Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Anomalous Hall effect at half filling in twisted bilayer graphene

Abstract

Magic-angle twisted bilayer graphene (tBLG) displays a variety of symmetry-broken phases, correlated Chern insulators, orbital magnetism and superconductivity1,2,3,4,5,6,7,8. In particular, the anomalous Hall effect has been observed when the bands are filled with an odd number of electrons per moiré unit cell5,6,9, indicating the emergence of a zero-field orbital magnetic state with spontaneously broken time-reversal symmetry10,11,12. Here we present measurements of two tBLG devices with twist angles slightly away from the magic angle and report the observation of the anomalous Hall effect at half filling of both the electron and hole moiré bands. We suggest that two factors—the increased band dispersion away from the magic angle, and substrate potentials from the encapsulating boron nitride—probably play critical roles in stabilizing a valley-polarized ground state at half filling. Our findings further expand the rich correlated phase diagram of tBLG, and indicate the need to develop a more complete understanding of its manifold of closely competing symmetry-breaking orders.

This is a preview of subscription content, access via your institution

Access options

Buy article

Get time limited or full article access on ReadCube.

$32.00

All prices are NET prices.

Fig. 1: The AHE at half filling in tBLG.
Fig. 2: Temperature dependence of the AHE in device D1.
Fig. 3: Symmetry-breaking at half filling and electrical switching of the magnetic state.
Fig. 4: Schematic illustration of candidate ground states with AHE at half filling.

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.

References

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

    ADS  Article  Google Scholar 

  3. Yankowitz, M. et al. Tuning superconductivity in twisted bilayer graphene. Science 363, 1059–1064 (2019).

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

  5. Sharpe, A. L. et al. Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene. Science 365, 605–608 (2019).

    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. Balents, L., Dean, C. R., Efetov, D. K. & Young, A. F. Superconductivity and strong correlations in moiré flat bands. Nat. Phys. 16, 725–733 (2020).

    Article  Google Scholar 

  8. Andrei, E. Y. & MacDonald, A. H. Graphene bilayers with a twist. Nat. Mater. 19, 1265–1275 (2020).

    ADS  Article  Google Scholar 

  9. Stepanov, P. et al. Competing zero-field Chern insulators in superconducting twisted bilayer graphene. Phys. Rev. Lett. 127, 197701 (2021).

    ADS  Article  Google Scholar 

  10. Zhang, Y.-A., Mao, D., Cao, Y., Jarillo-Herrero, P. & Senthil, T. Nearly flat Chern bands in moiré superlattices. Phys. Rev. B 99, 075127 (2019).

    ADS  Article  Google Scholar 

  11. Zhang, Y.-H., Mao, D. & Senthil, T. Twisted bilayer graphene aligned with hexagonal boron nitride: anomalous Hall effect and a lattice model. Phys. Rev. Res. 1, 033126 (2019).

    Article  Google Scholar 

  12. Bultinck, N., Chatterjee, S. & Zaletel, M. P. Mechanism for anomalous Hall ferromagnetism in twisted bilayer graphene. Phys. Rev. Lett. 124, 166601 (2020).

    ADS  MathSciNet  Article  Google Scholar 

  13. Bistritzer, R. & MacDonald, A. H. Moiré bands in twisted double-layer graphene. Proc. Natl Acad. Sci. USA 108, 12233–12237 (2011).

    ADS  Article  Google Scholar 

  14. Bultinck, N. et al. Ground state and hidden symmetry of magic-angle graphene at even integer filling. Phys. Rev. X 10, 031034 (2020).

    Google Scholar 

  15. Zhang, Y., Jiang, K., Wang, Z. & Zhang, F. Correlated insulating phases of twisted bilayer graphene at commensurate filling fractions: a Hartree–Fock study. Phys. Rev. B 102, 035136 (2020).

    ADS  Article  Google Scholar 

  16. Liu, J. & Dai, X. Theories for the correlated insulating states and quantum anomalous Hall effect phenomena in twisted bilayer graphene. Phys. Rev. B 103, 035427 (2021).

    ADS  Article  Google Scholar 

  17. 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 

  18. Lian, B. et al. Twisted bilayer graphene. IV. Exact insulator ground states and phase diagram. Phys. Rev. B 103, 205414 (2021).

    ADS  Article  Google Scholar 

  19. Kwan, Y. H. et al. Kekulé spiral order at all nonzero integer fillings in twisted bilayer graphene. Phys. Rev. X 11, 041063 (2021).

    Google Scholar 

  20. Wagner, G., Kwan, Y. H., Bultinck, N., Simon, S. H. & Parameswaran, S. A. Global phase diagram of the normal state of twisted bilayer graphene. Phys. Rev. Lett. 128, 156401 (2022).

    ADS  Article  Google Scholar 

  21. 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 

  22. Wong, D. et al. Cascade of electronic transitions in magic-angle twisted bilayer graphene. Nature 582, 198–202 (2020).

