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Programmable Quantum Anomalous Hall Insulator in Twisted Crystalline Flatbands
Phys. Rev. X 16, 011015 – Published 26 January, 2026Erratum Phys. Rev. X 16, 039901 (2026)
DOI: https://doi.org/10.1103/7m1b-hxy8
Abstract
The isospin flavors in condensed matters can be continuously broken, forming various symmetry-broken quantum states. In moiré crystals, the competition between different isospin configurations can be effectively tuned by the twist angles and stacking orders. Here we report twisted double rhombohedral-trilayer-graphene as a new twisted crystalline flatband system showing rich moiré dependent topological phenomena. In devices with small twist angles, programmable Chern insulators with Chern number at integer moiré filling have been observed. We have further revealed an exotic hidden order which can quench the Chern insulator as well as multiple first-order transitions between different symmetry-broken phases. Interestly, in the device with a slightly larger twist angle, multiple Chern insulators with at fractional moiré fillings including , , and have been observed, whereas the Chern insulator at is absent. Our study demonstrated the twisted flatbands form rhombohedral-multilayer-graphene as a new platform to study tunable high Chern insulators as well as new devices for quantum storage and computation.
Physics Subject Headings (PhySH)
Erratum
Erratum: Programmable Quantum Anomalous Hall Insulator in Twisted Crystalline Flatbands [Phys. Rev. X 16, 011015 (2026)]
Popular Summary
Quantum anomalous Hall insulators support dissipationless edge currents without magnetic fields but remain challenging to control experimentally. Here we demonstrate a programmable version of this topological state in twisted double rhombohedral trilayer graphene. By tuning the twist angle and gate voltage we generate flat electronic bands that host multiple quantum anomalous Hall phases, including high-Chern-number states and integer Chern insulators at fractional moiré fillings. We find that these states can be reversibly switched and distinct topological phases accessed simply by varying the carrier density and electric field. This tunable platform offers a promising route for exploring strongly correlated physics and developing energy efficient quantum memory devices.
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References (51)
- R. Bistritzer and A. H. MacDonald, Moire bands in twisted double-layer grapheme, Proc. Natl. Acad. Sci. U.S.A. 108, 12233 (2011).
- Y. Cao, Fatemi V., Demir A. S., Fang S. L., Tomarken J. Y., Luo J. D., Sanchez-Yamagishi K., Watanabe T., Taniguchi E. Kaxiras et al., Correlated insulator behaviour at half-filling in magic-angle graphene superlattices, Nature (London) 556, 80 (2018).
- Y. Cao, V. Fatemi, S. Fang, K. Watanabe, T. Taniguchi, E. Kaxiras, and P. Jarllo-Herrero, Unconventional superconductivity in magic-angle graphene superlattices, Nature (London) 556, 43 (2018).
- Z. Hao, A. M. Zimmerman, P. Ledwith, E. Khalaf, D. H. Najafabadi, K. Watanabe, T. Taniguchi, A. Vishwanath, and P. Kim, Electric field–tunable superconductivity in alternating-twist magic-angle trilayer grapheme, Science 371, 1133 (2021).
- J. M. Park, Y. Cao, K. Watanabe, T. Taniguchi, and P. Jarillo-Herrero, Tunable strongly coupled superconductivity in magic-angle twisted trilayer grapheme, Nature (London) 590, 249 (2021).
- Y. Cao, J. M. Park, K. Watanabe, T. Taniguchi, and P. Jarillo-Herrero, Pauli-limit violation and re-entrant superconductivity in moiré grapheme, Nature (London) 595, 526 (2021).
- J. M. Park, Y. Cao, L. Q. Xia, S. Sun, K. Watanabe, T. Taniguchi, and P. Jarillo-Herrero, Robust superconductivity in magic-angle multilayer graphene family, Nat. Mater. 21, 877 (2022).
- G. W. Burg, E. Khalaf, Y. Wang, K. Watanabe, T. Taniguchi, A. Vishwanath, and P. Kim, Emergence of correlations in alternating twist quadrilayer grapheme, Nat. Mater. 21, 884 (2022).
