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Displacement Field-Controlled Fractional Chern Insulators and Charge Density Waves in a Graphene/hBN Moiré Superlattice

Samuel H. Aronson1,*, Tonghang Han1,*, Zhengguang Lu1, Yuxuan Yao1, Jackson P. Butler1, Kenji Watanabe2, Takashi Taniguchi3, Long Ju1,†, and Raymond C. Ashoori1,‡

  • *These authors contributed equally to this work.
  • †Contact author: longju@mit.edu
  • ‡Contact author: ashoori@mit.edu
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Phys. Rev. X 15, 031026 – Published 24 July, 2025

DOI: https://doi.org/10.1103/75gl-jzl6

Abstract

Rhombohedral stacked graphene (RSG) contains two key ingredients for the realization of correlated topological phases of matter: flat electronic bands and concentrated Berry curvature. The fractional quantum anomalous Hall effect was recently observed in an RSG-hexagonal boron nitride (hBN) moiré heterostructure when the conduction electrons were pushed away from the moiré interface by an applied electric displacement field. The question then arises about whether such topological states can also develop in RSG-hBN in a strong moiré potential. Here, we explore the physics in the moiré-proximal limit through capacitance measurements that allow us to determine the electronic compressibility and extract energy gaps of incompressible states. We report the observation of integer and fractional Chern insulator states at low magnetic field in this limit at filling factors ν=1, 2/3, and 1/3 in addition to numerous trivial and topological charge density waves. We map out a correlated phase diagram that is highly sensitive to both displacement and magnetic fields, establishing the moiré-proximal regime as a tunable platform for studying the interplay between band topology and strong lattice effects.

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Popular Summary

Stacking two atomically flat, layered materials with different scales of lattice periodicity produces a moiré superlattice—a lattice that repeats over potentially longer scales than the underlying atomic lattices of the constituent materials. In these superlattices, electron interactions can dominate over quantum confinement energies. This can lead to unusual effects, such as insulating states that arise purely from correlations. Whereas previous studies focused on cases where electrons are pushed away from the moiré interface, we instead explore what happens when electrons are pushed toward the interface, where the superlattice potential is dramatically stronger.

To investigate this regime, we place a superlattice of five-layer graphene with a particular layer stacking known as “rhombohedral” and hexagonal boron nitride inside a parallel plate capacitor, connecting the graphene layer to electrical ground. By applying an ac voltage to one of the plates and detecting electric fields that penetrate the graphene, we can study the graphene’s screening properties. This reveals the electronic density of states in the graphene, which is related to its ability to absorb electrical charge.

Unsurprisingly, we observe low densities of states around regions with integer filling (superlattice cells containing one electron) and rational fractional filling of the superlattice potential. Such states are “charge density waves” that one might expect to arise classically. More surprising is that we also observe exotic “fractional charge states,” in which charges are not localized to individual cells but instead behave as though a fluid of fractional charges exists in the system and with equal but noninteger electron fillings of cells. While such fractionalization has been observed in the weak moiré regime, it is surprising to see it in a strong superlattice potential, where one might expect electrons to behave as classical whole electrons.

In the absence of a moiré potential, rhombohedral stacked graphene displays many remarkable superconducting phases along with potential “Wigner crystal” behavior, in which free electrons crystallize spontaneously. Future work with both weak and strong moiré potentials will provide a means for studying the competition between simple phases such as charge density waves and those that appear in the absence of a moiré potential such as Wigner crystals, fractional states, and exotic superconductors, providing vital clues to the nature of these states.

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References (52)

