Emergence of Chern Insulating States in Non-Magic Angle Twisted Bilayer Graphene

Cheng Shen; Jianghua Ying; Le Liu; Jianpeng Liu; Na Li; Shuopei Wang; Jian Tang; Yanchong Zhao; Yanbang Chu; Kenji Watanabe; Takashi Taniguchi; Rong Yang; Dongxia Shi; Fanming Qu; Li Lu; Wei Yang; Guangyu Zhang

doi:10.1088/0256-307X/38/4/047301

PDF (2852 KB)

Express Letter

Emergence of Chern Insulating States in Non-Magic Angle Twisted Bilayer Graphene

Cheng Shen^1,2,
Jianghua Ying^1,2,
Le Liu^1,2,
Jianpeng Liu^3,4,
Na Li^1,2,6,
Shuopei Wang^1,2,6,
Jian Tang^1,2,
Yanchong Zhao^1,2,
Yanbang Chu^1,2,
Kenji Watanabe⁷,
Takashi Taniguchi⁸,
Rong Yang^1,5,6,
Dongxia Shi^1,2,5,
Fanming Qu^1,2,6,
Li Lu^1,2,6,
Wei Yang^1,2,6*,
Guangyu Zhang^1,2,5,6*

¹Beijing National Laboratory for Condensed Matter Physics; Key Laboratory for Nanoscale Physics and Devices, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
²School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
³School of Physical Sciences and Technology, ShanghaiTech University, Shanghai 200031, China
⁴ShanghaiTech Laboratory for Topological Physics, ShanghaiTech University, Shanghai 200031, China
⁵Beijing Key Laboratory for Nanomaterials and Nanodevices, Beijing 100190, China
⁶Songshan-Lake Materials Laboratory, Dongguan 523808, China
⁷Research Center for Functional Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
⁸International Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan

Show all affliationsShow less

More Information |

PDF View FullText Get Citation

Received Date: February 10, 2021

Published Date: March 31, 2021

Abstract

Abstract

Twisting two layers into a magic angle (MA) of $\sim$ $1.1^{\circ}$ is found essential to create low energy flat bands and the resulting correlated insulating, superconducting, and magnetic phases in twisted bilayer graphene (TBG). While most of previous works focus on revealing these emergent states in MA-TBG, a study of the twist angle dependence, which helps to map an evolution of these phases, is yet less explored. Here, we report a magneto-transport study on one non-magic angle TBG device, whose twist angle $\theta$ changes from 1.25 $^{\circ}$ at one end to 1.43 $^{\circ}$ at the other. For $\theta =1.25^{\circ}$ we observe an emergence of topological insulating states at hole side with a sequence of Chern number $\left| C \right|=4-\left| v \right|$ , where $v$ is the number of electrons (holes) in moiré unite cell. When $\theta >1.25^{\circ}$ , the Chern insulator from flat band disappears and evolves into fractal Hofstadter butterfly quantum Hall insulator where magnetic flux in one moiré unite cell matters. Our observations will stimulate further theoretical and experimental investigations on the relationship between electron interactions and non-trivial band topology.

FullText(HTML)

Article Text

View FullText

References (39)

References

[1]	Bistritzer R and MacDonald A H 2011 Proc. Natl. Acad. Sci. USA 108 12233 doi: 10.1073/pnas.1108174108 CrossRef Google Scholar
[2]	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 doi: 10.1038/nature26154 CrossRef Google Scholar
[3]	Cao Y, Fatemi V, Fang S, Watanabe K, Taniguchi T, Kaxiras E and Jarillo-Herrero P 2018 Nature 556 43 doi: 10.1038/nature26160 CrossRef Google Scholar
[4]	Yankowitz M, Chen S, Polshyn H, Zhang Y, Watanabe K, Taniguchi T, Graf D, Young A F and Dean C R 2019 Science 363 1059 doi: 10.1126/science.aav1910 CrossRef Google Scholar
[5]	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 doi: 10.1038/s41586-019-1695-0 CrossRef Google Scholar
[6]	Choi Y, Kemmer J, Peng Y, Thomson A, Arora H, Polski R, Zhang Y, Ren H, Alicea J, Refael G, Oppen F V, Watanabe K, Taniguchi T and Nadj-Perge S 2019 Nat. Phys. 15 1174 doi: 10.1038/s41567-019-0606-5 CrossRef Google Scholar
[7]	Kerelsky A, McGilly L J, Kennes D M, Xian L, Yankowitz M, Chen S, Watanabe K, Taniguchi T, Hone J, Dean C, Rubio A and Pasupathy A N 2019 Nature 572 95 doi: 10.1038/s41586-019-1431-9 CrossRef Google Scholar
[8]	Xie Y, Lian B, Jäck B, Liu X, Chiu C L, Watanabe K, Taniguchi T, Bernevig B A and Yazdani A 2019 Nature 572 101 doi: 10.1038/s41586-019-1422-x CrossRef Google Scholar
[9]	Jiang Y, Lai X, Watanabe K, Taniguchi T, Haule K, Mao J and Andrei E Y 2019 Nature 573 91 doi: 10.1038/s41586-019-1460-4 CrossRef Google Scholar
[10]	Zhang Y H, Mao D, Cao Y, Jarillo-Herrero P and Senthil T 2019 Phys. Rev. B 99 075127 doi: 10.1103/PhysRevB.99.075127 CrossRef Google Scholar
[11]	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 doi: 10.1126/science.aaw3780 CrossRef Google Scholar
[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 doi: 10.1126/science.aay5533 CrossRef Google Scholar
[13]	Cao Y, Luo J Y, Fatemi V, Fang S, Sanchez-Yamagishi J D, Watanabe K, Taniguchi T, Kaxiras E and Jarillo-Herrero P 2016 Phys. Rev. Lett. 117 116804 doi: 10.1103/PhysRevLett.117.116804 CrossRef Google Scholar
[14]	Kim K, DaSilvab A, Huangc S, Fallahazada B, Larentisa S, Taniguchid T, Watanabe K, LeRoyc B J, MacDonald A H and Tutuc E 2017 Proc. Natl. Acad. Sci. USA 114 3364 doi: 10.1073/pnas.1620140114 CrossRef Google Scholar
[15]	Polshyn H, Zhu J, Kumar M A, Zhang Y, Yang F, Tschirhart C L, Serlin M, Watanabe K, Taniguchi T, MacDonald A H and Young A F 2020 arXiv:2004.11353v1 Google Scholar
[16]	Chen S, He M, Zhang Y H, Hsieh V, Fei Z, Watanabe K, Taniguchi T, Cobden D H, Xu X, Dean C R and Yankowitz M 2020 arXiv:2004.11340v1 Google Scholar
[17]	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 doi: 10.1038/s41586-020-2049-7 CrossRef Google Scholar
[18]	Wu S, Zhang Z, Watanabe K, Taniguchi T and Andrei E Y 2020 arXiv:2007.03735 Google Scholar
[19]	Nuckolls K P, Oh M, Wong D, Lian B, Watanabe K, Taniguchi T, Bernevig B A and Yazdani A 2020 arXiv:2007.03810 Google Scholar
[20]	Saito Y, Ge J, Rademaker L, Watanabe K, Taniguchi T, Abanin D A and Young A F 2020 arXiv:2007.06115 Google Scholar
[21]	Das I, Lu X, Herzog-Arbeitman J, Song Z D, Watanabe K, Taniguchi T, Bernevig B A and Efetov D K 2020 arXiv:2007.13390 Google Scholar
[22]	Liu J, Ma Z, Gao J and Dai X 2019 Phys. Rev. X 9 031021 doi: 10.1103/PhysRevX.9.031021 CrossRef Google Scholar
[23]	Bistritzer R and MacDonald A H 2011 Phys. Rev. B 84 035440 doi: 10.1103/PhysRevB.84.035440 CrossRef Google Scholar
[24]	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 doi: 10.1038/nature12186 CrossRef Google Scholar
[25]	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 doi: 10.1038/nature12187 CrossRef Google Scholar
[26]	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 doi: 10.1126/science.1237240 CrossRef Google Scholar
[27]	Yu G L, Gorbachev R V, Tu J S, Kretinin A V, Cao Y, Jalil R, Withers F, Ponomarenko L A, Piot B A, Potemski M, Elias D C, Chen X, Watanabe K, Taniguchi T, Grigorieva I V, Novoselov K S, Fal'ko V I, Geim A K and Mishchenko A 2014 Nat. Phys. 10 525 doi: 10.1038/nphys2979 CrossRef Google Scholar
[28]	Yang W, Lu X, Chen G, Wu S, Xie G, Cheng M, Wang D, Yang R, Shi D, Watanabe K, Taniguchi T, Voisin C, Plaçais B, Zhang Y and Zhang G 2016 Nano Lett. 16 2387 doi: 10.1021/acs.nanolett.5b05161 CrossRef Google Scholar
[29]	Choi Y, Kim H, Peng Y, Thomson A, Lewandowski C, Polski R, Zhang Y, Arora H S, Watanabe K, Taniguchi T, Alicea J and Nadj-Perge S 2020 arXiv:2008.11746 Google Scholar
[30]	Park J M, Cao Y, Watanabe K, Taniguchi T and Jarillo-Herrero P 2020 arXiv:2008.12296 Google Scholar
[31]	Liu J, Liu J and Dai X 2019 Phys. Rev. B 99 155415 doi: 10.1103/PhysRevB.99.155415 CrossRef Google Scholar
[32]	Nomura K and MacDonald A H 2006 Phys. Rev. Lett. 96 256602 doi: 10.1103/PhysRevLett.96.256602 CrossRef Google Scholar
[33]	Young A F, Dean C R, Wang L, Ren H, Cadden-Zimansky P, Watanabe K, Taniguchi T, Hone J, Shepard K L and Kim P 2012 Nat. Phys. 8 550 doi: 10.1038/nphys2307 CrossRef Google Scholar
[34]	Lucignano P, Cataudella D A V, Ninno D and Cantele G 2019 Phys. Rev. B 99 195419 doi: 10.1103/PhysRevB.99.195419 CrossRef Google Scholar
[35]	Angeli M, Tosatti E and Fabrizio M 2019 Phys. Rev. X 9 041010 doi: 10.1103/PhysRevX.9.041010 CrossRef Google Scholar
[36]	Kumar R K, Chen X, Auton G H, Mishchenko A, Bandurin D A, Morozov S V, Cao Y, Khestanova E, Shalom M B, Kretinin A V, Novoselov K S, Eaves L, Grigorieva I V, Ponomarenko L A, Fal'ko V I and Geim A K 2017 Science 357 181 doi: 10.1126/science.aal3357 CrossRef Google Scholar
[37]	Lee J Y, Khalaf E, Liu S, Liu X, Hao Z, Kim P and Vishwanath A 2019 Nat. Commun. 10 5333 doi: 10.1038/s41467-019-12981-1 CrossRef Google Scholar
[38]	Song Z D, Sun S, Xu Y F, Nie S M, Weng H M, Fang Z and Dai X 2015 arXiv:1512.05084 Google Scholar
[39]	Koshino M 2011 Phys. Rev. B 84 125427 doi: 10.1103/PhysRevB.84.125427 CrossRef Google Scholar

