Correlation, superconductivity and topology in graphene moiré superlattice
Lingxiao Li, Min Wu, Xiaobo Lu
Correlation, superconductivity and topology in graphene moiré superlattice
Moiré superlattices created by stacking different pieces of two-dimensional layered materials with a slight lattice mismatch have recently emerged as an exceptional platform for exploring emergent quantum phenomena. In stark contrast to the “parent” materials, the electronic band structures are significantly modified from moiré engineering due to the large-scale periodic moiré potential and interlayer hybridization. In this paper, we mainly focus on the recent progresses achieved in graphene-based moiré systems which have been a condensed-matter playground showing unprecedented abundance of quantum states such as strongly correlated states, superconductivity and novel band topologies.
twisted graphene / moiré superlattices / correlation / superconductivity / topology
[1] |
R. Bistritzer , A. H. MacDonald . Moiré bands in twisted double-layer graphene. Proc. Natl. Acad. Sci. USA, 2011, 108(30): 12233
CrossRef
ADS
Google scholar
|
[2] |
L. Balents , C. R. Dean , D. K. Efetov , A. F. Young . Superconductivity and strong correlations in moiré flat bands. Nat. Phys., 2020, 16(7): 725
CrossRef
ADS
Google scholar
|
[3] |
S. Lisi , X. B. Lu , T. Benschop , T. A. de Jong , P. Stepanov , J. R. Duran , F. Margot , I. Cucchi , E. Cappelli , A. Hunter , A. Tamai , V. Kandyba , A. Giampietri , A. Barinov , J. Jobst , V. Stalman , M. Leeuwenhoek , K. Watanabe , T. Taniguchi , L. Rademaker , S. J. van der Molen , M. P. Allan , D. K. Efetov , F. Baumberger . Observation of flat bands in twisted bilayer graphene. Nat. Phys., 2021, 17(2): 189
CrossRef
ADS
Google scholar
|
[4] |
M. I. B. Utama , R. J. Koch , K. Lee , N. Leconte , H. Y. Li , S. H. Zhao , L. L. Jiang , J. Y. Zhu , K. Watanabe , T. Taniguchi , P. D. Ashby , A. Weber-Bargioni , A. Zettl , C. Jozwiak , J. Jung , E. Rotenberg , A. Bostwick , F. Wang . Visualization of the flat electronic band in twisted bilayer graphene near the magic angle twist. Nat. Phys., 2021, 17(2): 184
CrossRef
ADS
Google scholar
|
[5] |
Y. Cao , V. Fatemi , A. Demir , S. Fang , S. L. Tomarken , J. Y. Luo , J. D. Sanchez-Yamagishi , K. Watanabe , T. Taniguchi , E. Kaxiras , R. C. Ashoori , P. Jarillo-Herrero . Correlated insulator behaviour at half-filling in magic-angle graphene superlattices. Nature, 2018, 556(7699): 80
CrossRef
ADS
Google scholar
|
[6] |
Y. H. Jiang , X. Y. Lai , K. Watanabe , T. Taniguchi , K. Haule , J. H. Mao , E. Y. Andrei . Charge order and broken rotational symmetry in magic-angle twisted bilayer graphene. Nature, 2019, 573(7772): 91
CrossRef
ADS
Google scholar
|
[7] |
A. Kerelsky , L. J. McGilly , D. M. Kennes , L. D. Xian , M. Yankowitz , S. W. Chen , K. Watanabe , T. Taniguchi , J. Hone , C. Dean , A. Rubio , A. N. Pasupathy . Maximized electron interactions at the magic angle in twisted bilayer graphene. Nature, 2019, 572(7767): 95
CrossRef
ADS
Google scholar
|
[8] |
Y. L. Xie , B. Lian , B. Jack , X. M. Liu , C. L. Chiu , K. Watanabe , T. Taniguchi , B. A. Bernevig , A. Yazdani . Spectroscopic signatures of many-body correlations in magic-angle twisted bilayer graphene. Nature, 2019, 572(7767): 101
CrossRef
ADS
Google scholar
|
[9] |
