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Broken-symmetry states at half-integer band fillings in twisted bilayer graphene


The dominance of Coulomb interactions over the kinetic energy of electrons in flat moiré bands of magic-angle twisted bilayer graphene (TBG) gives rise to a variety of correlated phases, including correlated insulators1,2,3, superconductivity2,4,5, orbital ferromagnetism2,6, Chern insulators7,8,9,10 and nematicity11. Most of these phases occur when the carrier density is at or near an integer number of carriers per moiré unit cell. However, the demonstration of ordered states at fractional moiré band fillings at zero applied magnetic field is more challenging. Here we report the observation of states near half-integer band fillings 0.5 and ±3.5 at near-zero magnetic field in TBG proximitized by tungsten diselenide. Furthermore, at a band filling near −0.5, a symmetry-broken Chern insulator emerges at high magnetic field that is compatible with the band structure calculations within a translational symmetry-broken supercell with twice the area of the original TBG moiré cell. Our results are consistent with a spin or charge density wave ground state in TBG in the zero-magnetic-field limit.

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Fig. 1: Electrical characterization and low-field Hall measurements in device D1, with θ ≈ 1.14°.
Fig. 2: Symmetry-broken states at ν ≈ −0.5 and ±3.5 in device D2, with θ ≈ 1.16°.
Fig. 3: Zero-field thermoelectricity.
Fig. 4: Degeneracy lifting of the folded bands.

Data availability

Data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request. Source data are provided with this paper.

Code availability

The codes that support the findings of this study are available from the corresponding author upon reasonable request.


  1. Cao, Y. et al. Correlated insulator behaviour at half-filling in magic-angle graphene superlattices. Nature 556, 80–84 (2018).

    ADS  Article  Google Scholar 

  2. Lu, X. et al. Superconductors, orbital magnets and correlated states in magic-angle bilayer graphene. Nature 574, 653–657 (2019).

    ADS  Article  Google Scholar 

  3. Po, H. C., Zou, L., Vishwanath, A. & Senthil, T. Origin of Mott insulating behavior and superconductivity in twisted bilayer graphene. Phys. Rev. X 8, 031089 (2018).

    Google Scholar 

  4. Cao, Y. et al. Unconventional superconductivity in magic-angle graphene superlattices. Nature 556, 43–50 (2018).

    ADS  Article  Google Scholar 

  5. Wu, F., MacDonald, A. H. & Martin, I. Theory of phonon-mediated superconductivity in twisted bilayer graphene. Phys. Rev. Lett. 121, 257001 (2018).

    ADS  Article  Google Scholar 

  6. Serlin, M. et al. Intrinsic quantized anomalous Hall effect in a moiré heterostructure. Science 367, 900–903 (2020).

    ADS  Article  Google Scholar 

  7. Nuckolls, K. P. et al. Strongly correlated Chern insulators in magic-angle twisted bilayer graphene. Nature 588, 610–615 (2020).

    ADS  Article  Google Scholar 

  8. Wu, S., Zhang, Z., Watanabe, K., Taniguchi, T. & Andrei, E. Y. Chern insulators, van Hove singularities and topological flat bands in magic-angle twisted bilayer graphene. Nat. Mater. 20, 488–494 (2021).

    ADS  Article  Google Scholar 

  9. Saito, Y. et al. Hofstadter subband ferromagnetism and symmetry-broken Chern insulators in twisted bilayer graphene. Nat. Phys. 17, 478–481 (2021).

    Article  Google Scholar 

  10. Das, I. et al. Symmetry-broken Chern insulators and Rashba-like Landau-level crossings in magic-angle bilayer graphene. Nat. Phys. 17, 710–714 (2021).

    Article  Google Scholar 

  11. Cao, Y. et al. Nematicity and competing orders in superconducting magic-angle graphene. Science 372, 264–271 (2021).

    ADS  Article  Google Scholar 

  12. Haldane, F. D. M. Model for a quantum hall effect without Landau levels: condensed-matter realization of the ‘parity anomaly’. Phys. Rev. Lett. 61, 2015–2018 (1988).