- Y. Zhang, R. Polski, C. Lewandowski, A. Thomson, Y. Peng, Y. Choi, H. Kim, K. Watanabe, T. Taniguchi, J. Alicea et al., Promotion of superconductivity in magic-angle graphene multilayers, Science 377, 1538 (2022).
- H. Polshyn, Y. Zhang, M. A. Kumar, T. Soejima, J. Herzog-Arbeitman, A. Georges, S. Nadj-Perge, M. P. Zaletel, and A. F. Young, Topological charge density waves at half-integer filling of a moiré superlattice, Nat. Phys. 18, 42 (2022).
- S. Xu, M. M. Al Ezzi, N. Balakrishnan, A. Garcia-Ruiz, B. Tsim, C. Mullan, J. Barrier, N. Xin, B. A. Piot, T. Taniguchi et al., Tunable van Hove singularities and correlated states in twisted monolayer–bilayer grapheme, Nat. Phys. 17, 619 (2021).
- S. Chen, M. He, Y. Zhang, V. Valkunas, V. Y. Chen, G. Azzolina, R. L. Lee, T. Taniguchi, K. Watanabe, and A. F. Young, Electrically tunable correlated and topological states in twisted monolayer–bilayer grapheme, Nat. Phys. 17, 374 (2021).
- H. Polshyn, J. Zhu, M. A. Kumar, Y. Zhang, F. Yang, C. L. Tschirhart, M. Serlin, K. Watanabe, T. Taniguchi, A. H. MacDonald et al., Electrical switching of magnetic order in an orbital Chern insulator, Nature (London) 588, 66 (2020).
- Y. Cao, D. Rodan-Legrain, O. Rubies-Bigorda, J. M. Park, K. Watanabe, T. Taniguchi, and P. Jarillo-Herrero, Tunable correlated states and spin-polarized phases in twisted bilayer–bilayer grapheme, Nature (London) 583, 215 (2020).
- X. Liu, Z. Hao, E. Khalaf, J. Y. Lee, Y. Ronen, H. Yoo, D. H. Najafabadi, K. Watanabe, T. Taniguchi, A. Vishwanath et al., Tunable spin-polarized correlated states in twisted double bilayer grapheme, Nature (London) 583, 221 (2020).
- C. Shen, Y. Chu, Q. Wu, N. Li, S. Wang, Y. Zhao, J. Tang, J. Liu, J. Tian, K. Watanabe et al., Correlated states in twisted double bilayer grapheme, Nat. Phys. 16, 520 (2020).
- M. He, Y. Li, J. Cai, Y. Liu, K. Watanabe, T. Taniguchi, X. Xu, and M. Yankowitz, Symmetry breaking in twisted double bilayer grapheme, Nat. Phys. 17, 26 (2021).
- R. Su, D. Waters, B. Zhou, K. Watanabe, T. Taniguchi, and J. Folk, moiré-driven topological electronic crystals in twisted grapheme, Nature (London) 637, 1084 (2025).
- D. Waters, E. Thompson, E. Arreguin-Martinez, Y. Zeng, N. F. Q. Yuan, K. Watanabe, T. Taniguchi, and P. Kim, Mixed-dimensional moiré systems of twisted graphitic thin films, Nature (London) 620, 750 (2023).
- S. Yang, Z. C. Gu, K. Sun, and S. Das Sarma, Topological flat band models with arbitrary Chern numbers, Phys. Rev. B 86, 241112(R) (2012).
- J. Liu, Z. Ma, J. Gao, and X. Dai, Quantum valley Hall effect, orbital magnetism, and anomalous Hall effect in twisted multilayer graphene systems, Phys. Rev. X 9, 031021 (2019).
- J. Wang and Z. Liu, Hierarchy of ideal flatbands in chiral twisted multilayer graphene models, Phys. Rev. Lett. 128, 176403 (2022).
