How Magical Is Magic-Angle Graphene?

Abstract

The observation of correlated insulating states and unconventional superconductivity on magic-angle twisted bilayer graphene (MATBG) by Cao and Jarillo-Herrero in 2018 has aroused intensive scientific interest in the beautiful moiré-patterned superlattice. The magic angles are a discrete set of angles (with the largest one around 1.1°) at which the twisted bilayer graphene exhibits a unique electronic structure (a nearly flat band) with the vanishing of the Fermi velocity at the Dirac points. Based on such a special platform, strong interlayer electron couplings generate at certain filling states of the flat band and allow the observation of extraordinary physical phenomena. The earliest prediction of the magic angle can date back to 2007, but the magical properties on MATBG have been partially uncovered experimentally only in the last 2 years, including the most recent emergent ferromagnetism with anomalous Hall and quantized anomalous Hall effects. With ongoing endeavors in low-energy physics, we believe that more fascinating phenomena on MATBG and analogues will be discovered in the near future. Meanwhile, great efforts still need to be devoted to elucidating the underlying mechanisms and developing new technologies that could bring these exceptional properties into practical applications. Manipulating the behavior of electrons in a material is essential for tuning its fundamental properties. The recent exciting experimental observations of extraordinary correlated insulating phase, unconventional superconductivity, and emergent ferromagnetic states on magic-angle twisted bilayer graphene (MATBG) have opened up a new era for “twistronics” and will shed substantial light on materials science and technology. This Perspective is intended to provide a roadmap of MATBG on how it originated, what exotic phenomena have been discovered experimentally, and where the future is headed. Manipulating the behavior of electrons in a material is essential for tuning its fundamental properties. The recent exciting experimental observations of extraordinary correlated insulating phase, unconventional superconductivity, and emergent ferromagnetic states on magic-angle twisted bilayer graphene (MATBG) have opened up a new era for “twistronics” and will shed substantial light on materials science and technology. This Perspective is intended to provide a roadmap of MATBG on how it originated, what exotic phenomena have been discovered experimentally, and where the future is headed. Graphene, as an atomic-thick plane composed by honeycomb lattice of sp2 hybridized carbon atoms, has a unique electronic structure and numerous exceptional properties. It has caused a profound sensation in our scientific and technological world since its first isolation from graphite.1Novoselov K.S. Geim A.K. Morozov S.V. Jiang D. Zhang Y. Dubonos S.V. Grigorieva I.V. Firsov A.A. Electric field effect in atomically thin carbon films.Science. 2004; 306: 666-669Crossref PubMed Scopus (52201) Google Scholar,2Novoselov K.S. Fal'ko V.I. Colombo L. Gellert P.R. Schwab M.G. Kim K. A roadmap for graphene.Nature. 2012; 490: 192-200Crossref PubMed Scopus (7304) Google Scholar Apart from the considerable progress in the synthesis and applications of graphene in the past 15 years, topological superlattices consisting of two graphene layers have recently been found to be excellent platforms for obtaining attractive physical features that were not previously expected.3Song Z.D. Wang Z.J. Shi W.J. Li G. Fang C. Bernevig B.A. All magic angles in twisted bilayer graphene are topological.Phys. Rev. Lett. 2019; 123: 036401Crossref Scopus (238) Google Scholar In contrast to the linear energy dispersion at the charge neutrality point in monolayer graphene, when two layers of graphene stack together with a relative twist/rotation angle (θ), forming a moiré-patterned superlattice, a dramatic change in the low-energy band takes place (Figure 1A).4Kim K. DaSilva A. Huang S. Fallahazad B. Larentis S. Taniguchi T. Watanabe K. LeRoy B.J. MacDonald A.H. Tutuc E. Tunable moiré bands and strong correlations in small-twist-angle bilayer graphene.Proc. Nat. Acad. Sci. U S A. 2017; 114: 3364-3369Crossref Scopus (337) Google Scholar,5Bistritzer R. MacDonald A.H. Moiré bands in twisted