Y. Choi , J. Kemmer , Y. Peng , A. Thomson , H. Arora , R. Polski , Y. R. Zhang , H. C. Ren , J. Alicea , G. Refael , F. von Oppen , K. Watanabe , T. Taniguchi , S. Nadj-Perge . Electronic correlations in twisted bilayer graphene near the magic angle. Nat. Phys., 2019, 15(11): 1174
CrossRef
ADS
Google scholar
|
[10] |
X. B. Lu , P. Stepanov , W. Yang , M. Xie , M. A. Aamir , I. Das , C. Urgell , K. Watanabe , T. Taniguchi , G. Y. Zhang , A. Bachtold , A. H. MacDonald , D. K. Efetov . Superconductors, orbital magnets and correlated states in magic-angle bilayer graphene. Nature, 2019, 574(7780): 653
CrossRef
ADS
Google scholar
|
[11] |
U. Zondiner , A. Rozen , D. Rodan-Legrain , Y. Cao , R. Queiroz , T. Taniguchi , K. Watanabe , Y. Oreg , F. von Oppen , A. Stern , E. Berg , P. Jarillo-Herrero , S. Ilani . Cascade of phase transitions and Dirac revivals in magic-angle graphene. Nature, 2020, 582(7811): 203
CrossRef
ADS
Google scholar
|
[12] |
M. Yankowitz , S. W. Chen , H. Polshyn , Y. X. Zhang , K. Watanabe , T. Taniguchi , D. Graf , A. F. Young , C. R. Dean . Tuning superconductivity in twisted bilayer graphene. Science, 2019, 363(6431): 1059
CrossRef
ADS
Google scholar
|
[13] |
L. Zhang , Y. Wang , R. D. Hu , P. H. Wan , O. Zheliuk , M. P. Liang , X. L. Peng , Y. J. Zeng , J. T. Ye . Correlated states in strained twisted bilayer graphenes away from the magic angle. Nano Lett., 2022, 22(8): 3204
CrossRef
ADS
Google scholar
|
[14] |
G. R. Chen , A. L. Sharpe , E. J. Fox , Y. H. Zhang , S. X. Wang , L. L. Jiang , B. Lyu , H. Y. Li , K. J. Watanabe , T. Taniguchi , Z. W. Shi , T. Senthil , D. Goldhaber-Gordon , Y. B. Zhang , F. Wang . Tunable correlated Chern insulator and ferromagnetism in a moiré superlattice. Nature, 2020, 579(7797): 56
CrossRef
ADS
Google scholar
|
[15] |
C. Shen , Y. B. Chu , Q. S. Wu , N. Li , S. P. Wang , Y. C. Zhao , J. Tang , J. Y. Liu , J. P. Tian , K. Watanabe , T. Taniguchi , R. Yang , Z. Y. Meng , D. X. Shi , O. V. Yazyev , G. Y. Zhang . Correlated states in twisted double bilayer graphene. Nat. Phys., 2020, 16(5): 520
CrossRef
ADS
Google scholar
|
[16] |
S. W. Chen , M. H. He , Y. H. Zhang , V. Hsieh , Z. Y. Fei , K. Watanabe , T. Taniguchi , D. H. Cobden , X. D. Xu , C. R. Dean , M. Yankowitz . Electrically tunable correlated and topological states in twisted monolayer-bilayer graphene. Nat. Phys., 2021, 17(3): 374
CrossRef
ADS
Google scholar
|
[17] |
G. R. Chen , L. L. Jiang , S. Wu , B. Lyu , H. Y. Li , B. L. Chittari , K. Watanabe , T. Taniguchi , Z. W. Shi , J. Jung , Y. B. Zhang , F. Wang . Evidence of a gate-tunable Mott insulator in a trilayer graphene moiré superlattice. Nat. Phys., 2019, 15(3): 237
CrossRef
ADS
Google scholar
|
[18] |
G. W. Burg , J. H. Zhu , T. Taniguchi , K. Watanabe , A. H. MacDonald , E. Tutuc . Correlated insulating states in twisted double bilayer graphene. Phys. Rev. Lett., 2019, 123(19): 197702
CrossRef
ADS
Google scholar
|
[19] |
Y. Cao , D. Rodan-Legrain , O. Rubies-Bigorda , J. M. Park , K. Watanabe , T. Taniguchi , P. Jarillo-Herrero . Tunable correlated states and spin-polarized phases in twisted bilayer−bilayer graphene. Nature, 2020, 583(7815): 215
CrossRef
ADS
Google scholar
|
[20] |
L. Liu , S. H. Zhang , Y. B. Chu , C. Shen , Y. Huang , Y. L. Yuan , J. P. Tian , J. Tang , Y. R. Ji , R. Yang , K. Watanabe , T. Taniguchi , D. X. Shi , J. P. Liu , W. Yang , G. Y. Zhang . Isospin competitions and valley polarized correlated insulators in twisted double bilayer graphene. Nat. Commun., 2022, 13(1): 3292