- P. J. Ledwith, A. Vishwanath, and E. Khalaf, Family of ideal Chern flatbands with arbitrary Chern number in chiral twisted graphene multilayers, Phys. Rev. Lett. 128, 176404 (2022).
- T. Han, Z. Lu, G. Scuri, J. Sung, R. K. Kumar, Y. Zhang, T. Taniguchi, K. Watanabe, and P. Kim, Orbital multiferroicity in pentalayer rhombohedral grapheme, Nature (London) 623, 41 (2023).
- T. Han, Z. Lu, G. Scuri, J. Sung, R. K. Kumar, Y. Zhang, T. Taniguchi, K. Watanabe, and P. Kim, Correlated insulator and Chern insulators in pentalayer rhombohedral-stacked grapheme, Nat. Nanotechnol. 19, 181 (2024).
- T. Arp, O. Sheekey, H. Zhou, K. Watanabe, T. Taniguchi, and A. F. Young, Intervalley coherence and intrinsic spin–orbit coupling in rhombohedral trilayer grapheme, Nat. Phys. 20, 1413 (2024).
- K. Liu, J. Zheng, Y. Sha, K. Watanabe, T. Taniguchi, and F. Zhang, Spontaneous broken-symmetry insulator and metals in tetralayer rhombohedral grapheme, Nat. Nanotechnol. 19, 188 (2024).
- W. Zhou, J. Ding, J. Hua, G. Chaudhary, X. Zhang, H. Gao, A. H. MacDonald, and J. Zhu, Layer-polarized ferromagnetism in rhombohedral multilayer grapheme, Nat. Commun. 15, 2597 (2024).
- Y. Sha, J. Zheng, K. Liu, K. Watanabe, T. Taniguchi, and F. Zhang, Observation of a Chern insulator in crystalline ABCA-tetralayer graphene with spin-orbit coupling, Science 384, 414 (2024).
- T. Han, Z. Lu, Y. Yao, A. P. Reddy, J. Yang, J. Seiler, F. Fan, R. K. Kumar, L. Fu, and P. Kim, Large quantum anomalous Hall effect in spin-orbit proximitized rhombohedral graphene, Science 384, 647 (2024).
- T. Han, Z. Lu, Z. Hadjri, K. Watanabe, T. Taniguchi, and P. Kim, Signatures of chiral superconductivity in rhombohedral graphene, Nature (London) 643, 654 (2025).
- J. Yang, X. Shi, S. Ye, Z. Han, K. Watanabe, T. Taniguchi, and L. Ju, Impact of spin–orbit coupling on superconductivity in rhombohedral graphene, Nat. Mater. 24, 1058 (2025).
- H. Zhou, T. Xie, A. Ghazaryan, T. Holder, E. Berg, M. Serlin, T. Taniguchi, K. Watanabe, and A. F. Young, Half- and quarter-metals in rhombohedral trilayer graphene, Nature (London) 598, 429 (2021).
- G. Chen, L. Jiang, S. Wu, B. Lyu, H. Li, B. Tong, J. Shi, T. Taniguchi, K. Watanabe, and Y. Zhang, Evidence of a gate-tunable Mott insulator in a trilayer graphene moiré superlattice, Nat. Phys. 15, 237 (2019).
- G. Chen, A. L. Sharpe, P. Gallagher, I. T. Rosen, E. J. Fox, L. Jiang, B. Lyu, H. Li, K. Watanabe, T. Taniguchi et al., Signatures of tunable superconductivity in a trilayer graphene moiré superlattice, Nature (London) 572, 215 (2019).
- G. Chen, A. L. Sharpe, E. J. Fox, Y. H. Zhang, S. Wang, L. Jiang, B. Lyu, H. Li, K. Watanabe, T. Taniguchi et al., Tunable correlated Chern insulator and ferromagnetism in a moiré superlattice, Nature (London) 579, 56 (2020).
- Z. Lu, T. Han, Y. Yao, A. P. Reddy, J. Yang, J. Seiler, F. Fan, R. K. Kumar, L. Fu, and P. Kim, Fractional quantum anomalous Hall effect in multilayer graphene, Nature (London) 626, 759 (2024).