double-layer graphene.Proc. Nat. Acad. Sci. U S A. 2011; 108: 12233-12237Crossref Scopus (1507) Google Scholar At a discrete set of critical twist angles, i.e., “magic angles,” the Fermi velocity vanishes at the Dirac points with the formation of a nearly flat band (Figure 1B). Such a dramatic electronic band change due to such a small physical tweak in the bilayer-graphene superlattice is so fascinating for low-energy physics and materials engineering that a new field called “twistronics” has been established. In the last 2 years, a series of exceptional phenomena have been discovered on magic-angle twisted bilayer graphene (MATBG), including correlated insulating states,6Cao Y. Fatemi V. Demir A. Fang S. Tomarken S.L. Luo J.Y. Sanchez-Yamagishi J.D. Watanabe K. Taniguchi T. Kaxiras E. et al.Correlated insulator behaviour at half-filling in magic-angle graphene superlattices.Nature. 2018; 556: 80-84Crossref PubMed Scopus (2291) Google Scholar,7Cao Y. Luo J.Y. Fatemi V. Fang S. Sanchez-Yamagishi J.D. Watanabe K. Taniguchi T. Kaxiras E. Jarillo-Herrero P. Superlattice-induced insulating states and valley-protected orbits in twisted bilayer graphene.Phys. Rev. Lett. 2016; 117: 116804Crossref Scopus (265) Google Scholar unconventional superconductivity,8Cao Y. Fatemi V. Fang S. Watanabe K. Taniguchi T. Kaxiras E. Jarillo-Herrero P. Unconventional superconductivity in magic-angle graphene superlattices.Nature. 2018; 556: 43-50Crossref PubMed Scopus (3833) Google Scholar and emergent ferromagnetism with anomalous Hall effect and even quantized anomalous Hall behavior.9Sharpe A.L. Fox E.J. Barnard A.W. Finney J. Watanabe K. Taniguchi T. Kastner M.A. Goldhaber-Gordon D. Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene.Science. 2019; 365: 605-608Crossref Scopus (775) Google Scholar, 10Pixley J.H. Andrei E.Y. Ferromagnetism in magic-angle graphene.Science. 2019; 365: 543Crossref Scopus (32) Google Scholar, 11Serlin M. Tschirhart C.L. Polshyn H. Zhang Y. Zhu J. Watanabe K. Taniguchi T. Balents L. Young A.F. Intrinsic quantized anomalous Hall effect in a moiré heterostructure.Science. 2020; 367: 900-903Crossref Scopus (541) Google Scholar These findings make MATBG more charming and scientifically vital. To provide a timely overview of this special area, herein we discuss the early predictions of magic angles in twisted bilayer graphene (TBG) and the successively observed exotic phenomena on MATBG. Furthermore, the current challenges and future perspectives of this emerging field/material are addressed. The first theoretical study on TBG was carried out by Castro Neto’s group early in 2007.12Lopes dos Santos J.M.B. Peres N.M.R. Castro Neto A.H. Graphene bilayer with a twist: electronic structure.Phys. Rev. Lett. 2007; 99: 256802Crossref Scopus (1054) Google Scholar They found that the low-energy properties of TBG was distinct from those of bilayer graphene with AB, or Bernal stacking, and that a pronouncedly reduced Fermi velocity would result in a very small twist angle. However, the exact value of the angle and the possible electronic properties that might be induced by the reduced velocity were not proposed. In 2010, Andrei’s group explored the moiré pattern on TBG (θ = 1.79°) fabricated by chemical vapor deposition (CVD) with scanning tunneling spectroscopy (STS), finding two prominent peaks flanking the zero point in the density of states (DOS), which suggests the generation of two low-energy Van Hove singularity (VHS; a saddle point that causes a divergence in the density of states in the electronic band structure) in the TBG system.13Li G. Luican A. Lopes dos Santos J.M.B. Castro Neto A.H. Reina A. Kong J. Andrei E.Y. Observation of Van Hove singularities in twisted graphene layers.Nat. Phys. 2010; 6: 109-113Crossref Scopus (817) Google Scholar With a smaller θ of 1.16°, the two peaks were both seated very close to the zero point (i.e., the Fermi energy) and merged almost into one with an energy difference of only ~12 meV. This would be the first experimental observation of the unique electronic state in TBG with a twist angle very close to a magic angle. Furthermore, it was emphasized by Andrei et al. that at this kind of state when the Fermi energy (EF) crosses a VHS, appealing properties such as superconductivity, magnetism, and density waves