超晶格结构在二维转角异质结中产生的新奇物态

薛禹承; 王英博; 姜宇航

doi:10.13922/j.cnki.cjvst.202310015

[1]

Novoselov K S, Geim A K, Morozov S V, et al. Electric field effect in atomically thin carbon films[J]. Science,2004,306(5696):666−669 doi: 10.1126/science.1102896

[2]

Cao Y, Fatemi V, Demir A, et al. Correlated insulator behaviour at half-filling in magic-angle graphene superlattices[J]. Nature,2018,556(7699):80−84 doi: 10.1038/nature26154

[3]

Cao Y, Fatemi V, Fang S, et al. Unconventional superconductivity in magic-angle graphene superlattices[J]. Nature,2018,556(7699):43−50 doi: 10.1038/nature26160

[4]

Yao W, Wang E, Bao C H, et al. Quasicrystalline 30° twisted bilayer graphene as an incommensurate superlattice with strong interlayer coupling[J]. Proceedings of the National Academy of Sciences of the United States of America,2018,115(27):6928−6933

[5]

Koren E, Duerig U. Superlubricity in quasicrystalline twisted bilayer graphene[J]. Physical Review B,2016,93(20):201404 doi: 10.1103/PhysRevB.93.201404

[6]

Woods C R, Britnell L, Eckmann A, et al. Commensurate–incommensurate transition in graphene on hexagonal boron nitride[J]. Nature Physics,2014,10(6):451−456 doi: 10.1038/nphys2954

[7]

dos Santos J M B L, Peres N M R, Castro Neto A H. Graphene bilayer with a twist: electronic structure[J]. Physical Review Letters,2007,99(25):256802 doi: 10.1103/PhysRevLett.99.256802

[8]

Yankowitz M, Xue J M, Cormode D, et al. Emergence of superlattice Dirac points in graphene on hexagonal boron nitride[J]. Nature Physics,2012,8(5):382−386 doi: 10.1038/nphys2272

[9]

Yang W, Chen G R, Shi Z W, et al. Epitaxial growth of single-domain graphene on hexagonal boron nitride[J]. Nature Materials,2013,12(9):792−797 doi: 10.1038/nmat3695

[10]

Rosenberger M R, Chuang H J, Phillips M, et al. Twist angle-dependent atomic reconstruction and Moiré patterns in transition metal dichalcogenide heterostructures[J]. ACS Nano,2020,14(4):4550−4558 doi: 10.1021/acsnano.0c00088

[11]

Woods C R, Withers F, Zhu M J, et al. Macroscopic self-reorientation of interacting two-dimensional crystals[J]. Nature Communications,2016,7(1):10800 doi: 10.1038/ncomms10800

[12]

Alden J S, Tsen A W, Huang P Y, et al. Strain solitons and topological defects in bilayer graphene[J]. Proceedings of the National Academy of Sciences of the United States of America,2013,110(28):11256−11260

[13]

Yoo H, Engelke R, Carr S, et al. Atomic and electronic reconstruction at the van der Waals interface in twisted bilayer graphene[J]. Nature Materials,2019,18(5):448−453 doi: 10.1038/s41563-019-0346-z

[14]

Lin J H, Fang W J, Zhou W, et al. AC/AB stacking boundaries in bilayer graphene[J]. Nano Letters,2013,13(7):3262−3268 doi: 10.1021/nl4013979

[15]

Butz B, Dolle C, Niekiel F, et al. Dislocations in bilayer graphene[J]. Nature,2014,505(7484):533−537 doi: 10.1038/nature12780

[16]

Park C H, Yang L, Son Y W, et al. New generation of massless Dirac fermions in graphene under external periodic potentials[J]. Physical Review Letters,2008,101(12):126804 doi: 10.1103/PhysRevLett.101.126804

[17]

Park C H, Yang L, Son Y W, et al. Anisotropic behaviours of massless Dirac fermions in graphene under periodic potentials[J]. Nature Physics,2008,4(3):213−217 doi: 10.1038/nphys890

[18]

Wolf T M R, Zilberberg O, Levkivskyi I, et al. Substrate-induced topological minibands in graphene[J]. Physical Review B,2018,98(12):125408 doi: 10.1103/PhysRevB.98.125408

[19]

Ortix C, Yang L P, van den Brink J. Graphene on incommensurate substrates: trigonal warping and emerging Dirac cone replicas with halved group velocity[J]. Physical Review B,2012,86(8):081405 doi: 10.1103/PhysRevB.86.081405

[20]

Wallbank J R, Mucha-Kruczyński M, Chen X, et al. Moiré superlattice effects in graphene/boron-nitride van der Waals heterostructures[J]. Annalen der Physik,2015,527(5−6):359−376 doi: 10.1002/andp.201400204

[21]

Wallbank J R, Patel A A, Mucha-Kruczyński M, et al. Generic miniband structure of graphene on a hexagonal substrate[J]. Physical Review B,2013,87(24):245408 doi: 10.1103/PhysRevB.87.245408

[22]

Yan H, Chu Z D, Yan W, et al. Superlattice Dirac points and space-dependent Fermi velocity in a corrugated graphene monolayer[J]. Physical Review B,2013,87(7):075405 doi: 10.1103/PhysRevB.87.075405

[23]