    ADS  Article  Google Scholar 

  13. Sun, K., Gu, Z., Katsura, H. & Das Sarma, S. Nearly flatbands with nontrivial topology. Phys. Rev. Lett. 106, 236803 (2011).

    ADS  Article  Google Scholar 

  14. Neupert, T., Santos, L., Chamon, C. & Mudry, C. Fractional quantum Hall states at zero magnetic field. Phys. Rev. Lett. 106, 236804 (2011).

    ADS  Article  Google Scholar 

  15. Polshyn, H. et al. Topological charge density waves at half-integer filling of a moiré superlattice. Nat. Phys. 18, 42–47 (2021).

    Article  Google Scholar 

  16. Hao, Z. et al. Electric field-tunable superconductivity in alternating-twist magic-angle trilayer graphene. Science 371, 1133–1138 (2021).

    ADS  Article  Google Scholar 

  17. Xie, Y. et al. Fractional Chern insulators in magic-angle twisted bilayer graphene. Nature 600, 439–443 (2021).

    ADS  Article  Google Scholar 

  18. Pierce, A. T. et al. Unconventional sequence of correlated Chern insulators in magic-angle twisted bilayer graphene. Nat. Phys. 17, 1210–1215 (2021).

    Article  Google Scholar 

  19. Wilhelm, P., Lang, T. C. & Läuchli, A. M. Interplay of fractional Chern insulator and charge density wave phases in twisted bilayer graphene. Phys. Rev. B 103, 125406 (2021).

    ADS  Article  Google Scholar 

  20. Wolf, T. M. R., Lado, J. L., Blatter, G. & Zilberberg, O. Electrically tunable flat bands and magnetism in twisted bilayer graphene. Phys. Rev. Lett. 123, 096802 (2019).

    ADS  Article  Google Scholar 

  21. Jonson, M. & Mahan, G. D. Mott’s formula for the thermopower and the Wiedemann-Franz law. Phys. Rev. B 21, 4223–4229 (1980).

    ADS  MathSciNet  Article  Google Scholar 

  22. Ghawri, B. et al. Excess entropy and breakdown of semiclassical description of thermoelectricity in twisted bilayer graphene close to half filling. Preprint at (2020).

  23. Kim, Y. et al. Charge inversion and topological phase transition at a twist angle induced van Hove singularity of bilayer graphene. Nano Lett. 16, 5053–5059 (2016).

    ADS  Article  Google Scholar 

  24. Wang, L. et al. Evidence for a fractional fractal quantum Hall effect in graphene superlattices. Science 350, 1231–1234 (2015).

    ADS  MathSciNet  Article  Google Scholar 

  25. DaSilva, A. M., Jung, J. & MacDonald, A. H. Fractional Hofstadter states in graphene on hexagonal boron nitride. Phys. Rev. Lett. 117, 036802 (2016).

    ADS  Article  Google Scholar 

  26. Gmitra, M. & Fabian, J. Graphene on transition-metal dichalcogenides: a platform for proximity spin-orbit physics and optospintronics. Phys. Rev. B 92, 155403 (2015).

    ADS  Article  Google Scholar 

  27. Li, Y. & Koshino, M. Twist-angle dependence of the proximity spin-orbit coupling in graphene on transition-metal dichalcogenides. Phys. Rev. B 99, 075438 (2019).

    ADS  Article  Google Scholar 

  28. Arora, H. S. et al. Superconductivity in metallic twisted bilayer graphene stabilized by WSe2. Nature 583, 379–384 (2020).

    ADS  Article  Google Scholar 

  29. Lin, J.-X. et al. Spin-orbit driven ferromagnetism at half moiré filling in magic-angle twisted bilayer graphene. Science 375, 437–441 (2022).

    ADS  Article  Google Scholar 

  30. Shin, J., Park, Y., Chittari, B. L., Sun, J.-H. & Jung, J. Electron-hole asymmetry and band gaps of commensurate double moiré patterns in twisted bilayer graphene on hexagonal boron nitride. Phys. Rev. B 103, 075423 (2021).

    ADS  Article  Google Scholar 

  31. Leconte, N., Javvaji, S., An, J. & Jung, J. Relaxation effects in twisted bilayer graphene: a multi-scale approach. Preprint at (2019).

