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.

Quantum anomalous Hall octet driven by orbital magnetism in bilayer graphene

Nature volume 598, pages 53–58 (2021)Cite this article

Subjects

Abstract

The quantum anomalous Hall (QAH) effect—a macroscopic manifestation of chiral band topology at zero magnetic field—has been experimentally realized only by the magnetic doping of topological insulators1,2,3 and the delicate design of moiré heterostructures4,5,6,7,8. However, the seemingly simple bilayer graphene without magnetic doping or moiré engineering has long been predicted to host competing ordered states with QAH effects9,10,11. Here we explore states in bilayer graphene with a conductance of 2 e2 h−1 (where e is the electronic charge and h is Planck’s constant) that not only survive down to anomalously small magnetic fields and up to temperatures of five kelvin but also exhibit magnetic hysteresis. Together, the experimental signatures provide compelling evidence for orbital-magnetism-driven QAH behaviour that is tunable via electric and magnetic fields as well as carrier sign. The observed octet of QAH phases is distinct from previous observations owing to its peculiar ferrimagnetic and ferrielectric order that is characterized by quantized anomalous charge, spin, valley and spin–valley Hall behaviour9.

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

Relevant articles

Open Access articles citing this article.

Access options

Rent or buy this article

Prices vary by article type

from$1.95

to$39.95

Learn more

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Exchange-interaction-driven quantum Hall states in dually gated, freestanding bilayer graphene.
Fig. 2: Extraordinary stability of the tunable ν = ±2 quantum Hall states towards zero magnetic field.
Fig. 3: Magnetic hysteresis observable in the quantum anomalous Hall ν = −2 in bilayer graphene.
Fig. 4: Temperature dependence of the ν = ±2 and ν = ±4 states show distinct electric field dependence.

Data availability

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

References

  1. Chang, C.-Z. et al. Experimental observation of the quantum anomalous Hall effect in a magnetic topological insulator. Science 340, 167–170 (2013).

    Article  ADS  CAS  Google Scholar 

  2. Tenasini, G. et al. Giant anomalous Hall effect in quasi-two-dimensional layered antiferromagnet Co1/3NbS2. Phys. Rev. Res. 2 (2020).

  3. Zhao, Y.-F. et al. Tuning the Chern number in quantum anomalous Hall insulators. Nature 588, 419–423 (2020).

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  8. Chen, G. et al. Tunable correlated Chern insulator and ferromagnetism in a moiré superlattice. Nature 579, 56–61 (2020).

    Article  ADS  CAS  Google Scholar 

  9. Zhang, F., Jung, J., Fiete, G. A., Niu, Q. & MacDonald, A. H. Spontaneous quantum Hall states in chirally stacked few-layer graphene systems. Phys. Rev. Lett. 106, 156801 (2011).

    Article  ADS  Google Scholar 

  10. Zhang, F. Spontaneous chiral symmetry breaking in bilayer graphene. Synth. Met. 210, 9–18 (2015).

    Article  CAS  Google Scholar 

  11. Nandkishore, R. & Levitov, L. Quantum anomalous Hall state in bilayer graphene. Phys. Rev. B 82 (2010).

  12. Yu, R. et al. Quantized anomalous Hall effect in magnetic topological insulators. Science 329, 61–64 (2010).

    Article  ADS  CAS  Google Scholar 

  13. Zhang, F., Kane, C. L. & Mele, E. J. Surface state magnetization and chiral edge states on topological insulators. Phys. Rev. Lett. 110, 46404 (2013).

    Article  ADS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  15. Xiao, D., Yao, W., Niu, Q. Valley-contrasting physics in graphene: magnetic moment and topological transport. Phys. Rev. Lett. 99, 236809 (2007).

    Article  ADS  Google Scholar 

  16. Lee, Y. et al. Tunable valley splitting due to topological orbital magnetic moment in bilayer graphene quantum point contacts. Phys. Rev. Lett. 124, 126802 (2020).

    Article  ADS  CAS  Google Scholar 

  17. Ju, L. et al. Tunable excitons in bilayer graphene. Science 358, 907–910 (2017).

    Article  ADS  CAS  Google Scholar 

  18. Shi, Y. et al. Electronic phase separation in multilayer rhombohedral graphite. Nature 584, 210–214 (2020).

    Article  ADS  CAS  Google Scholar 

  19. Jiang, L. et al. Soliton-dependent plasmon reflection at bilayer graphene domain walls. Nat. Mater. 15, 840–844 (2016).

    Article  ADS  CAS  Google Scholar 

  20. Ju, L. et al. Topological valley transport at bilayer graphene domain walls. Nature 520, 650–655 (2015).

    Article  ADS  CAS  Google Scholar 

  21. Geisenhof, F. R. et al. Anisotropic strain-induced soliton movement changes stacking order and band structure of graphene multilayers. Implications for charge transport. ACS Appl. Nano Mater. 2, 6067–6075 (2019).