  1. K. v. Klitzing, G. Dorda, and M. Pepper, New method for high-accuracy determination of the fine-structure constant based on quantized Hall resistance, Phys. Rev. Lett. 45, 494 (1980).
  2. D. C. Tsui, H. L. Stormer, and A. C. Gossard, Two-dimensional magnetotransport in the extreme quantum limit, Phys. Rev. Lett. 48, 1559 (1982).
  3. F. D. M. Haldane, Model for a quantum Hall effect without Landau levels: Condensed-matter realization of the “parity anomaly”, Phys. Rev. Lett. 61, 2015 (1988).
  4. E. Tang, J.-W. Mei, and X.-G. Wen, High-temperature fractional quantum Hall states, Phys. Rev. Lett. 106, 236802 (2011).
  5. K. Sun, Z. Gu, H. Katsura, and S. Das Sarma, Nearly flatbands with nontrivial topology, Phys. Rev. Lett. 106, 236803 (2011).
  6. T. Neupert, L. Santos, C. Chamon, and C. Mudry, Fractional quantum Hall states at zero magnetic field, Phys. Rev. Lett. 106, 236804 (2011).
  7. D. N. Sheng, Z.-C. Gu, K. Sun, and L. Sheng, Fractional quantum Hall effect in the absence of Landau levels, Nat. Commun. 2, 389 (2011).
  8. N. Regnault and B. A. Bernevig, Fractional Chern insulator, Phys. Rev. X 1, 021014 (2011).
  9. S. A. Parameswaran, R. Roy, and S. L. Sondhi, Fractional quantum Hall physics in topological flat bands, C.R. Phys. 14, 816 (2013).
  10. E. J. Bergholtz and Z. Liu, Topological flat band models and fractional Chern insulators, Int. J. Mod. Phys. B 27, 1330017 (2013).
  11. E. M. Spanton, A. A. Zibrov, H. Zhou, T. Taniguchi, K. Watanabe, M. P. Zaletel, and A. F. Young, Observation of fractional Chern insulators in a van der Waals heterostructure, Science 360, 62 (2018).
  12. 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, K. Watanabe, T. Taniguchi, A. Vishwanath, P. Jarillo-Herrero, and A. Yacoby, Fractional Chern insulators in magic-angle twisted bilayer graphene, Nature (London) 600, 439 (2021).
  13. 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, Signatures of fractional quantum anomalous Hall states in twisted MoTe2, Nature (London) 622, 63 (2023).
  14. Y. Zeng, Z. Xia, K. Kang, J. Zhu, P. Knüppel, C. Vaswani, K. Watanabe, T. Taniguchi, K. F. Mak, and J. Shan, Thermodynamic evidence of fractional Chern insulator in moiré MoTe2, Nature (London) 622, 69 (2023).
  15. 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, Observation of integer and fractional quantum anomalous Hall effects in twisted bilayer MoTe2, Phys. Rev. X 13, 031037 (2023).
  16. 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, Observation of fractionally quantized anomalous Hall effect, Nature (London) 622, 74 (2023).
  17. F. Wu, T. Lovorn, E. Tutuc, I. Martin, and A. H. MacDonald, Topological insulators in twisted transition metal dichalcogenide homobilayers, Phys. Rev. Lett. 122, 086402 (2019).
  18. T. Devakul, V. Crépel, Y. Zhang, and L. Fu, Magic in twisted transition metal dichalcogenide bilayers, Nat. Commun. 12, 6730 (2021).
  19. 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).
  20. J. Xie, Z. Huo, X. Lu, Z. Feng, Z. Zhang, W. Wang, Q. Yang, K. Watanabe, T. Taniguchi, K. Liu, Z. Song, X. C. Xie, J. Liu, and X. Lu, Tunable fractional Chern insulators in rhombohedral graphene superlattices, arXiv:2405.16944.
  21. Y. Choi, Y. Choi, M. Valentini, C. L. Patterson, L. F. W. Holleis, O. I. Sheekey, H. Stoyanov, X. Cheng, T. Taniguchi, K. Watanabe, and A. F. Young, Superconductivity and quantized anomalous Hall effect in rhombohedral graphene, Nature (London) 639, 342 (2025).
  22. Z. Dong, A. S. Patri, and T. Senthil, Theory of fractional quantum anomalous Hall phases in pentalayer rhombohedral graphene moiré structures, Phys. Rev. Lett. 133, 206502 (2023).
  23. B. Zhou, H. Yang, and Y.-H. Zhang, Fractional quantum anomalous Hall effect in rhombohedral multilayer graphene in the moiréless limit, Phys. Rev. Lett. 133, 206504 (2024).
  24. J. Dong, T. Wang, T. Wang, T. Soejima, M. P. Zaletel, A. Vishwanath, and D. E. Parker, Anomalous Hall crystals in rhombohedral multilayer graphene. I. Interaction-driven Chern bands and fractional quantum Hall states at zero magnetic field, Phys. Rev. Lett. 133, 206503 (2024).
  25. Y. H. Kwan, J. Yu, J. Herzog-Arbeitman, D. K. Efetov, N. Regnault, and B. A. Bernevig, Moiré Fractional Chern insulators III: Hartree-Fock phase diagram, magic angle regime for Chern insulator states, the role of the moiré potential and Goldstone gaps in rhombohedral graphene superlattices, arXiv:2312.11617 [Phys. Rev. B (to be published)].
  26. Z. Guo, X. Lu, B. Xie, and J. Liu, Fractional Chern insulator states in multilayer graphene moiré superlattices, Phys. Rev. B 110, 075109 (2024).
  27. K. Huang, X. Li, S. Das Sarma, and F. Zhang, Self-consistent theory of fractional quantum anomalous Hall states in rhombohedral graphene, Phys. Rev. B 110, 115146 (2024).
