| CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES |
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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 |
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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.
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Received: 16 September 2022
Revised: 10 January 2023
Accepted manuscript online: 13 January 2023
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PACS:
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73.22.Pr
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(Electronic structure of graphene)
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73.21.Cd
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(Superlattices)
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81.05.ue
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(Graphene)
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| 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
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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
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[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 |
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