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Erratum: Programmable Quantum Anomalous Hall Insulator in Twisted Crystalline Flatbands [Phys. Rev. X 16, 011015 (2026)]

Wenxuan Wang, Yijie Wang, Zaizhe Zhang, Zihao Huo, Gengdong Zhou, Shu Zhang, Kenji Watanabe, Takashi Taniguchi, Xiaoxia Yang et al.

Qing Dai, X. C. Xie, Kaihui Liu, Zhida Song, and Xiaobo Lu

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Phys. Rev. X 16, 039901 – Published 28 September, 2026

DOI: https://doi.org/10.1103/xyq4-kr2k

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Original Article

Programmable Quantum Anomalous Hall Insulator in Twisted Crystalline Flatbands

Wenxuan Wang, Yijie Wang, Zaizhe Zhang, Zihao Huo, Gengdong Zhou, Shu Zhang, Kenji Watanabe, Takashi Taniguchi, Xiaoxia Yang, Qing Dai, X. C. Xie, Kaihui Liu, Zhida Song, and Xiaobo Lu
Phys. Rev. X 16, 011015 (2026)

References (51)

  1. R. Bistritzer and A. H. MacDonald, Moiré bands in twisted double-layer graphene, Proc. Natl. Acad. Sci. U.S.A. 108, 12233 (2011).
  2. Y. Cao, V. Fatemi, A. Demir, 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).
  3. 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).
  4. 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 graphene, Science 371, 1133 (2021).
  5. J. M. Park, Y. Cao, K. Watanabe, T. Taniguchi, and P. Jarillo-Herrero, Tunable strongly coupled superconductivity in magic-angle twisted trilayer graphene, Nature (London) 590, 249 (2021).
  6. Y. Cao, J. M. Park, K. Watanabe, T. Taniguchi, and P. Jarillo-Herrero, Pauli-limit violation and re-entrant superconductivity in moiré graphene, Nature (London) 595, 526 (2021).
  7. 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).
  8. G. W. Burg, E. Khalaf, Y. Wang, K. Watanabe, T. Taniguchi, and E. Tutuc, Emergence of correlations in alternating twist quadrilayer graphene, Nat. Mater. 21, 884 (2022).
  9. 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).
  10. H. Polshyn, Y. Zhang, M. A. Kumar, T. Soejima, P. Ledwith, K. Watanabe, T. Taniguchi, A. Vishwanath, M. P. Zaletel, and A. F. Young, Topological charge density waves at half integer filling of a moiré superlattice, Nat. Phys. 18, 42 (2022).
  11. 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 graphene, Nat. Phys. 17, 619 (2021).
  12. S. Chen, M. He, Y. Zhang, V. Hsieh, Z. Fei, K. Watanabe, T. Taniguchi, D. H. Cobden, X. Xu, C. R. Dean, and M. Yankowitz, Electrically tunable correlated and topological states in twisted monolayer–bilayer graphene, Nat. Phys. 17, 374 (2021).
  13. 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).
  14. 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 graphene, Nature (London) 583, 215 (2020).
  15. 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 graphene, Nature (London) 583, 221 (2020).
  16. 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 graphene, Nat. Phys. 16, 520 (2020).
  17. M. He, Y. Li, J. Cai, Y. Liu, K. Watanabe, T. Taniguchi, X. Xu, and M. Yankowitz, Symmetry breaking in twisted double bilayer graphene, Nat. Phys. 17, 26 (2021).
  18. R. Su, D. Waters, B. Zhou, K. Watanabe, T. Taniguchi, Y. Zhang, M. Yankowitz, and J. Folk, Moiré-driven topological electronic crystals in twisted graphene, Nature (London) 637, 1084 (2025).
  19. D. Waters, E. Thompson, E. Arreguin-Martinez, M. Fujimoto, Y. Ren, K. Watanabe, T. Taniguchi, T. Cao, D. Xiao, and M. Yankowitz, Mixed-dimensional moiré systems of twisted graphitic thin films, Nature (London) 620, 750 (2023).
  20. S. Yang, Z. C. Gu, K. Sun, and S. D. Sarma, Topological flat band models with arbitrary Chern numbers, Phys. Rev. B 86, 241112(R) (2012).
  21. 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).
  22. J. Wang and Z. Liu, Hierarchy of ideal flatbands in chiral twisted multilayer graphene models, Phys. Rev. Lett. 128, 176403 (2022).
  23. 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).
  24. T. Han, Z. Lu, G. Scuri, J. Sung, J. Wang, T. Han, K. Watanabe, T. Taniguchi, L. Fu, H. Park, and L. Ju, Orbital multiferroicity in pentalayer rhombohedral graphene, Nature (London) 623, 41 (2023).
  25. T. Han, Z. Lu, G. Scuri, J. Sung, J. Wang, T. Han, K. Watanabe, T. Taniguchi, H. Park, and L. Ju, Correlated insulator and Chern insulators in pentalayer rhombohedral-stacked graphene, Nat. Nanotechnol. 19, 181 (2024).
  26. T. Arp, O. Sheekey, H. Zhou, C. L. Tshirhart, C. L. Patterson, H. M. Yoo, L. Holleis, E. Redekop, G. Babikyan, T. Xie et al., Intervalley coherence and intrinsic spin orbit coupling in rhombohedral trilayer graphene, Nat. Phys. 20, 1413 (2024).
  27. K. Liu, J. Zheng, Y. Sha, B. Lyu, F. Li, Y. Park, Y. Ren, K. Watanabe, T. Taniguchi et al., Spontaneous broken-symmetry insulator and metals in tetralayer rhombohedral graphene, Nat. Nanotechnol. 19, 188 (2024).
  28. W. Zhou, J. Ding, J. Hua, L. Zhang, K. Watanabe, T. Taniguchi, W. Zhu, and S. Xu, Layer-polarized ferromagnetism in rhombohedral multilayer graphene, Nat. Commun. 15, 2597 (2024).
  29. Y. Sha, J. Zheng, K. Liu, H. Du, K. Watanabe, T. Taniguchi, J. Jia, Z. Shi, R. Zhong, and G. Chen, Observation of a Chern insulator in crystalline ABCA-tetralayer graphene with spin-orbit coupling, Science 384, 414 (2024).
  30. T. Han, Z. Lu, Y. Yao, J. Yang, J. Seo, C. Yoon, K. Watanabe, T. Taniguchi, L. Fu, F. Zhang, and Long Ju, Large quantum anomalous Hall effect in spin-orbit proximitized rhombohedral graphene, Science 384, 647 (2024).
  31. T. Han, Z. Lu, Z. Hadjri, L. Shi, Z. Wu, Wei Xu, Y. Yao, A. A. Cotton, O. S. Sedeh, H. Weldeyesus et al., Signatures of chiral superconductivity in rhombohedral graphene, Nature (London) 643, 654 (2025).
  32. J. Yang, X. Shi, S. Ye, C. Yoon, Z. Lu, V. Kakani, T. Han, J. Seo, L. Shi, K. Watanabe et al., Impact of spin–orbit coupling on superconductivity in rhombohedral graphene, Nat. Mater. 24, 1058 (2025).
  33. H. Zhou, T. Xie, A. Ghazaryan, T. Holder, J. R. Ehrets, E. M. Spanton, T. Taniguchi, K. Watanabe, E. Berg, M. Serbyn et al., Half and quarter-metals in rhombohedral trilayer graphene, Nature (London) 598, 429 (2021).
  34. G. Chen, L. Jiang, S. Wu, B. Lyu, H. Li, B. L. Chittari, K. Watanabe, T. Taniguchi, Z. Shi, J. Jung et al. Evidence of a gate tunable Mott insulator in a trilayer graphene moiré superlattice, Nat. Phys. 15, 237 (2019).
  35. 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).
  36. 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).
  37. Z. Lu, T. Han, Y. Yao, A. P. Reddy, J. Yang, J. Seo, K. Watanabe, T. Taniguchi, L. Fu, and L. Ju, Fractional quantum anomalous Hall effect in multilayer graphene, Nature (London) 626, 759 (2024).
  38. Z. Lu, T. Han, Y. Yao, Z. Hadjri, J. Yang, J. Seo, L. Shi, S. Ye, K. Watanabe, T. Taniguchi et al., Extended quantum anomalous Hall states in graphene/hBN moiré superlattices, Nature (London) 637, 1090 (2025).
  39. S. H. Aronson, T. Han, Z. Lu, Y. Yao, J. P. Butler, K. Watanabe, T. Taniguchi, L. Ju, and R. C. Ashoori, Displacement field-controlled fractional Chern insulators and charge density waves in a graphene/hBN moiré superlattice, Phys. Rev. X 15, 031026 (2025).
  40. 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).
  41. Y. Choi, Y. Choi, M. Valentini, C. L. Patterson, L. F. W. Holleis, O. I. Sheekey, H. Stoyanov, X. Cheng, T. Taniguchi, K. Watanabe et al., Superconductivity and quantized anomalous Hall effect in rhombohedral graphene, Nature (London) 639, 342 (2025).
  42. J. Xie, Z. Huo, X. Lu, Z. Feng, W. Wang, Q. Yang, K. Watanabe, T. Taniguchi, K. Liu, Z. Song et al., Tunable fractional Chern insulators in rhombohedral graphene superlattices, Nat. Mater. 24, 1042 (2025).
  43. Z. Wang, Q. Liu, X. Han, Z. Li, W. Zhao, Z. Qu, C. Han, K. Watanabe, T. Taniguchi, Z. V. Han et al., Electrical switching of Chern insulators in moiré rhombohedral heptalayer graphene, arXiv:2503.00837.
  44. 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).
  45. M. L. Perrin, A. Jayaraj, B. Ghawri, K. Watanabe, T. Taniguchi, D. Passerone, M. Calame, and J. Zhang, Electric field tunable bandgap in twisted double trilayer graphene, npj 2D Mater. Appl. 8, 14 (2024).
  46. 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.
  47. 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).
  48. C. Rubio-Verdú, S. Turkel, Y. Song, L. Klebl, R. Samajdar, M. S. Scheurer, J. W. F. Venderbos, K. Watanabe, T. Taniguchi, H. Ochoa et al., Moiré nematic phase in twisted double bilayer graphene, Nat. Phys. 18, 196 (2022).
  49. Y. Xu, S. Liu, D. A. Rhodes, K. Watanabe, T. Taniguchi, J. Hone, V. Elser, K. F. Mak, and J. Shan, Correlated insulating states at fractional fillings of moiré superlattices, Nature (London) 587, 214 (2020).
  50. E. C. Regan, D. Wang, C. Jin, M. I. B. 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).
  51. J. Dong, L. Liu, J. Zhu, Z. Pan, Y. Hong, F. Wang, Z. Ren, Z. Jia, K. Watanabe, T. Taniguchi et al., Observation of integer and fractional Chern insulators in high Chern number flatbands, .

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Phys. Rev. X 16, 039901– Published 28 September, 2026
  • Received 9 August 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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