    Article  CAS  Google Scholar 

  22. Moser, J., Barreiro, A. & Bachtold, A. Current-induced cleaning of graphene. Appl. Phys. Lett. 91, 163513 (2007).

    Article  ADS  Google Scholar 

  23. Weitz, R. T., Allen, M. T., Feldman, B. E., Martin, J. & Yacoby, A. Broken-symmetry states in doubly gated suspended bilayer graphene. Science 330, 812–816 (2010).

    Article  ADS  CAS  Google Scholar 

  24. Velasco, J. et al. Transport spectroscopy of symmetry-broken insulating states in bilayer graphene. Nat. Nanotechnol. 7, 156–160 (2012).

    Article  ADS  CAS  Google Scholar 

  25. Freitag, F., Trbovic, J., Weiss, M. & Schönenberger, C. Spontaneously gapped ground state in suspended bilayer graphene. Phys. Rev. Lett. 108, 76602 (2012).

    Article  ADS  CAS  Google Scholar 

  26. Nam, Y., Ki, D.-K., Soler-Delgado, D. & Morpurgo, A. F. A family of finite-temperature electronic phase transitions in graphene multilayers. Science 362, 324–328 (2018).

    Article  ADS  CAS  Google Scholar 

  27. Nam, Y., Ki, D.-K., Soler-Delgado, D. & Morpurgo, A. F. Electron–hole collision limited transport in charge-neutral bilayer graphene. Nat. Phys. 13, 1207–1214 (2017).

    Article  CAS  Google Scholar 

  28. Zhao, Y., Cadden-Zimansky, P., Jiang, Z. & Kim, P. Symmetry breaking in the zero-energy Landau level in bilayer graphene. Phys. Rev. Lett. 104, 66801 (2010).

    Article  ADS  CAS  Google Scholar 

  29. Li, J., Tupikov, Y., Watanabe, K., Taniguchi, T. & Zhu, J. Effective Landau level diagram of bilayer graphene. Phys. Rev. Lett. 120, 47701 (2018).

    Article  ADS  CAS  Google Scholar 

  30. Martin, J., Feldman, B. E., Weitz, R. T., Allen, M. T. & Yacoby, A. Local compressibility measurements of correlated states in suspended bilayer graphene. Phys. Rev. Lett. 105, 256806 (2010).

    Article  ADS  CAS  Google Scholar 

  31. Lee, K. et al. Bilayer graphene. Chemical potential and quantum Hall ferromagnetism in bilayer graphene. Science 345, 58–61 (2014).

    Article  ADS  CAS  Google Scholar 

  32. Velasco, J. et al. Competing ordered states with filling factor two in bilayer graphene. Nat. Commun. 5, 4550 (2014).

    Article  ADS  CAS  Google Scholar 

  33. Shi, Y. et al. Energy gaps and layer polarization of integer and fractional quantum Hall states in bilayer graphene. Phys. Rev. Lett. 116, 56601 (2016).

    Article  ADS  Google Scholar 

  34. Zhang, J., Nandkishore, R. & Rossi, E. Disorder-tuned selection of order in bilayer graphene. Phys. Rev. B 91, 1–6 (2015).

    Google Scholar 

  35. Ki, D.-K. & Morpurgo, A. F. High-quality multiterminal suspended graphene devices. Nano Lett. 13, 5165–5170 (2013).

    Article  ADS  CAS  Google Scholar 

  36. Lee, D. S., Skákalová, V., Weitz, R. T., Klitzing, K. von & Smet, J. H. Transconductance fluctuations as a probe for interaction-induced quantum Hall states in graphene. Phys. Rev. Lett. 109, 56602 (2012).

    Article  ADS  Google Scholar 

  37. Kumar, M., Laitinen, A. & Hakonen, P. Unconventional fractional quantum Hall states and Wigner crystallization in suspended Corbino graphene. Nat. Commun. 9, 2776 (2018).

    Article  ADS  Google Scholar 

  38. Velasco, J. et al. Transport measurement of Landau level gaps in bilayer graphene with layer polarization control. Nano Lett. 14, 1324–1328 (2014).

    Article  ADS  CAS  Google Scholar 

  39. Ki, D.-K., Fal'ko, V. I., Abanin, D. A. & Morpurgo, A. F. Observation of even denominator fractional quantum Hall effect in suspended bilayer graphene. Nano Lett. 14, 2135–2139 (2014).

    Article  ADS  CAS  Google Scholar 

  40. Lian, B., Sun, X.-Q., Vaezi, A., Qi, X.-L. & Zhang, S.-C. Topological quantum computation based on chiral Majorana fermions. Proc. Natl Acad. Sci. USA 115, 10938–10942 (2018).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  41. Barlas, Y., Côté, R., Nomura, K. & MacDonald, A. H. Intra-Landau-level cyclotron resonance in bilayer graphene. Phys. Rev. Lett. 101, 97601 (2008).

    Article  ADS  Google Scholar 

  42. Zibrov, A. A. et al. Tunable interacting composite fermion phases in a half-filled bilayer-graphene Landau level. Nature 549, 360–364 (2017).