Ponomarenko L A, Gorbachev R V, Yu G L, et al. Cloning of Dirac fermions in graphene superlattices[J]. Nature,2013,497(7451):594−597 doi: 10.1038/nature12187

[24]

Hunt B, Sanchez-Yamagishi J D, Young A F, et al. Massive Dirac fermions and Hofstadter butterfly in a van der Waals heterostructure[J]. Science,2013,340(6139):1427−1430 doi: 10.1126/science.1237240

[25]

Chen G R, Sui M Q, Wang D M, et al. Emergence of tertiary Dirac points in graphene Moiré superlattices[J]. Nano Letters,2017,17(6):3576−3581 doi: 10.1021/acs.nanolett.7b00735

[26]

Finney N R, Yankowitz M, Muraleetharan L, et al. Tunable crystal symmetry in graphene-boron nitride heterostructures with coexisting Moiré superlattices[J]. Nature Nanotechnology,2019,14(11):1029−1034 doi: 10.1038/s41565-019-0547-2

[27]

Wang E Y, Lu X B, Ding S J, et al. Gaps induced by inversion symmetry breaking and second-generation Dirac cones in graphene/hexagonal boron nitride[J]. Nature Physics,2016,12(12):1111−1115 doi: 10.1038/nphys3856

[28]

Moon P, Koshino M. Electronic properties of graphene/hexagonal-boron-nitride Moiré superlattice[J]. Physical Review B,2014,90(15):155406 doi: 10.1103/PhysRevB.90.155406

[29]

Jung J, DaSilva A M, MacDonald A H, et al. Origin of band gaps in graphene on hexagonal boron nitride[J]. Nature Communications,2015,6(1):6308 doi: 10.1038/ncomms7308

[30]

Van Hove L. The occurrence of singularities in the elastic frequency distribution of a crystal[J]. Physical Review,1953,89(6):1189−1193 doi: 10.1103/PhysRev.89.1189

[31]

He W Y, Su Y, Yang M D, et al. Creating in-plane pseudomagnetic fields in excess of 1000 T by misoriented stacking in a graphene bilayer[J]. Physical Review B,2014,89(12):125418 doi: 10.1103/PhysRevB.89.125418

[32]

He W Y, Chu Z D, He L. Chiral tunneling in a twisted graphene bilayer[J]. Physical Review Letters,2013,111(6):066803 doi: 10.1103/PhysRevLett.111.066803

[33]

Yin L J, Qiao J B, Wang W X, et al. Landau quantization and Fermi velocity renormalization in twisted graphene bilayers[J]. Physical Review B,2015,92(20):201408 doi: 10.1103/PhysRevB.92.201408

[34]

Li G H, Luican A, dos Santos J M B L, et al. Observation of Van Hove singularities in twisted graphene layers[J]. Nature Physics,2010,6(2):109−113 doi: 10.1038/nphys1463

[35]

Cherkez V, de Laissardière G T, Mallet P, et al. Van Hove singularities in doped twisted graphene bilayers studied by scanning tunneling spectroscopy[J]. Physical Review B,2015,91(15):155428 doi: 10.1103/PhysRevB.91.155428

[36]

Brihuega I, Mallet P, González-Herrero H, et al. Unraveling the intrinsic and robust nature of van Hove singularities in twisted bilayer graphene by scanning tunneling microscopy and theoretical analysis[J]. Physical Review Letters,2012,109(19):196802 doi: 10.1103/PhysRevLett.109.196802

[37]

Luican A, Li G H, Reina A, et al. Single-layer behavior and its breakdown in twisted graphene layers[J]. Physical Review Letters,2011,106(12):126802 doi: 10.1103/PhysRevLett.106.126802

[38]

Miller D L, Kubista K D, Rutter G M, et al. Observing the quantization of zero mass carriers in graphene[J]. Science,2009,324(5929):924−927 doi: 10.1126/science.1171810

[39]

Wong D, Wang Y, Jung J, et al. Local spectroscopy of Moiré-induced electronic structure in gate-tunable twisted bilayer graphene[J]. Physical Review B,2015,92(15):155409 doi: 10.1103/PhysRevB.92.155409

[40]

Yan W, Meng L, Liu M X, et al. Angle-dependent van Hove singularities and their breakdown in twisted graphene bilayers[J]. Physical Review B,2014,90(11):115402 doi: 10.1103/PhysRevB.90.115402

[41]

de Laissardière G T, Mayou D, Magaud L. Localization of dirac electrons in rotated graphene bilayers[J]. Nano Letters,2010,10(3):804−808 doi: 10.1021/nl902948m

[42]

Yan W, Liu M X, Dou R F, et al. Angle-dependent van Hove singularities in a slightly twisted graphene bilayer[J]. Physical Review Letters,2012,109(12):126801 doi: 10.1103/PhysRevLett.109.126801

[43]

Nandkishore R, Levitov L S, Chubukov A V. Chiral superconductivity from repulsive interactions in doped graphene[J]. Nature Physics,2012,8(2):158−163 doi: 10.1038/nphys2208

[44]

Kim K, Coh S, Tan L Z, et al. Raman spectroscopy study of rotated double-layer graphene: misorientation-angle dependence of electronic structure[J]. Physical Review Letters,2012,108(24):246103 doi: 10.1103/PhysRevLett.108.246103

[45]

Yuan N F Q, Isobe H, Fu L. Magic of high-order van Hove singularity[J]. Nature Communications,2019,10(1):5769 doi: 10.1038/s41467-019-13670-9

[46]

Hofstadter D R. Energy levels and wave functions of Bloch electrons in rational and irrational magnetic fields[J]. Physical Review B,1976,14(6):2239−2249 doi: 10.1103/PhysRevB.14.2239

[47]

Albrecht C, Smet J H, Weiss D, et al. Fermiology of two-dimensional lateral superlattices[J]. Physical Review Letters,1999,83(11):2234−2237 doi: 10.1103/PhysRevLett.83.2234

[48]

Dean C R, Wang L, Maher P, et al. Hofstadter's butterfly and the fractal quantum Hall effect in Moiré superlattices[J]. Nature,2013,497(7451):598−602 doi: 10.1038/nature12186

[49]

Spanton E M, Zibrov A A, Zhou H X, et al. Observation of fractional Chern insulators in a van der Waals heterostructure[J]. Science,2018,360(6384):62−66 doi: 10.1126/science.aan8458

[50]

Yang W, Lu X B, Chen G R, et al. Hofstadter butterfly and many-body effects in epitaxial graphene superlattice[J]. Nano Letters,2016,16(4):2387−2392 doi: 10.1021/acs.nanolett.5b05161

[51]

Wang L, Gao Y D, Wen B, et al. Evidence for a fractional fractal quantum Hall effect in graphene superlattices[J]. Science,2015,350(6265):1231−1234 doi: 10.1126/science.aad2102

[52]

Cheng B, Pan C, Che S, et al. Fractional and symmetry-broken Chern insulators in tunable Moiré superlattices[J]. Nano Letters,2019,19(7):4321−4326 doi: 10.1021/acs.nanolett.9b00811

[53]

Saito Y, Ge J Y, Rademaker L, et al. Hofstadter subband ferromagnetism and symmetry-broken Chern insulators in twisted bilayer graphene[J]. Nature Physics,2021,17(4):478−481 doi: 10.1038/s41567-020-01129-4

[54]

Das I, Lu X B, Herzog-Arbeitman J, et al. Symmetry-broken Chern insulators and Rashba-like Landau-level crossings in magic-angle bilayer graphene[J]. Nature Physics,2021,17(6):710−714 doi: 10.1038/s41567-021-01186-3

[55]

Ye Z L, Waldecker L, Ma E Y, et al. Efficient generation of neutral and charged biexcitons in encapsulated WSe₂ monolayers[J]. Nature Communications,2018,9(1):3718 doi: 10.1038/s41467-018-05917-8

[56]

Zhang N, Surrente A, Baranowski M, et al. Moiré intralayer excitons in a MoSe₂/MoS₂ heterostructure[J]. Nano Letters,2018,18(12):7651−7657 doi: 10.1021/acs.nanolett.8b03266

[57]

Huang D, Choi J, Shih C K, et al. Excitons in semiconductor Moiré superlattices[J]. Nature Nanotechnology,2022,17(3):227−238 doi: 10.1038/s41565-021-01068-y

[58]

Liu Y P, Zeng C, Yu J, et al. Moire superlattices and related Moiré excitons in twisted van der Waals heterostructures[J]. Chemical Society Reviews,2021,50(11):6401−6422 doi: 10.1039/D0CS01002B

[59]

Tran K, Moody G, Wu F C, et al. Evidence for Moiré excitons in van der Waals heterostructures[J]. Nature,2019,567(7746):71−75 doi: 10.1038/s41586-019-0975-z

[60]

Seyler K L, Rivera P, Yu H Y, et al. Signatures of Moiré-trapped valley excitons in MoSe₂/WSe₂ heterobilayers[J]. Nature,2019,567(7746):66−70 doi: 10.1038/s41586-019-0957-1

[61]

Scuri G, Andersen T I, Zhou Y, et al. Electrically tunable valley dynamics in twisted WSe₂/WSe₂ bilayers[J]. Physical Review Letters,2020,124(21):217403 doi: 10.1103/PhysRevLett.124.217403

[62]

Andersen T I, Scuri G, Sushko A, et al. Excitons in a reconstructed Moiré potential in twisted WSe₂/WSe₂ homobilayers[J]. Nature Materials,2021,20(4):480−487 doi: 10.1038/s41563-020-00873-5

[63]

Sung J, Zhou Y, Scuri G, et al. Broken mirror symmetry in excitonic response of reconstructed domains in twisted MoSe₂/MoSe₂ bilayers[J]. Nature Nanotechnology,2020,15(9):750−754 doi: 10.1038/s41565-020-0728-z

[64]

Alexeev E M, Ruiz-Tijerina D A, Danovich M, et al. Resonantly hybridized excitons in Moiré superlattices in van der Waals heterostructures[J]. Nature,2019,567(7746):81−86 doi: 10.1038/s41586-019-0986-9

[65]

Jin C H, Regan E C, Yan A M, et al. Observation of Moiré excitons in WSe₂/WS₂ heterostructure superlattices[J]. Nature,2019,567(7746):76−80 doi: 10.1038/s41586-019-0976-y

[66]

Jin C H, Regan E C, Wang D Q, et al. Identification of spin, valley and Moiré quasi-angular momentum of interlayer excitons[J]. Nature Physics,2019,15(11):1140−1144 doi: 10.1038/s41567-019-0631-4

[67]

Hsu W T, Lin B H, Lu L S, et al. Tailoring excitonic states of van der Waals bilayers through stacking configuration, band alignment, and valley spin[J]. Science Advances,2019,5(12):eaax7407 doi: 10.1126/sciadv.aax7407

[68]

Suárez Morell E, Correa J D, Vargas P, et al. Flat bands in slightly twisted bilayer graphene: tight-binding calculations[J]. Physical Review B,2010,82(12):121407 doi: 10.1103/PhysRevB.82.121407

[69]

Bistritzer R, MacDonald A H. Moiré bands in twisted double-layer graphene[J]. Proceedings of the National Academy of Sciences of the United States of America,2011,108(30):12233−12237

[70]

Choi Y, Kemmer J, Peng Y, et al. Electronic correlations in twisted bilayer graphene near the magic angle[J]. Nature Physics,2019,15(11):1174−1180 doi: 10.1038/s41567-019-0606-5

[71]

Jiang Y H, Lai X Y, Watanabe K, et al. Charge order and broken rotational symmetry in magic-angle twisted bilayer graphene[J]. Nature,2019,573(7772):91−95 doi: 10.1038/s41586-019-1460-4

[72]

Kerelsky A, McGilly L J, Kennes D M, et al. Maximized electron interactions at the magic angle in twisted bilayer graphene[J]. Nature,2019,572(7767):95−100 doi: 10.1038/s41586-019-1431-9

[73]

Xie Y L, Lian B, Jäck B, et al. Spectroscopic signatures of many-body correlations in magic-angle twisted bilayer graphene[J]. Nature,2019,572(7767):101−105 doi: 10.1038/s41586-019-1422-x

[74]

Kim K, DaSilva A, Huang S Q, et al. Tunable Moiré bands and strong correlations in small-twist-angle bilayer graphene[J]. Proceedings of the National Academy of Sciences of the United States of America,2017,114(13):3364−3369

[75]

Mott N. On metal-insulator transitions[J]. Journal of Solid State Chemistry,1990,88(1):5−7 doi: 10.1016/0022-4596(90)90201-8

[76]

Lu X B, Stepanov P, Yang W, et al. Superconductors, orbital magnets and correlated states in magic-angle bilayer graphene[J]. Nature,2019,574(7780):653−657 doi: 10.1038/s41586-019-1695-0

[77]

Arora H S, Polski R, Zhang Y R, et al. Superconductivity in metallic twisted bilayer graphene stabilized by WSe₂[J]. Nature,2020,583(7816):379−384 doi: 10.1038/s41586-020-2473-8

[78]

Nuckolls K P, Oh M, Wong D, et al. Strongly correlated Chern insulators in magic-angle twisted bilayer graphene[J]. Nature,2020,588(7839):610−615 doi: 10.1038/s41586-020-3028-8

[79]

Saito Y, Ge J Y, Watanabe K, et al. Independent superconductors and correlated insulators in twisted bilayer graphene[J]. Nature Physics,2020,16(9):926−930 doi: 10.1038/s41567-020-0928-3

[80]

Stepanov P, Das I, Lu X B, et al. Untying the insulating and superconducting orders in magic-angle graphene[J]. Nature,2020,583(7816):375−378 doi: 10.1038/s41586-020-2459-6

[81]

Cao Y, Rodan-Legrain D, Park J M, et al. Nematicity and competing orders in superconducting magic-angle graphene[J]. Science,2021,372(6539):264−271 doi: 10.1126/science.abc2836

[82]

Xie M, MacDonald A H. Nature of the correlated insulator states in twisted bilayer graphene[J]. Physical Review Letters,2020,124(9):097601 doi: 10.1103/PhysRevLett.124.097601

[83]

Shen C, Ying J H, Liu L, et al. Emergence of Chern insulating states in non-magic angle twisted bilayer graphene[J]. Chinese Physics Letters,2021,38(4):047301 doi: 10.1088/0256-307X/38/4/047301

[84]

Adak P C, Sinha S, Ghorai U, et al. Tunable bandwidths and gaps in twisted double bilayer graphene on the verge of correlations[J]. Physical Review B,2020,101(12):125428 doi: 10.1103/PhysRevB.101.125428

[85]

Cao Y, Rodan-Legrain D, Rubies-Bigorda O, et al. Tunable correlated states and spin-polarized phases in twisted bilayer-bilayer graphene[J]. Nature,2020,583(7815):215−220 doi: 10.1038/s41586-020-2260-6

[86]

Cao Y, Park J M, Watanabe K, et al. Pauli-limit violation and re-entrant superconductivity in Moiré graphene[J]. Nature,2021,595(7868):526−531 doi: 10.1038/s41586-021-03685-y

[87]

Chen S W, He M H, Zhang Y H, et al. Electrically tunable correlated and topological states in twisted monolayer–bilayer graphene[J]. Nature Physics,2021,17(3):374−380 doi: 10.1038/s41567-020-01062-6

[88]

Xu Y, Liu S, Rhodes D A, et al. Correlated insulating states at fractional fillings of Moiré superlattices[J]. Nature,2020,587(7833):214−218 doi: 10.1038/s41586-020-2868-6

[89]

Yankowitz M, Chen S W, Polshyn H, et al. Tuning superconductivity in twisted bilayer graphene[J]. Science,2019,363(6431):1059−1064 doi: 10.1126/science.aav1910

[90]

Lee P A, Nagaosa N, Wen X G. Doping a Mott insulator: physics of high-temperature superconductivity[J]. Reviews of Modern Physics,2006,78(1):17−85 doi: 10.1103/RevModPhys.78.17

[91]

Keimer B, Kivelson S A, Norman M R, et al. From quantum matter to high-temperature superconductivity in copper oxides[J]. Nature,2015,518(7538):179−186 doi: 10.1038/nature14165

[92]

Codecido E, Wang Q Y, Koester R, et al. Correlated insulating and superconducting states in twisted bilayer graphene below the magic angle[J]. Science Advances,2019,5(9):eaaw9770 doi: 10.1126/sciadv.aaw9770

[93]

Polshyn H, Yankowitz M, Chen S W, et al. Large linear-in-temperature resistivity in twisted bilayer graphene[J]. Nature Physics,2019,15(10):1011−1016 doi: 10.1038/s41567-019-0596-3

[94]

Bruin J A N, Sakai H, Perry R S, et al. Similarity of scattering rates in metals showing T-linear resistivity[J]. Science,2013,339(6121):804−807 doi: 10.1126/science.1227612

[95]

Comin R, Sutarto R, He F, et al. Symmetry of charge order in cuprates[J]. Nature Materials,2015,14(8):796−800 doi: 10.1038/nmat4295

[96]

Mukhopadhyay S, Sharma R, Kim C K, et al. Evidence for a vestigial nematic state in the cuprate pseudogap phase[J]. Proceedings of the National Academy of Sciences of the United States of America,2019,116(27):13249−13254

[97]

Wu F C, Hwang E, Das Sarma S. Phonon-induced giant linear-in-T resistivity in magic angle twisted bilayer graphene: ordinary strangeness and exotic superconductivity[J]. Physical Review B,2019,99(16):165112 doi: 10.1103/PhysRevB.99.165112

[98]

Sharma G, Yudhistira I, Chakraborty N, et al. Carrier transport theory for twisted bilayer graphene in the metallic regime[J]. Nature Communications,2021,12(1):5737 doi: 10.1038/s41467-021-25864-1

[99]

Burg G W, Zhu J H, Taniguchi T, et al. Correlated insulating states in twisted double bilayer graphene[J]. Physical Review Letters,2019,123(19):197702 doi: 10.1103/PhysRevLett.123.197702

[100]

He M H, Li Y H, Cai J Q, et al. Symmetry breaking in twisted double bilayer graphene[J]. Nature Physics,2021,17(1):26−30 doi: 10.1038/s41567-020-1030-6

[101]

Liu X M, Hao Z Y, Khalaf E, et al. Tunable spin-polarized correlated states in twisted double bilayer graphene[J]. Nature,2020,583(7815):221−225 doi: 10.1038/s41586-020-2458-7

[102]

Shen C, Chu Y B, Wu Q S, et al. Correlated states in twisted double bilayer graphene[J]. Nature Physics,2020,16(5):520−525 doi: 10.1038/s41567-020-0825-9

[103]

Zhang C X, Zhu T C, Kahn S, et al. Visualizing delocalized correlated electronic states in twisted double bilayer graphene[J]. Nature Communications,2021,12(1):2516 doi: 10.1038/s41467-021-22711-1

[104]

Hao Z Y, Zimmerman A M, Ledwith P, et al. Electric field-tunable superconductivity in alternating-twist magic-angle trilayer graphene[J]. Science,2021,371(6534):1133−1138 doi: 10.1126/science.abg0399

[105]

Park J M, Cao Y, Watanabe K, et al. Tunable strongly coupled superconductivity in magic-angle twisted trilayer graphene[J]. Nature,2021,590(7845):249−255 doi: 10.1038/s41586-021-03192-0

[106]

Liu X X, Zhang N J, Watanabe K, et al. Isospin order in superconducting magic-angle twisted trilayer graphene[J]. Nature Physics,2022,18(5):522−527 doi: 10.1038/s41567-022-01515-0

[107]

Khalaf E, Chatterjee S, Bultinck N, et al. Charged skyrmions and topological origin of superconductivity in magic-angle graphene[J]. Science Advances,2021,7(19):eabf5299 doi: 10.1126/sciadv.abf5299

[108]

Fischer A, Goodwin Z A H, Mostofi A A, et al. Unconventional superconductivity in magic-angle twisted trilayer graphene[J]. npj Quantum Materials,2022,7(1):5 doi: 10.1038/s41535-021-00410-w

[109]

Polshyn H, Zhu J, Kumar M A, et al. Electrical switching of magnetic order in an orbital Chern insulator[J]. Nature,2020,588(7836):66−70 doi: 10.1038/s41586-020-2963-8

[110]

Xu S G, Al Ezzi M M, Balakrishnan N, et al. Tunable van Hove singularities and correlated states in twisted monolayer–bilayer graphene[J]. Nature Physics,2021,17(5):619−626 doi: 10.1038/s41567-021-01172-9

[111]

Polshyn H, Zhang Y, Kumar M A, et al. Topological charge density waves at half-integer filling of a Moiré superlattice[J]. Nature Physics,2022,18(1):42−47 doi: 10.1038/s41567-021-01418-6

[112]