  28. Y.-H. Zhang, D. Mao, Y. Cao, P. Jarillo-Herrero, and T. Senthil, Nearly flat Chern bands in moiré superlattices, Phys. Rev. B 99, 075127 (2019).
  29. H. Zhou, T. Xie, A. Ghazaryan, T. Holder, J. R. Ehrets, E. M. Spanton, T. Taniguchi, K. Watanabe, E. Berg, M. Serbyn, and A. F. Young, Half- and quarter-metals in rhombohedral trilayer graphene, Nature (London) 598, 429 (2021).
  30. See Supplemental Material at http://link.aps.org/supplemental/10.1103/75gl-jzl6 for additional compressibility and transport measurements, statistical fits to features in Landau fans, circuit diagrams, and a discussion on extracting gap widths from capacitance data.
  31. S. C. Dultz and H. W. Jiang, Thermodynamic signature of a two-dimensional metal-insulator transition, Phys. Rev. Lett. 84, 4689 (2000).
  32. 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).
  33. M. Bello, E. Levin, B. Shklovskii, and A. L. Efros, Density of localized states in the surface band of a metal-insulator-semiconductor structure, Zh. Eksp. Teor. Fiz. 53, 822 (1981).
  34. B. Tanatar and D. M. Ceperley, Ground state of the two-dimensional electron gas, Phys. Rev. B 39, 5005 (1989).
  35. J. P. Eisenstein, L. N. Pfeiffer, and K. W. West, Negative compressibility of interacting two-dimensional electron and quasiparticle gases, Phys. Rev. Lett. 68, 674 (1992).
  36. T. Tan and T. Devakul, Parent Berry curvature and the ideal anomalous Hall crystal, Phys. Rev. X 14, 041040 (2024).
  37. L. Wang, Y. Gao, B. Wen, Z. Han, T. Taniguchi, K. Watanabe, M. Koshino, J. Hone, and C. R. Dean, Evidence for a fractional fractal quantum Hall effect in graphene superlattices, Science 350, 1231 (2015).
  38. D. R. Hofstadter, Energy levels and wave functions of Bloch electrons in rational and irrational magnetic fields, Phys. Rev. B 14, 2239 (1976).
  39. D. J. Thouless, M. Kohmoto, M. P. Nightingale, and M. den Nijs, Quantized Hall conductance in a two-dimensional periodic potential, Phys. Rev. Lett. 49, 405 (1982).
  40. P. Streda, Theory of quantised Hall conductivity in two dimensions, J. Phys. C 15, L717 (1982).
  41. M. Koshino and E. McCann, Trigonal warping and Berry’s phase Nπ in ABC-stacked multilayer graphene, Phys. Rev. B 80, 165409 (2009).
  42. 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).
  43. B. L. Chittari, G. Chen, Y. Zhang, F. Wang, and J. Jung, Gate-tunable topological flat bands in trilayer graphene boron-nitride moiré superlattices, Phys. Rev. Lett. 122, 016401 (2019).
  44. Y. Park, Y. Kim, B. L. Chittari, and J. Jung, Topological flat bands in rhombohedral tetralayer and multilayer graphene on hexagonal boron nitride moiré superlattices, Phys. Rev. B 108, 155406 (2023).
  45. J. Dong, T. Wang, T. Wang, T. Soejima, M. P. Zaletel, A. Vishwanath, and D. E. Parker, Anomalous Hall crystals in rhombohedral multilayer graphene I: Interaction-driven Chern bands and fractional quantum Hall states at zero magnetic field, Phys. Rev. Lett. 133, 206503 (2024).
  46. Y. Xu, C. Horn, J. Zhu, Y. Tang, L. Ma, L. Li, S. Liu, K. Watanabe, T. Taniguchi, J. C. Hone, J. Shan, and K. F. Mak, Creation of moiré bands in a monolayer semiconductor by spatially periodic dielectric screening, Nat. Mater. 20, 645 (2021).
  47. Sayed Ali Akbar Ghorashi, A. Dunbrack, A. Abouelkomsan, J. Sun, X. Du, and J. Cano, Topological and stacked flat bands in bilayer graphene with a superlattice potential, Phys. Rev. Lett. 130, 196201 (2023).
  48. Z. Zhang, J. Xie, W. Zhao, R. Qi, C. Sanborn, S. Wang, S. Kahn, K. Watanabe, T. Taniguchi, A. Zettl, M. Crommie, and F. Wang, Engineering correlated insulators in bilayer graphene with a remote Coulomb superlattice, Nat. Mater. 23, 189 (2024).
  49. D. S. Kim et al., Electrostatic moiré potential from twisted hexagonal boron nitride layers, Nat. Mater. 23, 65 (2024).
  50. X. Wang, C. Xu, S. Aronson, D. Bennett, N. Paul, P. J. D. Crowley, C. Collignon, K. Watanabe, T. Taniguchi, R. Ashoori, E. Kaxiras, Y. Zhang, P. Jarillo-Herrero, and K. Yasuda, Band structure engineering using a moiré polar substrate, Nat. Commun. 16, 178 (2025).
  51. G. A. Steele, Imaging transport resonances in the quantum Hall effect, Ph.D. thesis, MIT, 2006.
  52. S. H. Aronson, Data for Displacement field-controlled fractional Chern insulators and charge density waves in a graphene/hBN moire superlattice, Zenodo, 10.5281/zenodo.15732368 (2025).

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Phys. Rev. X 15, 031026– Published 24 July, 2025
  • Received 15 January 2025
  • Revised 17 April 2025
  • Accepted 11 June 2025
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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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