[1]	Jiawei Hu, Shiyu Zhu, Qianying Hu, Yunhao Wang, Chengmin Shen, Haitao Yang, Xiaoshan Zhu, Qing Huan, Yang Xu, Hong-Jun Gao. Visualizing the Local Twist Angle Variation within and between Domains of Twisted Bilayer Graphene [J]. Chin. Phys. Lett., 2024, 41(3): 037401. doi: 10.1088/0256-307X/41/3/037401
[2]	Jia-Jun Ma, Zhen-Yu Wang, Shui-Gang Xu, Yu-Xiang Gao, Yu-Yang Zhang, Qing Dai, Xiao Lin, Shi-Xuan Du, Jindong Ren, Hong-Jun Gao. Local Density of States Modulated by Strain in Marginally Twisted Bilayer Graphene [J]. Chin. Phys. Lett., 2022, 39(4): 047403. doi: 10.1088/0256-307X/39/4/047403
[3]	Xiao-Feng Li, Ruo-Xuan Sun, Su-Yun Wang, Xiao Li, Zhi-Bo Liu, Jian-Guo Tian. Recent Advances in Moiré Superlattice Structures of Twisted Bilayer and Multilayer Graphene [J]. Chin. Phys. Lett., 2022, 39(3): 037301. doi: 10.1088/0256-307X/39/3/037301
[4]	Xu Zhang, Gaopei Pan, Yi Zhang, Jian Kang, Zi Yang Meng. Momentum Space Quantum Monte Carlo on Twisted Bilayer Graphene [J]. Chin. Phys. Lett., 2021, 38(7): 077305. doi: 10.1088/0256-307X/38/7/077305
[5]	WANG Tao, GUO Qing, AO Zhi-Min, LIU Yan, WANG Wen-Bo, SHENG Kuang, YU Bin. The Tunable Bandgap of AB-Stacked Bilayer Graphene on SiO₂ with H₂O Molecule Adsorption [J]. Chin. Phys. Lett., 2011, 28(11): 117302. doi: 10.1088/0256-307X/28/11/117302
[6]	LIU Yan, AO Zhi-Min, WANG Tao, WANG Wen-Bo, SHENG Kuang, YU Bin. Transformation from AA to AB-Stacked Bilayer Graphene on α−SiO₂ under an Electric Field [J]. Chin. Phys. Lett., 2011, 28(8): 087303. doi: 10.1088/0256-307X/28/8/087303
[7]	WANG Lin-Jun, CAO Gang, TU Tao, LI Hai-Ou, ZHOU Cheng, HAO Xiao-Jie, GUO Guang-Can, GUO Guo-Ping. Ground States and Excited States in a Tunable Graphene Quantum Dot [J]. Chin. Phys. Lett., 2011, 28(6): 067301. doi: 10.1088/0256-307X/28/6/067301
[8]	LI Xiao-Wei. Heat Transport in Graphene Ferromagnet-Insulator-Superconductor Junctions [J]. Chin. Phys. Lett., 2011, 28(4): 047401. doi: 10.1088/0256-307X/28/4/047401
[9]	OUYANG Fang-Ping, CHEN Li-Jian, XIAO Jin, ZHANG Hua. Electronic Properties of Bilayer Zigzag Graphene Nanoribbons: First Principles Study [J]. Chin. Phys. Lett., 2011, 28(4): 047304. doi: 10.1088/0256-307X/28/4/047304
[10]	SHEN Yi-min, KAJI Hironori, HORII Fumitaka. An Analytical Expression of Magic Angle Spinning Nuclear Magnetic Resonance Free Induction Decay in Two-Site Exchange Problem [J]. Chin. Phys. Lett., 1998, 15(6): 453-454.