- Z. Lu, T. Han, Y. Yao, A. P. Reddy, J. Yang, J. Seiler, F. Fan, R. K. Kumar, L. Fu, and P. Kim, Extended quantum anomalous Hall states in graphene/hBN moiré superlattices, Nature (London) 637, 1090 (2025).
- S. H. Aronson, T. Han, Z. Lu, K. Watanabe, T. Taniguchi, and P. Kim, Displacement field-controlled fractional Chern insulators and charge density waves in a graphene/hBN moiré superlattice, Phys. Rev. X 15, 031026 (2025).
- D. Waters, A. Okounkova, R. Su, B. Zhou, J. Yao, K. Watanabe, T. Taniguchi, X. Xu, Y. H. Zhang, J. Folk, and M. Yankowitz, Chern insulators at integer and fractional filling in moiré pentalayer graphene, Phys. Rev. X 15, 011045 (2025).
- Y. Choi, Y. Choi, M. Valentini, R. Kuzian, I. Robredo, K. Watanabe, T. Taniguchi, J. L. Manes, M. G. Vergniory, A. Bergara et al., Superconductivity and quantized anomalous Hall effect in rhombohedral graphene, Nature (London) 639, 342 (2025).
- J. Xie, Z. Huo, X. Lu, K. Watanabe, T. Taniguchi, and X. Lin, Tunable fractional Chern insulators in rhombohedral graphene superlattices, Nat. Mater. 24, 1042 (2025).
- Z. Wang, Q. Liu, X. Han, Y. Zhang, K. Watanabe, T. Taniguchi, and L. He, Electrical switching of Chern insulators in moire rhombohedral heptalayer graphene, arXiv:2503.00837.
- S. J. Hong, D. Wang, D. Wulferding, P. Lemmens, and R. J. Haug, Twisted double ABC-stacked trilayer graphene with weak interlayer coupling, Phys. Rev. B 105, 205404 (2022).
- M. L. Perrin, A. Jayaraj, B. Ghawri, S. H. Arora, N. F. Q. Yuan, L. Fu, E. Berg, P. Kim, and A. Yacoby, Electric field tunable bandgap in twisted double trilayer graphene, npj 2D Mater. Appl. 8, 14 (2024).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/7m1b-hxy8 for methods of device fabrication, transport measurements, twist angle determination, the continuum model, Landau-Ginzburg theory for first order transitions, Hartree-Fock calculations,si and supplemental texts with supplemental data.
- Z. Feng, W. Wang, Y. You, Y. Chen, K. Watanabe, T. Taniguchi, C. Liu, K. Liu, and X. Lu, Rapid infrared imaging of rhombohedral graphene, Phys. Rev. Appl. 23, 034012 (2025).
- C. Rubio-Verdú, S. Turkel, Y. Song, L. Klebl, R. Samajdar, D. Calugaru, K. Watanabe, T. Taniguchi, A. Vishwanath, K. Haule et al., moiré nematic phase in twisted double bilayer graphene, Nat. Phys. 18, 196 (2022).
- Y. Xu, S. Liu, D. A. Rhodes, K. Watanabe, T. Taniguchi, J. C. Hone, V. Elser, K. F. Mak, and J. Shan, Correlated insulating states at fractional fillings of moiré superlattices, Nature (London) 587, 214 (2020).
- E. C. Regan, D. Wang, C. Jin, M. I. Bakti Utama, B. Gao, X. Wei, S. Zhao, W. Zhao, Z. Zhang, K. Yumigeta et al., Mott and generalized Wigner crystal states in WSe2/WS2 moiré superlattices, Nature (London) 579, 359 (2020).
- J. L. Liu, J. Zhu, Y. Wang, C. Xu, K. Watanabe, T. Taniguchi, and J. Shan, Observation of Integer and Fractional Chern insulators in high Chern number flatbands, arXiv:2507.09908.