CrossRef
ADS
Google scholar
|
[21] |
X. M. Liu , Z. Y. Hao , E. Khalaf , J. Y. Lee , Y. Ronen , H. Yoo , D. H. Najafabadi , K. Watanabe , T. Taniguchi , A. Vishwanath , P. Kim . Tunable spin-polarized correlated states in twisted double bilayer graphene. Nature, 2020, 583(7815): 221
CrossRef
ADS
Google scholar
|
[22] |
Y. M. Wang , J. Herzog-Arbeitman , G. W. Burg , J. H. Zhu , K. Watanabe , T. Taniguchi , A. H. MacDonald , B. A. Bernevig , E. Tutuc . Bulk and edge properties of twisted double bilayer graphene. Nat. Phys., 2022, 18(1): 48
CrossRef
ADS
Google scholar
|
[23] |
H. Polshyn , J. Zhu , M. A. Kumar , Y. Zhang , F. Yang , C. L. Tschirhart , M. Serlin , K. Watanabe , T. Taniguchi , A. H. MacDonald , A. F. Young . Electrical switching of magnetic order in an orbital Chern insulator. Nature, 2020, 588(7836): 66
CrossRef
ADS
Google scholar
|
[24] |
G. W. Burg , E. Khalaf , Y. M. Wang , K. Watanabe , T. Taniguchi , E. Tutuc . Emergence of correlations in alternating twist quadrilayer graphene. Nat. Mater., 2022, 21(8): 884
CrossRef
ADS
Google scholar
|
[25] |
M. Christos , S. Sachdev , M. S. Scheurer . Correlated insulators, semimetals, and superconductivity in twisted trilayer graphene. Phys. Rev. X, 2022, 12(2): 021018
CrossRef
ADS
Google scholar
|
[26] |
M. Liang , M. M. Xiao , Z. Ma , J. H. Gao . Moiré band structures of the double twisted few-layer graphene. Phys. Rev. B, 2022, 105(19): 195422
CrossRef
ADS
Google scholar
|
[27] |
Y. R. Zhang , R. Polski , C. Lewandowski , A. Thomson , Y. Peng , Y. Choi , H. Kim , K. Watanabe , T. Taniguchi , J. Alicea , F. von Oppen , G. Refael , S. Nadj-Perge . Promotion of superconductivity in magic-angle graphene multilayers. Science, 2022, 377(6614): 1538
CrossRef
ADS
Google scholar
|
[28] |
Y. Cao , V. Fatemi , S. Fang , K. Watanabe , T. Taniguchi , E. Kaxiras , P. Jarillo-Herrero . Unconventional superconductivity in magic-angle graphene superlattices. Nature, 2018, 556(7699): 43
CrossRef
ADS
Google scholar
|
[29] |
H. S. Arora , R. Polski , Y. R. Zhang , A. Thomson , Y. Choi , H. Kim , Z. Lin , I. Z. Wilson , X. D. Xu , J. H. Chu , K. Watanabe , T. Taniguchi , J. Alicea , S. Nadj-Perge . Superconductivity in metallic twisted bilayer graphene stabilized by WSe2. Nature, 2020, 583(7816): 379
CrossRef
ADS
Google scholar
|
[30] |
X. X. Liu , Z. Wang , K. Watanabe , T. Taniguchi , O. K. R. Vafek , A. Li . Tuning electron correlation in magic-angle twisted bilayer graphene using Coulomb screening. Science, 2021, 371(6535): 1261
CrossRef
ADS
Google scholar
|
[31] |
P. Stepanov , I. Das , X. B. Lu , A. Fahimniya , K. Watanabe , T. Taniguchi , F. H. L. Koppens , J. Lischner , L. Levitov , D. K. Efetov . Untying the insulating and superconducting orders in magic-angle graphene. Nature, 2020, 583(7816): 375
CrossRef
ADS
Google scholar
|
[32] |
M. Oh , K. P. Nuckolls , D. Wong , R. L. Lee , X. M. Liu , K. Watanabe , T. Taniguchi , A. Yazdani . Evidence for unconventional superconductivity in twisted bilayer graphene. Nature, 2021, 600(7888): 240
CrossRef
ADS
Google scholar
|
[33] |
Z. Y. Hao , A. M. Zimmerman , P. Ledwith , E. Khalaf , D. H. Najafabadi , K. Watanabe , T. Taniguchi , A. Vishwanath , P. Kim . Electric field-tunable superconductivity in alternating-twist magic-angle trilayer graphene. Science, 2021, 371(6534): 1133