Supplements (1)

Supplements
Other Related Supplements
- Cover image
  71KB

Cited By

Cited by

Periodical cited type(24)

1.	Tian, Z.-Y., Li, S.-Y., Zhou, H.-T. et al. Moiré physics in two-dimensional materials: Novel quantum phases and electronic properties. Chinese Physics B, 2025, 34(2): 027301. DOI:10.1088/1674-1056/ad9e96
2.	Yang, S., Chen, J., Liu, C.-F. et al. Evolution of flat bands in MoSe2/WSe2 moiré lattices: A study combining machine learning and band unfolding methods. Physical Review B, 2024, 110(23): 235410. DOI:10.1103/PhysRevB.110.235410
3.	Xue, Y., Wang, Y., Jiang, Y. Novel States Induced by Superlattice Structures in Twisted Two-Dimensional Heterostructures \| [超晶格结构在二维转角异质结中产生的新奇物态]. Zhenkong Kexue yu Jishu Xuebao/Journal of Vacuum Science and Technology, 2024, 44(4): 279-305. DOI:10.13922/j.cnki.cjvst.202310015
4.	Wang, R., Song, Z. Flat Band and η-Pairing States in a One-Dimensional Moiré Hubbard Model. Chinese Physics Letters, 2024, 41(4): 047101. DOI:10.1088/0256-307X/41/4/047101
5.	Lu, X., Xie, B., Yang, Y. et al. Magic Momenta and Three-Dimensional Landau Levels from a Three-Dimensional Graphite Moiré Superlattice. Physical Review Letters, 2024, 132(5): 056601. DOI:10.1103/PhysRevLett.132.056601
6.	de Vries, F.K., Slizovskiy, S., Tomić, P. et al. Kagome Quantum Oscillations in Graphene Superlattices. Nano Letters, 2024, 24(2): 601-606. DOI:10.1021/acs.nanolett.3c03524
7.	Yang, W., Zhang, G. Hofstadter butterfly in graphene. Encyclopedia of Condensed Matter Physics, 2024. DOI:10.1016/B978-0-323-90800-9.00054-8
8.	Huang, Y.. Topological Floquet flat bands in irradiated alternating twist multilayer graphene. Physical Review B, 2023, 108(16): 165139. DOI:10.1103/PhysRevB.108.165139
9.	Xie, B., Liu, J. Lattice distortions, moire phonons, and relaxed electronic band structures in magic-angle twisted bilayer graphene. Physical Review B, 2023, 108(9): 094115. DOI:10.1103/PhysRevB.108.094115
10.	Herzog-Arbeitman, J., Song, Z.-D., Elcoro, L. et al. Hofstadter Topology with Real Space Invariants and Reentrant Projective Symmetries. Physical Review Letters, 2023, 130(23): 236601. DOI:10.1103/PhysRevLett.130.236601
11.	Wang, M., Shan, W., Wang, H. Unique Electronic Properties of the Twisted Bilayer Graphene. Physica Status Solidi (B) Basic Research, 2023, 260(5): 2200344. DOI:10.1002/pssb.202200344
12.	Zhang, S., Xie, B., Wu, Q. et al. Chiral Decomposition of Twisted Graphene Multilayers with Arbitrary Stacking. Nano Letters, 2023, 23(7): 2921-2926. DOI:10.1021/acs.nanolett.3c00275
13.	Zhang, S.-H., Xie, B., Peng, R. et al. Novel electrical properties of moiré graphene systems \| [莫尔石墨烯体系的新奇电学性质]. Wuli Xuebao/Acta Physica Sinica, 2023, 72(6): 067302. DOI:10.7498/aps.72.20230120
14.	Wu, F., Li, L., Xu, Q. et al. Coupled Ferroelectricity and Correlated States in a Twisted Quadrilayer MoS2 Moiré Superlattice. Chinese Physics Letters, 2023, 40(4): 047303. DOI:10.1088/0256-307X/40/4/047303
15.	Liu, L., Zhang, S., Chu, Y. et al. Isospin competitions and valley polarized correlated insulators in twisted double bilayer graphene. Nature Communications, 2022, 13(1): 3292. DOI:10.1038/s41467-022-30998-x
16.	Liu, X., Peng, R., Sun, Z. et al. Moiré Phonons in Magic-Angle Twisted Bilayer Graphene. Nano Letters, 2022, 22(19): 7791-7797. DOI:10.1021/acs.nanolett.2c02010
17.	Zhan, Z., Zhang, Y.-L., Yuan, S.-J. Lattice relaxation and substrate effects of graphene moiré superlattice \| [石墨烯莫尔超晶格的晶格弛豫与衬底效应]. Wuli Xuebao/Acta Physica Sinica, 2022, 71(18): 187302. DOI:10.7498/aps.71.20220872
18.	Chu, Y., Liu, L., Ji, Y. et al. Observation of quadratic magnetoresistance in twisted double bilayer graphene. Chinese Physics B, 2022, 31(10): 107201. DOI:10.1088/1674-1056/ac6866
19.	Chen, R., Wang, Y.-F., Wang, Y.-X. et al. First-principles study of transition metal atoms X (X = Mn, Tc, Re) doped two-dimensional WS2 materials \| [过渡金属原子 X (X = Mn, Tc, Re) 掺杂二维 WS2 第一性原理研究]. Wuli Xuebao/Acta Physica Sinica, 2022, 71(12): 127301. DOI:10.7498/aps.71.20212439
20.	Liu, C., Wang, J. Spectroscopic Evidence for Electron Correlations in Epitaxial Bilayer Graphene with Interface-Reconstructed Superlattice Potentials. Chinese Physics Letters, 2022, 39(7): 077301. DOI:10.1088/0256-307X/39/7/077301
21.	Ma, J.-J., Wang, Z.-Y., Xu, S.-G. et al. Local Density of States Modulated by Strain in Marginally Twisted Bilayer Graphene. Chinese Physics Letters, 2022, 39(4): 047403. DOI:10.1088/0256-307X/39/4/047403
22.	Li, X.-F., Sun, R.-X., Wang, S.-Y. et al. Recent Advances in Moiré Superlattice Structures of Twisted Bilayer and Multilayer Graphene. Chinese Physics Letters, 2022, 39(3): 037301. DOI:10.1088/0256-307X/39/3/037301
23.	Zhang, X., Pan, G., Zhang, Y. et al. Momentum Space Quantum Monte Carlo on Twisted Bilayer Graphene. Chinese Physics Letters, 2021, 38(7): 077305. DOI:10.1088/0256-307X/38/7/077305
24.	Ji, Y.-R., Chu, Y.-B., Xian, L.-D. et al. From magic angle twisted bilayer graphene to moiré superlattice quantum simulator \| [从"魔角"石墨烯到摩尔超晶格量子模拟器]. Wuli Xuebao/Acta Physica Sinica, 2021, 70(11): 118101. DOI:10.7498/aps.70.20210476

Other cited types(0)

Article views (1345) PDF downloads (1332) Cited by(24)

Turn off MathJax

Article Contents

Abstract

Article Text

References

Emergence of Chern Insulating States in Non-Magic Angle Twisted Bilayer Graphene

Abstract

Article Text

References

Related Articles

Supplements

Other Related Supplements

Cover image

Cited by

Periodical cited type(24)

Other cited types(0)

About This Article

Cite this article:

Catalog

Emergence of Chern Insulating States in Non-Magic Angle Twisted Bilayer Graphene

Abstract

Article Text

References

Related Articles

Supplements

Other Related Supplements

Cover image

Cited by

Periodical cited type(24)

Other cited types(0)

About This Article

Cite this article:

Catalog

Export File

Citation

Format

Content