    ADS  Article  Google Scholar 

  23. Zondiner, U. et al. Cascade of phase transitions and dirac revivals in magic-angle graphene. Nature 582, 203–208 (2020).

    ADS  Article  Google Scholar 

  24. Polshyn, H. et al. Electrical switching of magnetic order in an orbital Chern insulator. Nature 588, 66–70 (2020).

    ADS  Article  Google Scholar 

  25. Grover, S. et al. Chern mosaic and Berry-curvature magnetism in magic-angle graphene. Nat. Phys. (2022). https://doi.org/10.1038/s41567-022-01635-7

  26. Zhu, J., Su, J.-J. & MacDonald, A. H. Voltage-controlled magnetic reversal in orbital Chern insulators. Phys. Rev. Lett. 125, 227702 (2020).

    ADS  Article  Google Scholar 

  27. Tschirhart, C. L. et al. Imaging orbital ferromagnetism in a moiré Chern insulator. Science 372, 1323–1327 (2021).

    ADS  Article  Google Scholar 

  28. Sharpe, A. L. et al. Evidence of orbital ferromagnetism in twisted bilayer graphene aligned to hexagonal boron nitride. Nano Lett. 21, 4299–4303 (2021).

    ADS  Article  Google Scholar 

  29. Khalaf, E., Ledwith, P. & Vishwanath, A. Symmetry constraints on superconductivity in twisted bilayer graphene: fractional vortices, 4e condensates or non-unitary pairing. Phys. Rev. B 105, 224508 (2020).

    ADS  Article  Google Scholar 

  30. Diez-Merida, J. et al. Magnetic Josephson junctions and superconducting diodes in magic angle twisted bilayer graphene. Preprint at https://arxiv.org/abs/2110.01067 (2021).

  31. Stepanov, P. et al. Untying the insulating and superconducting orders in magic-angle graphene. Nature 583, 375–378 (2020).

    ADS  Article  Google Scholar 

  32. Codecido, E. et al. Correlated insulating and superconducting states in twisted bilayer graphene below the magic angle. Sci. Adv. 5, eaaw9770 (2019).

    ADS  Article  Google Scholar 

  33. Saito, Y., Ge, J., Watanabe, K., Taniguchi, T. & Young, A. F. Independent superconductors and correlated insulators in twisted bilayer graphene. Nat. Phys. 16, 926–930 (2020).

    Article  Google Scholar 

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

    ADS  Article  Google Scholar 

  35. Wang, L. et al. One-dimensional electrical contact to a two-dimensional material. Science 342, 614–617 (2013).

    ADS  Article  Google Scholar 

  36. Hunt, B. et al. Massive Dirac fermions and Hofstadter butterfly in a van der Waals heterostructure. Science 340, 1427–1430 (2013).

    ADS  Article  Google Scholar 

  37. Shi, J., Zhu, J. & MacDonald, A. H. Moiré commensurability and the quantum anomalous Hall effect in twisted bilayer graphene on hexagonal boron nitride. Phys. Rev. B 103, 075122 (2021).

    ADS  Article  Google Scholar 

  38. Lin, X., Su, K. & Ni, J. Misalignment instability in magic-angle twisted bilayer graphene on hexagonal boron nitride. 2D Mater. 8, 025025 (2021).

    Article  Google Scholar 

  39. Mao, D. & Senthil, T. Quasiperiodicity, band topology and moiré graphene. Phys. Rev. B 103, 115110 (2021).

    ADS  Article  Google Scholar 

Download references

Acknowledgements

We thank Y. Zhang, N. Bultinck and Z.-D. Song for helpful discussions. This work was supported as part of Programmable Quantum Materials, an Energy Frontier Research Center funded by the US Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES), under award no. DE-SC0019443 to M.Y. and J.-H.C.; the Army Research Office under grant no. W911NF-20-1-0211 to M.Y.; and the Gordon and Betty Moore Foundation’s EPiQS Initiative, grant no. GBMF6759 to J.-H.C. J.-H.C. also acknowledges support from the David and Lucile Packard Foundation. M.Y. and J.-H.C. acknowledge support from the State of Washington-funded Clean Energy Institute. This research acknowledges the usage of a dilution refrigerator system that was provided by NSF DMR-1725221, and of the millikelvin optoelectronic quantum material laboratory supported by the M.J. Murdock Charitable Trust. 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. 19H05790, 20H00354 and 21H05233).

Author information

Authors and Affiliations

Authors

Contributions

C.-C.T. and X.M. fabricated the devices. C.-C.T., X.M. and Z.L. performed the measurements. K.W. and T.T. provided the bulk BN crystals. C.-C.T., X.M., Z.L., J.-H.C. and M.Y. analysed the data and wrote the paper.