He M H, Zhang Y H, Li Y H, et al. Competing correlated states and abundant orbital magnetism in twisted monolayer-bilayer graphene[J]. Nature Communications,2021,12(1):4727 doi: 10.1038/s41467-021-25044-1

[113]

Tong L H, Tong Q J, Yang L Z, et al. Spectroscopic visualization of flat bands in magic-angle twisted monolayer-bilayer graphene: coexistence of localization and delocalization[J]. Physical Review Letters,2022,128(12):126401 doi: 10.1103/PhysRevLett.128.126401

[114]

Li S Y, Wang Z W, Xue Y C, et al. Imaging topological and correlated insulating states in twisted monolayer-bilayer graphene[J]. Nature Communications,2022,13(1):4225 doi: 10.1038/s41467-022-31851-x

[115]

Wang L, Shih E M, Ghiotto A, et al. Correlated electronic phases in twisted bilayer transition metal dichalcogenides[J]. Nature Materials,2020,19(8):861−866 doi: 10.1038/s41563-020-0708-6

[116]

Wang G, Chernikov A, Glazov M M, et al. Colloquium: excitons in atomically thin transition metal dichalcogenides[J]. Reviews of Modern Physics,2018,90(2):021001 doi: 10.1103/RevModPhys.90.021001

[117]

Raja A, Chaves A, Yu J, et al. Coulomb engineering of the bandgap and excitons in two-dimensional materials[J]. Nature Communications,2017,8(1):15251 doi: 10.1038/ncomms15251

[118]

Huang X, Wang T M, Miao S N, et al. Correlated insulating states at fractional fillings of the WS₂/WSe₂ Moiré lattice[J]. Nature Physics,2021,17(6):715−719 doi: 10.1038/s41567-021-01171-w

[119]

Wigner E. On the interaction of electrons in metals[J]. Physical Review,1934,46(11):1002−1011 doi: 10.1103/PhysRev.46.1002

[120]

Grimes C C, Adams G. Crystallization of electrons on the surface of liquid helium[J]. Surface Science,1980,98(1−3):1−7 doi: 10.1016/0039-6028(80)90465-3

[121]

Chaplik A V. Possible crystallization of charge carriers in low-density inversion layers[J]. Soviet Journal of Experimental and Theoretical Physics,1972,35:395−398

[122]

Andrei E Y, Deville G, Glattli D C, et al. Observation of a magnetically induced Wigner solid[J]. Physical Review Letters,1988,60(26):2765−2768 doi: 10.1103/PhysRevLett.60.2765

[123]

Regan E C, Wang D Q, Jin C H, et al. Mott and generalized Wigner crystal states in WSe₂/WS₂ Moiré superlattices[J]. Nature,2020,579(7799):359−363 doi: 10.1038/s41586-020-2092-4

[124]

Mott N F. The basis of the electron theory of metals, with special reference to the transition metals[J]. Proceedings of the Physical Society. Section A,1949,62(7):416−422 doi: 10.1088/0370-1298/62/7/303

[125]

Padhi B, Phillips P W. Pressure-induced metal-insulator transition in twisted bilayer graphene[J]. Physical Review B,2019,99(20):205141 doi: 10.1103/PhysRevB.99.205141

[126]

Wu C J, Bergman D, Balents L, et al. Flat bands and Wigner crystallization in the honeycomb optical lattice[J]. Physical Review Letters,2007,99(7):070401 doi: 10.1103/PhysRevLett.99.070401

[127]

Padhi B, Setty C, Phillips P W. Doped twisted bilayer graphene near magic angles: proximity to Wigner crystallization, not Mott insulation[J]. Nano Letters,2018,18(10):6175−6180 doi: 10.1021/acs.nanolett.8b02033

[128]

Hubbard J. Generalized Wigner lattices in one dimension and some applications to tetracyanoquinodimethane (TCNQ) salts[J]. Physical Review B,1978,17(2):494−505 doi: 10.1103/PhysRevB.17.494

[129]

Zhang Y, Yuan N F Q, Fu L. Moiré quantum chemistry: charge transfer in transition metal dichalcogenide superlattices[J]. Physical Review B,2020,102(20):201115 doi: 10.1103/PhysRevB.102.201115

[130]

Xiao D, Liu G B, Feng W X, et al. Coupled spin and valley physics in monolayers of MoS₂ and other group-VI dichalcogenides[J]. Physical Review Letters,2012,108(19):196802 doi: 10.1103/PhysRevLett.108.196802

[131]

Chen G R, Jiang L L, Wu S, et al. Evidence of a gate-tunable Mott insulator in a trilayer graphene Moiré superlattice[J]. Nature Physics,2019,15(3):237−241 doi: 10.1038/s41567-018-0387-2

[132]

Chen G R, Sharpe A L, Gallagher P, et al. Signatures of tunable superconductivity in a trilayer graphene Moiré superlattice[J]. Nature,2019,572(7768):215−219 doi: 10.1038/s41586-019-1393-y

[133]

Li H Y, Li S W, Regan E C, et al. Imaging two-dimensional generalized Wigner crystals[J]. Nature,2021,597(7878):650−654 doi: 10.1038/s41586-021-03874-9

[134]

Jin C H, Tao Z, Li T X, et al. Stripe phases in WSe₂/WS₂ Moiré superlattices[J]. Nature Materials,2021,20(7):940−944 doi: 10.1038/s41563-021-00959-8

[135]

Smoleński T, Dolgirev P E, Kuhlenkamp C, et al. Signatures of Wigner crystal of electrons in a monolayer semiconductor[J]. Nature,2021,595(7865):53−57 doi: 10.1038/s41586-021-03590-4

[136]

Drummond N D, Needs R J. Phase diagram of the low-density two-dimensional homogeneous electron gas[J]. Physical Review Letters,2009,102(12):126402 doi: 10.1103/PhysRevLett.102.126402

[137]

Zarenia M, Neilson D, Partoens B, et al. Wigner crystallization in transition metal dichalcogenides: a new approach to correlation energy[J]. Physical Review B,2017,95(11):115438 doi: 10.1103/PhysRevB.95.115438

[138]

Shimazaki Y, Kuhlenkamp C, Schwartz I, et al. Optical signatures of periodic charge distribution in a Mott-like correlated insulator state[J]. Physical Review X,2021,11(2):021027 doi: 10.1103/PhysRevX.11.021027

[139]

Zhou Y, Sung J, Brutschea E, et al. Bilayer Wigner crystals in a transition metal dichalcogenide heterostructure[J]. Nature,2021,595(7865):48−52 doi: 10.1038/s41586-021-03560-w

[140]

Świerkowski L, Neilson D, Szymański J. Enhancement of Wigner crystallization in multiple-quantum-well structures[J]. Physical Review Letters,1991,67(2):240−243 doi: 10.1103/PhysRevLett.67.240

[141]

Li S Y, Wang Z, Xue Y, et al. Imaging topological and correlated insulating states in twisted monolayer-bilayer graphene[J]. Nat Commun, 2022, 13(1): 4225

[142]

Tong Q J, Yu H Y, Zhu Q Z, et al. Topological mosaics in Moiré superlattices of van der Waals heterobilayers[J]. Nature Physics,2016,13(4):356−362

[143]

Huang S Q, Kim K, Efimkin D K, et al. Topologically protected helical states in minimally twisted bilayer graphene[J]. Physical Review Letters,2018,121(3):037702 doi: 10.1103/PhysRevLett.121.037702

[144]

Liu J P, Liu J W, Dai X. Pseudo Landau level representation of twisted bilayer graphene: band topology and implications on the correlated insulating phase[J]. Physical Review B,2019,99(15):155415 doi: 10.1103/PhysRevB.99.155415

[145]

Po H C, Zou L J, Vishwanath A, et al. Origin of Mott insulating behavior and superconductivity in twisted bilayer graphene[J]. Physical Review X,2018,8(3):031089 doi: 10.1103/PhysRevX.8.031089

[146]

Bultinck N, Khalaf E, Liu S, et al. Ground state and hidden symmetry of magic-angle graphene at even integer filling[J]. Physical Review X,2020,10(3):031034 doi: 10.1103/PhysRevX.10.031034

[147]

Liu J P, Dai X. Orbital magnetic states in Moiré graphene systems[J]. Nature Reviews Physics,2021,3(5):367−382 doi: 10.1038/s42254-021-00297-3

[148]

Bultinck N, Chatterjee S, Zaletel M P. Mechanism for anomalous hall ferromagnetism in twisted bilayer graphene[J]. Physical Review Letters,2020,124(16):166601 doi: 10.1103/PhysRevLett.124.166601

[149]

Zhang Y H, Mao D, Senthil T. Twisted bilayer graphene aligned with hexagonal boron nitride: anomalous Hall effect and a lattice model[J]. Physical Review Research,2019,1(3):033126 doi: 10.1103/PhysRevResearch.1.033126

[150]

Chatterjee S, Bultinck N, Zaletel M P. Symmetry breaking and skyrmionic transport in twisted bilayer graphene[J]. Physical Review B,2020,101(16):165141 doi: 10.1103/PhysRevB.101.165141

[151]

Liu C X, Qi X L, Dai X, et al. Quantum anomalous hall effect in Hg_{1- y}Mn_yTe quantum wells[J]. Physical Review Letters,2008,101(14):146802 doi: 10.1103/PhysRevLett.101.146802

[152]

Xu S Y, Neupane M, Liu C, et al. Hedgehog spin texture and Berry’s phase tuning in a magnetic topological insulator[J]. Nature Physics,2012,8(8):616−622 doi: 10.1038/nphys2351

[153]

Chang C Z, Zhang J S, Feng X, et al. Experimental observation of the quantum anomalous Hall effect in a magnetic topological insulator[J]. Science,2013,340(6129):167−170 doi: 10.1126/science.1234414

[154]

Serlin M, Tschirhart C L, Polshyn H, et al. Intrinsic quantized anomalous Hall effect in a Moiré heterostructure[J]. Science,2019,367(6480):900−903

[155]

Tomarken S L, Cao Y, Demir A, et al. Electronic compressibility of magic-angle graphene superlattices[J]. Physical Review Letters,2019,123(4):046601 doi: 10.1103/PhysRevLett.123.046601

[156]

Tang Y H, Li L Z, Li T X, et al. Simulation of Hubbard model physics in WSe₂/WS₂ Moiré superlattices[J]. Nature,2020,579(7799):353−358 doi: 10.1038/s41586-020-2085-3

[157]

Merino J, Powell B J, McKenzie R H. Ferromagnetism, paramagnetism, and a Curie-Weiss metal in an electron-doped Hubbard model on a triangular lattice[J]. Physical Review B,2006,73(23):235107 doi: 10.1103/PhysRevB.73.235107

[158]

Li G, Antipov A E, Rubtsov A N, et al. Competing phases of the Hubbard model on a triangular lattice: insights from the entropy[J]. Physical Review B,2014,89(16):161118 doi: 10.1103/PhysRevB.89.161118

[159]

Rohringer G, Hafermann H, Toschi A, et al. Diagrammatic routes to nonlocal correlations beyond dynamical mean field theory[J]. Reviews of Modern Physics,2018,90(2):025003 doi: 10.1103/RevModPhys.90.025003

[160]

Zheng W H, Singh R R P, McKenzie R H, et al. Temperature dependence of the magnetic susceptibility for triangular-lattice antiferromagnets with spatially anisotropic exchange constants[J]. Physical Review B,2005,71(13):134422 doi: 10.1103/PhysRevB.71.134422

[161]

Liu J P, Ma Z, Gao J H, et al. Quantum valley hall effect, orbital magnetism, and anomalous hall effect in twisted multilayer graphene systems[J]. Physical Review X,2019,9(3):031021 doi: 10.1103/PhysRevX.9.031021

[162]

Choi Y, Kim H, Peng Y, et al. Correlation-driven topological phases in magic-angle twisted bilayer graphene[J]. Nature,2021,589(7843):536−541 doi: 10.1038/s41586-020-03159-7

[163]

Park J M, Cao Y, Watanabe K, et al. Flavour Hund's coupling, Chern gaps and charge diffusivity in Moiré graphene[J]. Nature,2021,592(7852):43−48 doi: 10.1038/s41586-021-03366-w

[164]

Wu S, Zhang Z Y, Watanabe K, et al. Chern insulators, van Hove singularities and topological flat bands in magic-angle twisted bilayer graphene[J]. Nature Materials,2021,20(4):488−494 doi: 10.1038/s41563-020-00911-2

[165]

Chen G R, Sharpe A L, Fox E J, et al. Tunable correlated Chern insulator and ferromagnetism in a Moiré superlattice[J]. Nature,2020,579(7797):56−61 doi: 10.1038/s41586-020-2049-7

[166]

Stepanov P, Xie M, Taniguchi T, et al. Competing zero-field Chern insulators in superconducting twisted bilayer graphene[J]. Physical Review Letters,2021,127(19):197701 doi: 10.1103/PhysRevLett.127.197701

[167]

Pierce A T, Xie Y L, Park J M, et al. Unconventional sequence of correlated Chern insulators in magic-angle twisted bilayer graphene[J]. Nature Physics,2021,17(11):1210−1215 doi: 10.1038/s41567-021-01347-4

[168]

Xie Y L, Pierce A T, Park J M, et al. Fractional Chern insulators in magic-angle twisted bilayer graphene[J]. Nature,2021,600(7889):439−443 doi: 10.1038/s41586-021-04002-3

[169]

Ledwith P J, Tarnopolsky G, Khalaf E, et al. Fractional Chern insulator states in twisted bilayer graphene: an analytical approach[J]. Physical Review Research,2020,2(2):023237 doi: 10.1103/PhysRevResearch.2.023237

[170]

Abouelkomsan A, Liu Z, Bergholtz E J. Particle-hole duality, emergent Fermi liquids, and fractional Chern insulators in Moiré flatbands[J]. Physical Review Letters,2020,124(10):106803 doi: 10.1103/PhysRevLett.124.106803

[171]

Bhowmik S, Ghawri B, Leconte N, et al. Broken-symmetry states at half-integer band fillings in twisted bilayer graphene[J]. Nature Physics,2022,18(6):639−643 doi: 10.1038/s41567-022-01557-4

[172]

Liao J Y, Wu J X, Dang C H, et al. Methods of transferring two-dimensional materials[J]. Acta Physica Sinica,2021,70(2):028201 doi: 10.7498/aps.70.20201425

[173]

Schneider G F, Calado V E, Zandbergen H, et al. Wedging transfer of nanostructures[J]. Nano Letters,2010,10(5):1912−1916 doi: 10.1021/nl1008037

[174]

Wang Y, Zheng Y, Xu X F, et al. Electrochemical delamination of CVD-grown graphene film: toward the recyclable use of copper catalyst[J]. ACS Nano,2011,5(12):9927−9933 doi: 10.1021/nn203700w

[175]

Dean C R, Young A F, Meric I, et al. Boron nitride substrates for high-quality graphene electronics[J]. Nature Nanotechnology,2010,5(10):722−726 doi: 10.1038/nnano.2010.172

[176]

Li H, Wu J, Huang X, et al. A universal, rapid method for Clean transfer of nanostructures onto various substrates[J]. ACS Nano,2014,8(7):6563−6570 doi: 10.1021/nn501779y

[177]

Pizzocchero F, Gammelgaard L, Jessen B S, et al. The hot pick-up technique for batch assembly of van der Waals heterostructures[J]. Nature Communications,2016,7(1):11894 doi: 10.1038/ncomms11894

[178]

Castellanos-Gomez A, Buscema M, Molenaar R, et al. Deterministic transfer of two-dimensional materials by all-dry viscoelastic stamping[J]. 2D Materials,2014,1(1):011002 doi: 10.1088/2053-1583/1/1/011002