  32. Kane, C. L. & Mele, E. J. Quantum spin Hall effect in graphene. Phys. Rev. Lett. 95, 226801 (2005).

    ADS  Article  Google Scholar 

  33. Plimpton, S. Fast parallel algorithms for short-range molecular dynamics. J. Comput. Phys. 117, 1–19 (1995).

    ADS  Article  Google Scholar 

  34. Leconte, N., Jung, J., Lebègue, S. & Gould, T. Moiré-pattern interlayer potentials in van der Waals materials in the random-phase approximation. Phys. Rev. B 96, 195431 (2017).

    ADS  Article  Google Scholar 

  35. Lehoucq, R. B., Sorensen, D. C. & Yang, C. Solution of Large Scale Eigenvalue Problems by Implicitly Restarted Arnoldi Methods. ARPACK Users’ Guide (SIAM, 1998).

  36. Jung, J. & MacDonald, A. H. Tight-binding model for graphene π-bands from maximally localized Wannier functions. Phys. Rev. B 87, 195450 (2013).

    ADS  Article  Google Scholar 

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We gratefully acknowledge the usage of the MNCF and NNFC facilities at CeNSE, IISc. U.C. acknowledges funding from SERB via grants nos. ECR/2017/001566 and SPG/2020/000164. N.L. was supported by the Korean National Research Foundation grant no. NRF-2020R1A2C3009142 and A.S. by grant no. NRF-2020R1A5A1016518. D.L. was supported by the Korean Ministry of Land, Infrastructure and Transport (MOLIT) from the Innovative Talent Education Program for Smart Cities. J.J. was supported by the Samsung Science and Technology Foundation under project no. SSTF-BAA1802-06. We acknowledge computational support from KISTI through grant no. KSC-2021-CRE-0389 and the resources of the Urban Big Data and AI Institute (UBAI) at the University of Seoul and the network support from KREONET. K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by the MEXT, Japan (grant no. JPMXP0112101001) and JSPS KAKENHI (grants nos. JP19H05790 and JP20H00354).

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Authors and Affiliations



S.B. fabricated the devices, performed the measurements and analysed the data. B.G., M.P. and P.S.M. assisted with measurements and analysis. K.W. and T.T. grew the hBN crystals. A.G. and U.C. advised on experiments. N.L., S.A., D.L. and J.J. performed the theoretical calculations. S.B., N.L., J.J. and U.C. wrote the manuscript, with input from other authors.

Corresponding authors

Correspondence to Saisab Bhowmik, Jeil Jung or U. Chandni.

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Extended data

Extended Data Fig. 1 Low-field Hall data in device D1, θ ≈ 1.140.

a. nH − ν plot for B = 0.3 − 1.2 T. b. σxy as a function of ν for the same range of B. The zero crossings at ν = 0.5, 1 and 3.5 and reset at ν = 2 and 3 are robust with B.

Source data

Extended Data Fig. 2 Low-field Hall data in device D2, θ ≈ 1.160.

a. nH − ν plot for B = 0.2 − 2 T. The sign change at ν = 3.5 appears at the lowest B-field of 0.2 T. In addition, the reset at charge carriers is observed at ν = ± 2. b. σxy as a function of ν for the same range of B.

Extended Data Fig. 3 Hall conductivity at B = 9 T in device D2.

σxy shows plateaus as σxy = Ce2/h associated with the minima in σxx. Different color bars (blue for the CNP, green for ν = 1, ± 2, 3 and red for ν = − 0.5) have been used to show the sequence of symmetry-broken nearly quantized states nucleating from several partial fillings of flat bands.

Extended Data Fig. 4 Magneto-thermoelectricity measurements in device D1.

Thermoelectric voltage V measured at B = 0, 1, 1.5, and 2 T and T = 3 K for a heating current of 300 nA. The feature at ν = 3.5 is clearly visible at all B. A tiny shoulder develops in the vicinity of ν = 0.5, that is particularly prominent at B = 2 T.

Source data

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Supplementary Figs. 1–8.

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Bhowmik, S., Ghawri, B., Leconte, N. et al. Broken-symmetry states at half-integer band fillings in twisted bilayer graphene. Nat. Phys. 18, 639–643 (2022).

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