Corresponding author

Correspondence to Matthew Yankowitz.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Physics thanks the anonymous reviewers for their contribution to the peer review of this work

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Extended Data Fig. 1 Optical micrographs of the devices.

a, Device D1. b, Device D2. The twist angle measured between neighboring pairs of contacts is also shown. The scale bars are 5 μm.

Extended Data Fig. 2 Electric-field-reversal of the magnetic state in Device D1.

a,b, ρxy acquired by sweeping ν from small to large values (a), and from large to small values (b), at fixed B and T = 20 mK. c,d, The same measurements performed at T = 1.5 K. At both temperatures, we observe hysteresis at low magnetic fields depending on the direction the doping is swept.

Source data

Extended Data Fig. 3 Possible alignment of tBLG and BN.

Optical micrographs of the completed heterostructures of a, Device D1 and b, Device D2 prior to device fabrication. The top and bottom BN flakes are outlined in green and blue dashed lines, respectively. Angular alignment between the tBLG and BN is estimated by comparing the orientation of the straight crystallographic edges of each. A representative graphene edge is denoted by the white dashed line, and the angular offset with a selected BN edge is denoted next to the corresponding black dashed lines. A few selected BN corners with modulo-30 angles are denoted by the solid black lines, establishing that these are likely zigzag or armchair edges. In both devices, the top BN and tBLG appear to have a 29–30 angular offset. This indicates a high likelihood of few-degree or smaller alignment of the graphene and top BN crystals, although there is inherent uncertainty in identifying perfect crystalline edges of graphene. The scale bars are 5 μm.

Extended Data Fig. 4 Thermal activation of the CNP in Device D1.

a, Resistivity of Device D1 at the CNP (ν = 0) measured as a function of temperature, exhibiting insulating behavior below approximately 25 K. The red curve is measured in a VTI down to 1.5 K, and the blue curve is measured in a dilution fridge down to 20 mk. b, The same data shown on an Arrhenius plot. The CNP exhibits a small region of (approximately) activated behavior. We extract the band gap, Δ = 2.2 meV, from the slope of the linear fit (red dashed line) using \(\rho \,\propto \,e^{\frac{\Delta }{2kT}}\), where k is the Boltzmann constant.

Source data

Extended Data Fig. 5 Transport measurements from additional contact pairs in Device D2.

ac, ρxx and df, ρxy Landau fan diagrams measured between different pairs of contacts corresponding to the contact labeling scheme in Extended Data Fig. 1b. The strength of the coexisting trivial insulating state at ν = − 2 varies substantially depending on the contact pair. gi, Measurements of the AHE near ν = − 2 acquired using the same contacts as the associated ρxy fans shown in (df). The data are acquired at the same gate voltage, which corresponds to a slightly different value of ν due to the twist angle disorder in the sample. The AHE is only observed in contact pairs A–F, despite the overall similarities of the Landau fans. For contacts B–G in particular, there is a large offset from ρxy = 0 due to mixing with ρxx. All measurements are acquired at T = 100 mK.

Source data

Extended Data Fig. 6 Landau fan diagrams from additional contact pairs in Device D1.

ac, Landau fan diagrams of ρxx and df, ρxy measured between different pairs of contacts corresponding to the contact labeling scheme in Extended Data Fig. 1a. All measurements are acquired at T = 20 mK.

Source data

Extended Data Fig. 7 AHE near ν = + 2 measured in additional contact pairs in Device D1.

a,b, ρxx and c,f, ρxy acquired with the contacts denoted above each plot, following the labeling scheme shown in Extended Data Fig. 1a. The data are all acquired at the same gate voltage, which corresponds to a slightly different value of ν due to the twist angle disorder in the sample. All measurements are acquired at T = 20 mK.

Source data

Extended Data Fig. 8 AHE versus doping in Device D2.

ρxy measured as B is swept back and forth around at selected values of ν around ν = − 2 in Device D2. The measurements are acquired at T = 100 mK.

Source data

Source data

Source Data Fig. 1

Source data for Fig. 1, all panels.

Source Data Fig. 2

Source data for Fig. 2, all panels.

Source Data Fig. 3

Source data for Fig. 3, panels a–b, d–g.

Source Data Extended Data Fig. 2

Source data for ED Fig. 2, all panels.

Source Data Extended Data Fig. 4

Source data for ED Fig. 4, all panels.

Source Data Extended Data Fig. 5

Source data for ED Fig. 5, all panels.

Source Data Extended Data Fig. 6

Source data for ED Fig. 6, all panels.

Source Data Extended Data Fig. 7

Source data for ED Fig. 7, all panels.

Source Data Extended Data Fig. 8

Source data for ED Fig. 8.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Tseng, CC., Ma, X., Liu, Z. et al. Anomalous Hall effect at half filling in twisted bilayer graphene. Nat. Phys. 18, 1038–1042 (2022). https://doi.org/10.1038/s41567-022-01697-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41567-022-01697-7

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing