature 579 56
[6] Choi Y, Kemmer J, Peng Y, Thomson A, Arora H, Polski R, Zhang Y R, Ren H C, Alicea J, Refael G, von Oppen F, Watanabe K, Taniguchi T and Nadj-Perge S 2019 Nat. Phys. 15 1205
[7] Jiang Y H, Lai X Y, Watanabe K, Taniguchi T, Haule K, Mao J H and Andrei E Y 2019 Nature 573 91
[8] Kerelsky A, McGilly L J, Kennes D M, Xian L D, Yankowitz M, Chen S W, Watanabe K, Taniguchi T, Hone J, Dean C, Rubio A and Pasupathy A N 2019 Nature 572 95
[9] Lu X B, Stepanov P, Yang W, Xie M, Aamir M A, Das I, Urgell C, Watanabe K, Taniguchi T, Zhang G Y, Bachtold A, MacDonald A H and Efetov D K 2019 Nature 574 653
[10] Polshyn H, Yankowitz M, Chen S W, Zhang Y X, Watanabe K, Taniguchi T, Dean C R and Young A F 2019 Nat. Phys. 15 1011
[11] Saito Y, Ge J Y, Watanabe K, Taniguchi T and Young A F 2020 Nat. Phys. 16 926
[12] 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
[13] 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
[14] Stepanov P, Das I, Lu X B, Fahimniya A, Watanabe K, Taniguchi T, Koppens F H L, Lischner J, Levitov L and Efetov D K 2020 Nature 583 375
[15] Stepanov P, Xie M, Taniguchi T, Watanabe K, Lu X B, MacDonald A H, Bernevig B A and Efetov D K 2021 Phys. Rev. Lett. 127 197701
[16] Wong D L, Nuckolls K P, Oh M, Lian B, Xie Y L, Jeon S, Watanabe K, Taniguchi T, Bernevig B A and Yazdani A 2020 Nature 582 198
[17] Xie Y L, Lian B, Jack B, Liu X M, Chiu C L, Watanabe K, Taniguchi T, Bernevig B A and Yazdani A 2019 Nature 572 101
[18] 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
[19] Zondiner U, Rozen A, Rodan-Legrain D, Cao Y, Queiroz R, Taniguchi T, Watanabe K, Oreg Y, von Oppen F, Stern A, Berg E, Jarillo-Herrero P and Ilani S 2020 Nature 582 203
[20] Bistritzer R and MacDonald A H 2011 Proc. Natl. Acad. Sci. USA 108 12233
[21] de Laissardiere G T, Mayou D and Magaud L 2010 Nano Lett. 10 804
[22] de Laissardiere G T, Mayou D and Magaud L 2012 Phys. Rev. B 86 125413
[23] Morell E S, Correa J D, Vargas P, Pacheco M and Barticevic Z 2010 Phys. Rev. B 82 121407
[24] Bi Z, Yuan N F Q and Fu L 2019 Phys. Rev. B 100 035448
[25] Moon P and Koshino M 2013 Phys. Rev. B 87 205404
[26] Xie M and MacDonald A H 2020 Phys. Rev. Lett. 124 097601
[27] Bultinck N, Khalaf E, Liu S, Chatterjee S, Vishwanath A and Zaletel M P 2020 Phys. Rev. X 10 031034
[28] Carr S, Fang S and Kaxiras E 2020 Nat. Rev. Mater. 5 748
[29] dos Santos J M B L, Peres N M R and Castro Neto A H 2012 Phys. Rev. B 86 155449
[30] Guinea F and Walet N R 2018 Proc. Natl. Acad. Sci. USA 115 13174
[31] Kang J and Vafek O 2018 Phys. Rev. X 8 031088
[32] Koshino M 2015 New J. Phys. 17 015014
[33] Koshino M, Yuan N F Q, Koretsune T, Ochi M, Kuroki K and Fu L 2018 Phys. Rev. X 8 031087
[34] Liu J P and Dai X 2021 Phys. Rev. B 103 035427
[35] Po H C, Zou L J, Vishwanath A and Senthil T 2018 Phys. Rev. X 8 031089
[36] Yu G, Wen L, Luo G and Wang Y 2021 Phys. Scr. 96 125874
[37] Zhang Y, Jiang K, Wang Z Q and Zhang F C 2020 Phys. Rev. B 102 035136
[38] Dai Z B, He Y and Li Z 2021 Phys. Rev. B 104 045403
[39] Nakatsuji N and Koshino M 2022 Phys. Rev. B 105 245408
[40] Huder L, Artaud A, Quang T L, de Laissardiere G T, Jansen A G M, Lapertot G, Chapelier C and Renard V T 2018 Phys. Rev. Lett. 120 156405
[41] Wen L, Li Z and He Y 2021 Chin. Phys. B 30 017303
[42] Kaplan D, Holder T and Yan B H 2022 Phys. Rev. Res. 4 013209
[43] Mannai M and Haddad S 2021 Phys. Rev. B 103 L201112
[44] Zhai D and Yao W 2020 Phys. Rev. Mater. 4 094002
[45] dos Santos J M B L, Peres N M R and Castro A H 2007 Phys. Rev. Lett. 99 256802
[46] Nam N N T and Koshino M 2017 Phys. Rev. B 96 075311
[47] Koshino M and Nam N N T 2020 Phys. Rev. B 101 195425
[48] Gao Y, Kim S, Zhou S, Chiu H C, Nelias D, Berger C, de Heer W, Polloni L, Sordan R, Bongiorno A and Riedo E 2015 Nat. Mater. 14 714
[49] Novoselov K S, Mishchenko A, Carvalho A and Neto A H C 2016 Science 353 aac9439
[50] Tan P H, Han W P, Zhao W J, Wu Z H, Chang K, Wang H, Wang Y F, Bonini N, Marzari N, Pugno N, Savini G, Lombardo A and Ferrari A C 2012 Nat. Mater. 11 294
[51] Yao J D and Yang G W 2022 J. Appl. Phys. 131 0087503
[52] Frisenda R, Druppel M, Schmidt R, de Vasconcellos S M, de Lara D P, Bratschitsch R, Rohlfing M and Castellanos-Gomez A 2017 Npj 2d Mater. Appl. 1 10
[53] Guinea F 2012 Solid State Commun. 152 1437
[1] Emergence of correlations in twisted monolayer-trilayer graphene heterostructures
Zhang Zhou(周璋), Kenji Watanabe, Takashi Taniguchi, Xiao Lin(林晓), Jinhai Mao(毛金海), and Hong-Jun Gao(高鸿钧). Chin. Phys. B, 2023, 32(9): 097203.