could appear, although immediate evidence for these special properties was not provided. The concept of “magic angle” was first put by Bistritzer and MacDonald in 2011, when they addressed the formation of moiré Bloch bands due to the moiré pattern periodicity in the continuum Dirac model of TBG.5Bistritzer R. MacDonald A.H. Moiré bands in twisted double-layer graphene.Proc. Nat. Acad. Sci. U S A. 2011; 108: 12233-12237Crossref Scopus (1507) Google Scholar Specifically, they predicted that the velocity at the Dirac point oscillates with the twist angle and quenches at a discrete set of magic angles (θ ≈ 1.05°, 0.5°, 0.35°, 0.24°, and 0.2°) where the lowest moiré band flattens with an intensively enhanced counterflow conductivity. Despite a wide awareness of the distinct phenomena associated with MATBG in the years after the initial predictions, little experimental progress had been made until the sensational discoveries by Cao and coworkers in 2018.6Cao Y. Fatemi V. Demir A. Fang S. Tomarken S.L. Luo J.Y. Sanchez-Yamagishi J.D. Watanabe K. Taniguchi T. Kaxiras E. et al.Correlated insulator behaviour at half-filling in magic-angle graphene superlattices.Nature. 2018; 556: 80-84Crossref PubMed Scopus (2291) Google Scholar, 7Cao Y. Luo J.Y. Fatemi V. Fang S. Sanchez-Yamagishi J.D. Watanabe K. Taniguchi T. Kaxiras E. Jarillo-Herrero P. Superlattice-induced insulating states and valley-protected orbits in twisted bilayer graphene.Phys. Rev. Lett. 2016; 117: 116804Crossref Scopus (265) Google Scholar, 8Cao Y. Fatemi V. Fang S. Watanabe K. Taniguchi T. Kaxiras E. Jarillo-Herrero P. Unconventional superconductivity in magic-angle graphene superlattices.Nature. 2018; 556: 43-50Crossref PubMed Scopus (3833) Google Scholar In their work, the twist angle of a TBG was precisely controlled with a smart “tear and stack” technique (Figure 2A) developed by Kim et al.4Kim K. DaSilva A. Huang S. Fallahazad B. Larentis S. Taniguchi T. Watanabe K. LeRoy B.J. MacDonald A.H. Tutuc E. Tunable moiré bands and strong correlations in small-twist-angle bilayer graphene.Proc. Nat. Acad. Sci. U S A. 2017; 114: 3364-3369Crossref Scopus (337) Google Scholar,14Kim K. Yankowitz M. Fallahazad B. Kang S. Movva H.C.P. Huang S. Larentis S. Corbet C.M. Taniguchi T. Watanabe K. et al.van der Waals heterostructures with high accuracy rotational alignment.Nano Lett. 2016; 16: 1989-1995Crossref Scopus (369) Google Scholar They observed experimentally that when the twist angle was close to the magic angle of ~1.1°, the electronic band structure near the Fermi energy turned flat, just as theoretically predicted. Furthermore, with half filling of the flat band (i.e., n/ns = ±1/2, where n is the carrier density and ns is the density of the superlattice with each of its bands at full-filling state), a metal-insulator transition was unexpectedly observed at a critical temperature of 4 K (Figure 2B), indicating a Mott-like insulator behavior.6Cao Y. Fatemi V. Demir A. Fang S. Tomarken S.L. Luo J.Y. Sanchez-Yamagishi J.D. Watanabe K. Taniguchi T. Kaxiras E. et al.Correlated insulator behaviour at half-filling in magic-angle graphene superlattices.Nature. 2018; 556: 80-84Crossref PubMed Scopus (2291) Google Scholar This insulating state at half filling was highly correlated with the strong interlayer electron coupling within the MATBG, without which the insulating behavior could not be observed. More profoundly, when turning the Fermi energy EF away from charge neutrality (EF = 0) to be near half filling of the lower flat band (EF < 0), superconductivity with zero resistance was stunningly detected with a four-probe device at extremely low temperatures (<2 K) (Figures 2C and 2D).8Cao Y. Fatemi V. Fang S. Watanabe K. Taniguchi T. Kaxiras E. Jarillo-Herrero P. Unconventional superconductivity in magic-angle graphene superlattices.Nature. 2018; 556: 43-50Crossref PubMed Scopus (3833) Google Scholar The superconducting states could be obtained on TBGs with both θ ≈ 1.16 and 1.05°, but the critical temperature (1.7 K) achieved by the device with θ ≈ 1.05° was much higher than that with θ ≈ 1.16° (0.5 K). The phase diagrams of the TBGs (Figures 2E and 2F), where the two superconducting domes flanked the Mott insulator states, are analogous to those of strongly interacting high-temperature superconductors. However, the pure-carbon-based superconducting behavior occurred at extremely low carrier densities (on the order of 1011 cm−2), which are orders of magnitude lower than those of typical two-dimensional superconductors. Therefore, MATBG could be an excellent platform for thorough study of strongly correlated physics.15Huang T.Y. Zhang L.F. Ma T.X. Antiferromagnetically ordered Mott insulator and d plus id superconductivity in twisted bilayer graphene: a quantum Monte Carlo study.Sci. Bull. 2019; 64: 310-314Crossref Scopus (90) Google Scholar,16Lian B. Wang Z.J. Bernevig B.A. Twisted bilayer graphene: a phonon-driven superconductor.Phys. Rev. Lett. 2019; 122: 257002Crossref Scopus (196) Google Scholar The stimulating findings by Cao et al. soon aroused an explosion of interest in revealing the extraordinary electronic behaviors,17Yoo H. Engelke R. Carr S. Fang S. Zhang K. Cazeaux P. Sung S.H. Hovden R. Tsen A.W. Taniguchi T. et al.Atomic and electronic reconstruction at the van der Waals interface in twisted bilayer graphene.Nat. Mater. 2019; 18: 448-453Crossref Scopus (322) Google Scholar, 18Tarnopolsky G. Kruchkov A.J. Vishwanath A. Origin of magic angles in twisted bilayer graphene.Phys. Rev. Lett. 2019; 122: 106405Crossref Scopus (312) Google Scholar, 19Ochi M. Koshino M. Kuroki K. Possible correlated insulating states in magic-angle twisted bilayer graphene under strongly competing interactions.Phys. Rev. B. 2018; 98: 081102Crossref Scopus (109) Google Scholar, 20Venderbos J.W. Fernandes R.M. Correlations and electronic order in a two-orbital honeycomb lattice model for twisted bilayer graphene.Phys. Rev. B. 2018; 98: 245103Crossref Scopus (105) Google Scholar, 21Zou L.J. Po H.C. Vishwanath A. Senthi T. Band structure of twisted bilayer graphene: emergent symmetries, commensurate approximants, and Wannier obstructions.Phys. Rev. B. 2018; 98: 085435Crossref Scopus (205) Google Scholar, 22Gonzalez J. Stauber T. Kohn-Luttinger superconductivity in twisted bilayer graphene.Phys. Rev. Lett. 2019; 122: 026801Crossref Scopus (168) Google Scholar predicting other possible exotic phenomena23Dodaro J.F. Kivelson S.A. Schattner Y. Sun X.-Q. Wang C. Phases of a phenomenological model of twisted bilayer graphene.Phys. Rev. B. 2018; 98: 075154Crossref Scopus (181) Google Scholar, 24Thomson A. Chatterjee S. Sachdev S. Scheurer M.S. Triangular antiferromagnetism on the honeycomb lattice of twisted bilayer graphene.Phys. Rev. B. 2018; 98: 075109Crossref Scopus (103) Google Scholar, 25Xie M. MacDonald A.H. On the nature of the correlated insulator states in twisted bilayer graphene.arXiv. 2018; (arXiv:181204213)Google Scholar, 26Kang J. Vafek O. Strong coupling phases of partially filled twisted bilayer graphene narrow bands.Phys. Rev. Lett. 2019; 122: 246401Crossref Scopus (185) Google Scholar, 27Seo K. Kotov V.N. Uchoa B. Ferromagnetic mott state in twisted graphene bilayers at the magic angle.Phys. Rev. Lett. 2019; 122: 246402Crossref Scopus (113) Google Scholar, 28Zhang Y.-H. Mao D. Cao Y. Jarillo-Herrero P. Senthil T. Nearly flat Chern bands in moiré superlattices.Phys. Rev. B. 2019; 99: 075127Crossref Scopus (225) Google Scholar, 29Liu C.C. Zhang L.D. Chen W.Q. Yang F. Chiral spin density wave and d+id superconductivity in the magic-angle-twisted bilayer graphene.Phys. Rev. Lett. 2018; 121: 217001Crossref Scopus (205) Google Scholar and exploring alternative ways to achieve anomalous properties.30Yankowitz M. Chen S. Polshyn H. Zhang Y. Watanabe K. Taniguchi T. Graf D. Young A.F. Dean C.R. Tuning superconductivity in twisted bilayer graphene.Science. 2019; 363: 1059-1064Crossref Scopus (1064) Google Scholar, 31Padhi B. Phillips P.W. Pressure-induced metal-insulator transition in twisted bilayer graphene.Phys. Rev. B. 2019; 99: 205141Crossref Scopus (29) Google Scholar, 32Padhi B. Setty C. Phillips P.W. Doped twisted bilayer graphene near magic angles: proximity to wigner crystallization, not mott insulation.Nano Lett. 2018; 18: 6175-6180Crossref Scopus (131) Google Scholar Notably, by reinvestigating the MATBG with scanning tunneling microscopy (STM) and STS, Andrei's group obtained clear visualizations of the changes in DOSs and the charge distributions when the flat band was doped with different numbers of electrons.33Jiang Y. Lai X. Watanabe K. Taniguchi T. Haule K. Mao J. Andrei E.Y. Charge order and broken rotational symmetry in magic-angle twisted bilayer graphene.Nature. 2019; 573: 91-95Crossref Scopus (366) Google Scholar Specifically, a pseudo-gap phase accompanied by a global stripe charge order that broke the rotational symmetry of the moiré superlattice was found at partial-filling states. Similar findings are associated also with high-temperature superconductors such as iron pnictides34Rosenthal E.P. Andrade E.F. Arguello C.J. Fernandes R.M. Xing L.Y. Wang X. Jin C.Q. Millis A.J. Pasupathy A.N. Visualization of electron nematicity and unidirectional antiferroic fluctuations at high temperatures in NaFeAs.Nat. Phys. 2014; 10: 225Crossref Scopus (146) Google Scholar and copper oxides,35da Silva Neto E.H. Aynajian P. Frano A. Comin R. Schierle E. Weschke E. Gyenis A. Wen J. Schneeloch J. Xu Z. et al.Ubiquitous interplay between charge ordering and high-temperature superconductivity in cuprates.Science. 2014; 343: 393-396Crossref Scopus (447) Google Scholar verifying the deep correlation between MATBG and the high-temperature superconductors. Also by virtue of STM and STS, strong many-body correlations in MATBG,36Xie Y.L. Lian B. Jack B. Liu X.M. Chiu C.L. Watanabe K. Taniguchi T. Bernevig B.A. Yazdani A. Spectroscopic signatures of many-body correlations in magic-angle twisted bilayer graphene.Nature. 2019; 572: 101-105Crossref Scopus (340) Google Scholar smaller magic angles with stronger electron correlation, and doping-related electronic behaviors37Kerelsky A. McGilly L.J. Kennes D.M. Xian L.D. Yankowitz M. Chen S.W. Watanabe K. Taniguchi T. Hone J. Dean C. et al.Maximized electron interactions at the magic angle in twisted bilayer graphene.Nature. 2019; 572: 95-100Crossref Scopus (472) Google Scholar have been evaluated, providing new understanding of the superconducting phases in MATBG. Choi et al. suggested that with small deviations (on the order of 0.1°) from the magic angle, the band structure of the flat bands would become considerably broader and comparable with the Coulomb interaction energy scale.38Choi Y. Kemmer J. Peng Y. Thomson A. Arora H. Polski R. Zhang Y. Ren H. Alicea J. Rafael G. et al.Electronic correlations in twisted bilayer graphene near the magic angle.Nat. Phys. 2019; 15: 1174-1180Crossref Scopus (334) Google Scholar For very clean samples at charge neutrality, the ground state would exhibit nematic order and break C3 symmetry via exchange interactions. Recently, in MATBG devices with highly uniform twist angles and thus a reduced twist-angle disorder, Lu and coworkers observed insulating states at all integer occupancies of the four-fold spin-valley degenerate flat conduction and valence bands, i.e., at moiré band filling factors ν = 0, ±1, ±2, ±3, corresponding to n/ns = 0, ±1/4, ±1/2, ±3/4.39Lu X. Stepanov P. Yang W. Xie M. Aamir M.A. Das I. Urgell C. Watanabe K. Taniguchi T. Zhang G. et al.Superconductors, orbital magnets and correlated states in magic-angle bilayer graphene.Nature. 2019; 574: 653-657Crossref Scopus (712) Google Scholar More notably, at temperatures below 1 K, three new superconducting domes were detected close to charge neutrality point (CNP), around ν = 0 and ν = ±1 insulating states. Their low charge density (~3 × 1011 cm−2, counting from CNP) verified that the superconducting states should stem from the broken spin-valley degeneracy of the insulating states rather than high-density states of the non-interacted bands. These new superconducting domes were also associated with adjacent correlated insulator states, suggesting an exotic pairing phenomenon. However, it is still possible that the superconductivity could arise from a conventional electron-phonon coupling mechanism as in superconducting metals. A consensus on the origin of these superconducting states has not yet been reached. In contrast to the investigations at ultra-low temperatures, Polshyn et al. studied the temperature (T)-dependent change of resistivity, ρ, in TBG, up to room temperature, to acquire some possible implications for the origin of the observed superconductivity.40Polshyn H. Yankowitz M. Chen S. Zhang Y. Watanabe K. Taniguchi T. Dean C.R. Young A.F. Large linear-in-temperature resistivity in twisted bilayer graphene.Nat. Phys. 2019; 15: 1011-1016Crossref Scopus (172) Google Scholar With varying θ between 0.75° and 2°, three different behaviors of ρ (T) at three distinct temperature regimes (not universally demarcated due to their dependence on the twist angle and carrier density) were identified. In the high-temperature regime, ρ rose sublinearly with increasing T until attaining a maximum value at a critical temperature (TH). In the intermediate-temperature regime, ρ scaled linearly with T, and the T-linear response was much larger than that observed in monolayer graphene. At the lowest temperatures, where the emergent insulating and superconducting behaviors were observed, ρ (T) diverged from T-linear dependence. Particularly, the device with θ around the magic angle exhibited the most dramatic linear increase and lowest TH for its smallest bandwidth and band gap. Additionally, Yankowitz et al. revealed that variation of the interlayer distance could shift the values of magic angles in MATBG.30Yankowitz M. Chen S. Polshyn H. Zhang Y. Watanabe K. Taniguchi T. Graf D. Young A.F. Dean C.R. Tuning superconductivity in twisted bilayer graphene.Science. 2019; 363: 1059-1064Crossref Scopus (1064) Google Scholar When the twist angle of van der Waals bilayer graphene was larger than 1.1°, correlated states and superconductivity were absent because of the reduced interlayer electron coupling. However, as the interlayer coupling was re-enhanced by reducing the interlayer spacing with hydrostatic pressure in a certain range, the superconducting states appeared again at the shifted magic angle. This was further confirmed by theoretical simulation, which indicated that the metal state in one-quarter filling could transfer to an insulating state under pressure.31Padhi B. Phillips P.W. Pressure-induced metal-insulator transition in twisted bilayer graphene.Phys. Rev. B. 2019; 99: 205141Crossref Scopus (29) Google Scholar While the puzzles associated with the magic angle in its Mott insulator phase remained elusive, Sharpe and coworkers reported the emergent superstable ferromagnetism in the magical superlattice.9Sharpe A.L. Fox E.J. Barnard A.W. Finney J. Watanabe K. Taniguchi T. Kastner M.A. Goldhaber-Gordon D. Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene.Science. 2019; 365: 605-608Crossref Scopus (775) Google Scholar,10Pixley J.H. Andrei E.Y. Ferromagnetism in magic-angle graphene.Science. 2019; 365: 543Crossref Scopus (32) Google Scholar This exotic ferromagnetism was reflected by the observation of an anomalous Hall (AH) effect with a scanning magnetic field in a TBG with θ = 1.20° ± 0.01° at three-quarters filling of the conduction band. The discovery, as a new part of the rich phase diagram of MATBG, is important, especially for TBG without any magnetism-associated transition metals or any heavy elements, impurities, or defects that could provide spin-orbit coupling.41Esquinazi P. Spemann D. Höhne R. Setzer A. Han K.-H. Butz T. Induced magnetic ordering by proton irradiation in graphite.Phys. Rev. Lett. 2003; 91: 227201Crossref PubMed Scopus (776) Google Scholar, 42Červenka J. Katsnelson M. Flipse C. Room-temperature ferromagnetism in graphite driven by two-dimensional networks of point defects.Nat. Phys. 2009; 5: 840Crossref Scopus (517) Google Scholar, 43Kopelevich Y. Pantoja J.M. da Silva R. Mrowka F. Esquinazi P. Anomalous Hall effect in graphite.Phys. Lett. A. 2006; 355: 233-236Crossref Scopus (15) Google Scholar In the work by Sharp’s group, the high-quality near-magic-angle TBG was prepared using the same “tear and stack” technique7Cao Y. Luo J.Y. Fatemi V. Fang S. Sanchez-Yamagishi J.D. Watanabe K. Taniguchi T. Kaxiras E. Jarillo-Herrero P. Superlattice-induced insulating states and valley-protected orbits in twisted bilayer graphene.Phys. Rev. Lett. 2016; 117: 116804Crossref Scopus (265) Google Scholar,14Kim K. Yankowitz M. Fallahazad B. Kang S. Movva H.C.P. Huang S. Larentis S. Corbet C.M. Taniguchi T. Watanabe K. et al.van der Waals heterostructures with high accuracy rotational alignment.Nano Lett. 2016; 16: 1989-1995Crossref Scopus (369) Google Scholar and assembled in a TBG Hall bar device (Figure 3A, inset). Two hexagonal boron nitride (hBN) layers were cladded on the two sides of the TBG to avoid disorder and function as the dielectrics for electrostatic gating. Silicon and Ti/Au were employed as the back and