CrossRef
ADS
Google scholar
|
[34] |
E. Khalaf , A. J. Kruchkov , G. Tarnopolsky , A. Vishwanath . Magic angle hierarchy in twisted graphene multilayers. Phys. Rev. B, 2019, 100(8): 085109
CrossRef
ADS
Google scholar
|
[35] |
C. Mora , N. Regnault , B. A. Bernevig . Flatbands and perfect metal in trilayer moiré graphene. Phys. Rev. Lett., 2019, 123(2): 026402
CrossRef
ADS
Google scholar
|
[36] |
J. M. Park , Y. Cao , K. Watanabe , T. Taniguchi , P. Jarillo-Herrero . Tunable strongly coupled superconductivity in magic-angle twisted trilayer graphene. Nature, 2021, 590(7845): 249
CrossRef
ADS
Google scholar
|
[37] |
H. Kim , Y. Choi , C. Lewandowski , A. Thomson , Y. R. Zhang , R. Polski , K. Watanabe , T. Taniguchi , J. Alicea , S. Nadj-Perge . Evidence for unconventional superconductivity in twisted trilayer graphene. Nature, 2022, 606(7914): 494
CrossRef
ADS
Google scholar
|
[38] |
J. M. Park , Y. Cao , L. Q. Xia , S. W. Sun , K. Watanabe , T. Taniguchi , P. Jarillo-Herrero . Robust superconductivity in magic-angle multilayer graphene family. Nat. Mater., 2022, 21(8): 877
CrossRef
ADS
Google scholar
|
[39] |
A. L. Sharpe , E. J. Fox , A. W. Barnard , J. Finney , K. Watanabe , T. Taniguchi , M. A. Kastner , D. Goldhaber-Gordon . Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene. Science, 2019, 365(6453): 605
CrossRef
ADS
Google scholar
|
[40] |
P. Stepanov , M. Xie , T. Taniguchi , K. Watanabe , X. B. Lu , A. H. MacDonald , B. A. Bernevig , D. K. Efetov . Competing zero-field Chern insulators in superconducting twisted bilayer graphene. Phys. Rev. Lett., 2021, 127(19): 197701
CrossRef
ADS
Google scholar
|
[41] |
M. Serlin , C. L. Tschirhart , H. Polshyn , Y. Zhang , J. Zhu , K. Watanabe , T. Taniguchi , L. Balents , A. F. Young . Intrinsic quantized anomalous Hall effect in a moiré heterostructure. Science, 2020, 367(6480): 900
CrossRef
ADS
Google scholar
|
[42] |
N. Bultinck , S. Chatterjee , M. P. Zaletel . Mechanism for anomalous Hall ferromagnetism in twisted bilayer graphene. Phys. Rev. Lett., 2020, 124(16): 166601
CrossRef
ADS
Google scholar
|
[43] |
J. P. Liu , X. Dai . Theories for the correlated insulating states and quantum anomalous Hall effect phenomena in twisted bilayer graphene. Phys. Rev. B, 2021, 103(3): 035427
CrossRef
ADS
Google scholar
|
[44] |
Y. H. Zhang , D. Mao , T. Senthil . Twisted bilayer graphene aligned with hexagonal boron nitride: Anomalous Hall effect and a lattice model. Phys. Rev. Res., 2019, 1(3): 033126
CrossRef
ADS
Google scholar
|
[45] |
W. Y. He , D. Goldhaber-Gordon , K. T. Law . Giant orbital magnetoelectric effect and current-induced magnetization switching in twisted bilayer graphene. Nat. Commun., 2020, 11(1): 1650
CrossRef
ADS
Google scholar
|
[46] |
Y. Choi , H. Kim , Y. Peng , A. Thomson , C. Lewandowski , R. Polski , Y. R. Zhang , H. S. Arora , K. Watanabe , T. Taniguchi , J. Alicea , S. Nadj-Perge . Correlation-driven topological phases in magic-angle twisted bilayer graphene. Nature, 2021, 589(7843): 536
CrossRef
ADS
Google scholar
|
[47] |
K. P. Nuckolls , M. Oh , D. Wong , B. Lian , K. Watanabe , T. Taniguchi , B. A. Bernevig , A. Yazdani . Strongly correlated Chern insulators in magic-angle twisted bilayer graphene. Nature, 2020, 588(7839): 610
CrossRef
ADS
Google scholar
|
[48] |