[2] Intercalation of hafnium oxide between epitaxially-grown monolayer graphene and Ir(111) substrate
Yi Biao(表奕), Hong-Liang Lu(路红亮), Hao Peng(彭浩), Zhi-Peng Song(宋志朋), Hui Guo(郭辉), and Xiao Lin(林晓). Chin. Phys. B, 2023, 32(9): 098102.
[3] Rashba spin-orbit coupling induced rectified currents in monolayer graphene with exchange field and sublattice potential
Liang Chen(陈亮), Feng Li(李峰), and Xiao-Ming Ding(丁晓明). Chin. Phys. B, 2023, 32(8): 087103.
[4] Epitaxial growth of trilayer graphene moiré superlattice
Yalong Yuan(袁亚龙), Yanbang Chu(褚衍邦), Cheng Hu(胡成), Jinpeng Tian(田金朋), Le Liu(刘乐), Fanfan Wu(吴帆帆), Yiru Ji(季怡汝), Jiaojiao Zhao(赵交交), Zhiheng Huang(黄智恒), Xiaozhou Zan(昝晓洲), Luojun Du(杜罗军), Kenji Watanabe, Takashi Taniguchi, Dongxia Shi(时东霞), Zhiwen Shi(史志文), Wei Yang(杨威), and Guangyu Zhang(张广宇). Chin. Phys. B, 2023, 32(7): 077304.
[5] Controlled crossover of electron transport in graphene nanoconstriction: From Coulomb blockade to electron interference
Wei Yu(余炜), Xiao Guo(郭潇), Yuwen Cai(蔡煜文), Xiaotian Yu(俞晓天), and Wenjie Liang(梁文杰). Chin. Phys. B, 2023, 32(7): 077202.
[6] Gate-controlled localization to delocalization transition of flat band wavefunction in twisted monolayer-bilayer graphene
Siyu Li(李思宇), Zhengwen Wang(王政文), Yucheng Xue(薛禹承), Lu Cao(曹路), Kenji Watanabe, Takashi Taniguchi, Hongjun Gao(高鸿钧), and Jinhai Mao(毛金海). Chin. Phys. B, 2023, 32(6): 067304.
[7] Er intercalation and its impact on transport properties of epitaxial graphene
Mingmin Yang(杨明敏), Yong Duan(端勇), Wenxia Kong(孔雯霞), Jinzhe Zhang(章晋哲), Jianxin Wang(王剑心), and Qun Cai(蔡群). Chin. Phys. B, 2023, 32(6): 066103.
[8] Morphological features and nanostructures generated during SiC graphitization process
Wen-Xia Kong(孔雯霞), Yong Duan(端勇), Jin-Zhe Zhang(章晋哲),Jian-Xin Wang(王剑心), and Qun Cai(蔡群). Chin. Phys. B, 2023, 32(6): 068103.
[9] Tunable correlation in twisted monolayer-trilayer graphene
Dongdong Ding(丁冬冬), 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(6): 067204.
[10] Probing photocarrier dynamics of pressurized graphene using time-resolved terahertz spectroscopy
Yunfeng Wang(王云峰), Shujuan Xu(许淑娟), Jin Yang(杨金), and Fuhai Su(苏付海). Chin. Phys. B, 2023, 32(6): 067802.
[11] Grand canonical Monte Carlo simulation study of hydrogen storage by Li-decorated pha-graphene
Meng-Meng Zhang(张蒙蒙), Feng Zhang(张凤), Qiang Wu(吴强), Xin Huang(黄欣), Wei Yan(闫巍),Chun-Mei Zhao(赵春梅), Wei Chen(陈伟), Zhi-Hong Yang(杨志红),Yun-Hui Wang(王允辉), and Ting-Ting Wu(武婷婷). Chin. Phys. B, 2023, 32(6): 066803.
[12] Long-range adsorbate interactions mediated by two-dimensional Dirac fermions
Xiaohui Wang(王晓慧), Zhen-Guo Fu(付振国), Zhigang Wang(王志刚), Feng Chi(迟锋), and Ping Zhang(张平). Chin. Phys. B, 2023, 32(5): 057201.
[13] Machine learning of the Γ-point gap and flat bands of twisted bilayer graphene at arbitrary angles
Xiaoyi Ma(马宵怡), Yufeng Luo(罗宇峰), Mengke Li(李梦可), Wenyan Jiao(焦文艳), Hongmei Yuan(袁红梅), Huijun Liu(刘惠军), and Ying Fang(方颖). Chin. Phys. B, 2023, 32(5): 057306.
[14] 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.
[15] 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.
No Suggested Reading articles found!