top gates, respectively, which allowed independent tuning of the charge density n in the TBG and the perpendicular displacement field D. The longitudinal and Hall resistances (Rxx and Ryx, respectively) in relation with the n and D at 2.1 K (Figure 3A) revealed that strong resistances (red and yellow regions) existed at the CNP (n/ns = 0) and at the full-filling state of mini-Brillouin zone (mBZ, i.e., n/ns = ±1). Additional resistance peaks also occurred at n/ns = 1/4, 1/2, and 3/4, respectively. Besides the interaction between the two graphene layers, the correlation of the top graphene layer and the hBN sheet in a lattice alignment of 0.81° ± 0.02° was also observed, according to the appearance of a resistance peak at n/ns = −1.15 and a shoulder on the peak around n/ns = 1 (Figure 3B).44Hunt B. Sanchez-Yamagishi J.D. Young A.F. Yankowitz M. LeRoy B.J. Watanabe K. Taniguchi T. Moon P. Koshino M. Jarillo-Herrero P. Ashoori R.C. Massive Dirac fermions and hofstadter butterfly in a van der Waals heterostructure.Science. 2013; 340: 1427-1430Crossref PubMed Scopus (1156) Google Scholar Among these resistant regions, the narrow range of n/ns = 3/4 was the most unique. Only at this range, the magneto transport exhibited a hysteretic behavior (i.e., an AH effect) under an applied external magnetic field B (Figures 3C and 3D). The magnetization was superstable with the residual AH resistance (RyxAH) persisting over a course of 6 h in zero field after the removal of an applied field of −500 mT. When a field that showed a direction opposite to that of the training field and an intensity beyond the coercive field (100 mT) was applied, the magnetization direction could be reversed. This AH effect could be observed over a wide range of D but with varied intensities for the different D parameters. While the AH resistance peaked at 6.6 kΩ at n/ns = 0.758 for D/ε0 ≈ −0.6 V nm−1 (Figure 3C), the peak value detected for D/ε0 ≈ −0.22 V/nm was even higher (10.4 kΩ) at n/ns = 0.774. As the temperature increased, the coercive field (half the difference between the fields where the largest jumps in Ryx occurred) decreased gradually, quenching at 3.9 K, while the magnitude of RyxAH went up smoothly until 2.8 K followed by a rapid reduction to zero at 5 K (Figures 3E and 3F). Furthermore, the ferromagnetic insulating state was extremely sensitive to the direction of the applied current. A hysteresis loop was formed between ±50 nA dc bias in plus to 5 nA ac bias (Figure 3G), implying great potential of this state of TBG for extremely low-power magnetic memory apparatuses. Meanwhile, non-local transport, which resembled that in the chiral edge modes of a ferromagnetic topological insulator (Chern insulator) with quantized AH (QAH), was observed in the magnetic state of the TBG, along with dissipative or chiral transport in the network of the domain walls. States with non-zero Chern numbers in a similar but more uniform system have been observed by Lu et al. as well at ±1/4-filling with a sharp hysteretic resistance enhancement under a perpendicular magnetic field greater than 3.6 T.39Lu X. Stepanov P. Yang W. Xie M. Aamir M.A. Das I. Urgell C. Watanabe K. Taniguchi T. Zhang G. et al.Superconductors, orbital magnets and correlated states in magic-angle bilayer graphene.Nature. 2019; 574: 653-657Crossref Scopus (712) Google Scholar However, a QAH effect showing Ryx·C = h/e2 (where C ≠ 0 is the total Chern number of the filled bands, h is Planck's constant, and e is the electron charge) was not observed in these systems. As a significant progress, very recently, Serlin et al. reported the observation of a QAH effect with C = 1 in an MATBG (θ ≈ 1.15 ± 0.01°) aligned to hBN at 1.6–4 K.11Serlin M. Tschirhart C.L. Polshyn H. Zhang Y. Zhu J. Watanabe K. Taniguchi T. Balents L. Young A.F. Intrinsic quantized anomalous Hall effect in a moiré heterostructure.Science. 