I. Das , X. B. Lu , J. Herzog-Arbeitman , Z. D. Song , K. Watanabe , T. Taniguchi , B. A. Bernevig , D. K. Efetov . Symmetry-broken Chern insulators and Rashba-like Landau-level crossings in magic-angle bilayer graphene. Nat. Phys., 2021, 17(6): 710
CrossRef
ADS
Google scholar
|
[49] |
S. Wu , Z. Y. Zhang , K. Watanabe , T. Taniguchi , E. Y. Andrei . Chern insulators, van Hove singularities and topological flat bands in magic-angle twisted bilayer graphene. Nat. Mater., 2021, 20(4): 488
CrossRef
ADS
Google scholar
|
[50] |
J. P. Liu , J. W. Liu , X. Dai . Pseudo Landau level representation of twisted bilayer graphene: Band topology and implications on the correlated insulating phase. Phys. Rev. B, 2019, 99(15): 155415
CrossRef
ADS
Google scholar
|
[51] |
Y. L. Xie , A. T. Pierce , J. M. Park , D. E. Parker , E. Khalaf , P. Ledwith , Y. Cao , S. H. Lee , S. W. Chen , P. R. Forrester , K. Watanabe , T. Taniguchi , A. Vishwanath , P. Jarillo-Herrero , A. Yacoby . Fractional Chern insulators in magic-angle twisted bilayer graphene. Nature, 2021, 600(7889): 439
CrossRef
ADS
Google scholar
|
[52] |
E. M. Spanton , A. A. Zibrov , H. X. Zhou , T. Taniguchi , K. Watanabe , M. P. Zaletel , A. F. Young . Observation of fractional Chern insulators in a van der Waals heterostructure. Science, 2018, 360(6384): 62
CrossRef
ADS
Google scholar
|
[53] |
J. X. Z. Lin , P. Siriviboon , H. D. Scammell , S. Liu , D. Rhodes , K. Watanabe , T. Taniguchi , J. Hone , M. S. Scheurer , J. I. A. Li . Zero-field superconducting diode effect in small-twist-angle trilayer graphene. Nat. Phys., 2022, 18(10): 1221
CrossRef
ADS
Google scholar
|
[54] |
C. Liu , Z. Li , R. Qiao , Q. Wang , Z. Zhang , F. Liu , Z. Zhou , N. Shang , H. Fang , M. Wang , Z. Liu , Z. Feng , Y. Cheng , H. Wu , D. Gong , S. Liu , Z. Zhang , D. Zou , Y. Fu , J. He , H. Hong , M. Wu , P. Gao , P. Tan , X. Wang , D. Yu , E. Wang , Z. Wang , K. Liu . Designed growth of large bilayer graphene with arbitrary twist angles. Nat. Mater., 2022, 21(11): 1263
CrossRef
ADS
Google scholar
|
[55] |
Y. Saito , J. Ge , K. Watanabe , T. Taniguchi , A. F. Young . Independent superconductors and correlated insulators in twisted bilayer graphene. Nat. Phys., 2020, 16(9): 926
CrossRef
ADS
Google scholar
|
[56] |
J. X. Z. Lin , P. Siriviboon , H. D. Scammell , S. Liu , D. Rhodes , K. Watanabe , T. Taniguchi , J. Hone , M. S. Scheurer , J. I. A. Li . Zero-field superconducting diode effect in small-twist-angle trilayer graphene. Nat. Phys., 2022, 18(10): 1221
CrossRef
ADS
Google scholar
|
[57] |
A.D. C. J. Diez-MeridaS.Y. YangY.M. XieX.J. GaoK.WatanabeT.TaniguchiX.LuK.T. LawK.D. Efetov, Magnetic Josephson junctions and superconducting diodes in magic angle twisted bilayer graphene, arXiv: 2110.01067 (2021)
|
[58] |
C. Rubio-Verdú , S. Turkel , Y. Song , L. Klebl , R. Samajdar , M. S. Scheurer , J. W. F. Venderbos , K. Watanabe , T. Taniguchi , H. Ochoa , L. D. Xian , D. M. Kennes , R. M. Fernandes , A. Rubio , A. N. Pasupathy . Moiré nematic phase in twisted double bilayer graphene. Nat. Phys., 2022, 18(2): 196
CrossRef
ADS
Google scholar
|
[59] |
D. R. Klein , L. Q. Xia , D. MacNeill , K. Watanabe , T. Taniguchi , P. Jarillo-Herrero . Electrical switching of a bistable moiré superconductor. Nat. Nanotechnol., 2023, 18(4): 331
CrossRef
ADS
Google scholar
|
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