2020; 367: 900-903Crossref Scopus (541) Google Scholar Similar to the observation by Sharpe et al., the anomalous phenomenon presented around three-quarters filling of the flat band. Differently, the Rxy of this TBG system showed a value close to h/e2 at electron density n = 2.37 × 1012 cm−2 (corresponding to ν = 3) at 1.6 K with B = 150 mT (Figure 4A). The magnetic field dependence of both Rxx and Rxy at ν = 3 and T = 1.6 K (Figure 4B) revealed that the Hall resistivity was hysteretic and the well-quantized Rxy = h/e2 persisted through B = 0 along with Rxx < 1 kΩ, indicating a QAH state stabilized by spontaneously broken time-reversal symmetry. The effect could be driven by the intrinsic strong interaction in the MATBG, which drove the formation of an excessive spin- and valley-polarized Chern band, spontaneously breaking time-reversal symmetry (Figure 4C). Like the other exceptional phenomena, the QAH behavior survived only at extremely low temperatures (1.6–4 K). With increasing temperature, the resistance quantization diminished and the hysteresis shrunk (Figures 4D and 4E). This discovery of the QAH effect holds topological significance and shows potential to provide more robust quantization for quantum computation, low-power consumption electronics, and metrology. However, the origin of the Chern insulating modes in these systems, which requires opening a topologically nontrivial gap, remained ambiguous. As recently pointed out by Xie and MacDonald, at the MATBG insulating states with ±1/4 and ±3/4 filling, the spin/valley flavor symmetries could break spontaneously due to an intrinsic energetic preference for equal occupations in opposite valleys and produce moiré bands with finite Chern numbers that lead to a QAH effect and non-zero orbital polarization.25Xie M. MacDonald A.H. On the nature of the correlated insulator states in twisted bilayer graphene.arXiv. 2018; (arXiv:181204213)Google Scholar However, given the high sensitivity of the TBG system to details and the observation that hBN substrates can generate energy gaps as large as 30 meV in monolayer graphene, the hBN layer, with which the TBGs were aligned, could play a role in breaking the sublattice symmetry.11Serlin M. Tschirhart C.L. Polshyn H. Zhang Y. Zhu J. Watanabe K. Taniguchi T. Balents L. Young A.F. Intrinsic quantized anomalous Hall effect in a moiré heterostructure.Science. 2020; 367: 900-903Crossref Scopus (541) Google Scholar,44Hunt B. Sanchez-Yamagishi J.D. Young A.F. Yankowitz M. LeRoy B.J. Watanabe K. Taniguchi T. Moon P. Koshino M. Jarillo-Herrero P. Ashoori R.C. Massive Dirac fermions and hofstadter butterfly in a van der Waals heterostructure.Science. 2013; 340: 1427-1430Crossref PubMed Scopus (1156) Google Scholar, 45Amet F. Williams J. Watanabe K. Taniguchi T. Goldhaber-Gordon D. Insulating behavior at the neutrality point in single-layer graphene.Phys. Rev. Lett. 2013; 110: 216601Crossref Scopus (84) Google Scholar, 46Jung J. DaSilva A.M. MacDonald A.H. Adam S. Origin of band gaps in graphene on hexagonal boron nitride.Nat. Commun. 2015; 6: 6308Crossref Scopus (211) Google Scholar, 47Zhang Y.-H. Mao D. Senthil T. Twisted bilayer graphene aligned with hexagonal boron nitride: anomalous hall effect and a lattice model.arXiv. 2019; (arXiv:190108209)Google Scholar, 48Bultinck N. Chatterjee S. Zaletel M.P. Anomalous Hall ferromagnetism in twisted bilayer graphene.arXiv. 2019; (arXiv:190108110)Google Scholar Accordingly, the hBN aligned TBGs may constitute a distinct type of TBG device.11Serlin M. Tschirhart C.L. Polshyn H. Zhang Y. Zhu J. Watanabe K. Taniguchi T. Balents L. Young A.F. Intrinsic quantized anomalous Hall effect in a moiré heterostructure.Science. 2020; 367: 900-903Crossref Scopus (541) Google Scholar Nevertheless, further experimental and theoretical endeavors are still needed to elucidate the magnetic order and the contribution of the various interactions. The exotic quantum phenomena, including correlated insulator phases, gate-tunable superconductivity, and ferromagnetic behaviors, experimentally spotted on the magic-angle or near-magic-angle TBG are particularly intriguing and profoundly meaningful for quantum physics and materials science. However, despite a flood of theoretical studies and an increasing number of experimental observations, the underlying reason for the unique properties remains elusive. Due to the complexity of the correlated systems, it is challenging, though critically important, to thoroughly explain the experimental results and predict new principles or unknown properties associated with MATBGs. While an intimate cooperation of the theoretical and experimental efforts may provide a solution, novel experimental designs are encouraged to address the issue.