    Article  ADS  CAS  Google Scholar 

  43. Abanin, D. A. & Levitov, L. S. Conformal invariance and shape-dependent conductance of graphene samples. Phys. Rev. B 78 (2008).

Download references

Acknowledgements

R.T.W. and F.R.G. acknowledge funding from the Center for Nanoscience (CeNS) and by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy-EXC-2111-390814868 (MCQST). F.Z. and T.X. acknowledge support from the Army Research Office under grant number W911NF-18-1-0416 and by the National Science Foundation under grant numbers DMR-1945351 through the CAREER programme and DMR-1921581 through the DMREF programme.

Author information

Authors and Affiliations

  1. Physics of Nanosystems, Department of Physics, Ludwig-Maximilians-Universität München, Munich, Germany

    Fabian R. Geisenhof, Felix Winterer, Anna M. Seiler, Jakob Lenz & R. Thomas Weitz

  2. Department of Physics, University of Texas at Dallas, Richardson, TX, USA

    Tianyi Xu & Fan Zhang

  3. Center for Nanoscience (CeNS), Munich, Germany

    R. Thomas Weitz

  4. Munich Center for Quantum Science and Technology (MCQST), Munich, Germany

    R. Thomas Weitz

  5. 1st Physical Institute, Faculty of Physics, University of Göttingen, Göttingen, Germany

    R. Thomas Weitz

Authors
  1. Fabian R. Geisenhof
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Felix Winterer
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Anna M. Seiler
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jakob Lenz
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Tianyi Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Fan Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. R. Thomas Weitz
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

F.R.G. fabricated the devices and conducted the measurements and data analysis. F.Z. and T.X. contributed the theoretical part. All authors discussed and interpreted the data. R.T.W. supervised the experiments and the analysis. The manuscript was prepared by F.R.G., F.Z. and R.T.W with input from all authors.

Corresponding authors

Correspondence to Fan Zhang or R. Thomas Weitz.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature thanks Kayoung Lee, Sergey Slizovskiy and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

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

Extended data figures and tables

Extended Data Fig. 1 Current annealing, contact resistance and device quality.

a, Rd.c. as a function of Vd.c. during multiple annealing cycles. b, The resistance of quantum Hall plateaus shown as a function of inverse filling factor at B = 2 T and E⊥ = 20 mV nm−1. c, The conductance as a function of density for E⊥ = 0 mV nm−1 and 60 mV nm−1 at B = 0 T.

Extended Data Fig. 2 Representatives of the five competing broken symmetry ground states in bilayer graphene at n = E⊥ = B = 0.

a–e, Bottom panel: layer polarizations of the four spin-valley species. Top-left and top-right panels: bulk (classical) and edge (quantum) pictures of the corresponding spontaneous quantum Hall effect. Note that the edge roughness can produce couplings between counter-propagating edge states (of the same spin but different valleys) and thus gap them. Spin degeneracy is implicit in a and b. See the text for details. T and B refer to the top and bottom graphene layers, respectively.

Extended Data Fig. 3 Possible 'ALL' quantum anomalous Hall phases in bilayer graphene.

a–h, Eight different 'ALL' phases that can be classified by the layer polarizations of their two spin species, by which spin species being in which QAH or QVH phases, and by their charge Hall conductivities.

Extended Data Fig. 4 Additional measurements showing the electric and magnetic field dependence of the ν = ±2 state.

a–h, Maps of the conductance as a function of electric field and density for various magnetic fields. The dashed lines in e–h are guides to the eye, and the arrows indicate the range of negative electric field at which the ν = −2 state emerges. i, Conductance as a function of electric and magnetic fields at a fixed filling factor near ν = −2 (at exactly ν = −2.25). The black (white) dots indicating the maximum (minimum) electric field for the ν = −2 to emerge are extracted from the data shown in e–h. The dashed lines are guides to the eye, highlighting the region where the ν = −2 state emerges at negative electric fields.

Extended Data Fig. 5 Tracing quantum Hall states towards zero magnetic field.

Derivative of the differential conductance δσ/δn plotted as a function of magnetic field and density for various E⊥. The amount of conductance fluctuations corresponding to the ν = 0, −2 and −4 state are indicated by the number of white, blue and yellow lines in the top of each image.

Extended Data Fig. 6 Quantum transport data in a second device.

a, b, Maps of the conductance as a function of E⊥ and n for B = 0.2 T and 0.5 T, respectively. c, Conductance as a function of electric and magnetic field for fixed filling factor of ν = −2. The dashed lines indicate the region where the ν = −2 state at negative electric fields emerges with a conductance of 2 e2 h−1. d, Two-terminal conductance hysteresis measured for ν = −2 and E⊥ = −19 mV nm−1. The hysteresis loop area is shaded for clarity. The forward (reverse) sweep is shown in blue (red), as indicated by the arrows.

Extended Data Fig. 7 Magnetic hysteresis loop for different magnetic field ranges.

Two-terminal conductance hysteresis measured for different magnetic field ranges at ν = −2 and E⊥ = −17 mV nm−1. The hysteresis loop areas are shaded for clarity. The forward (reverse) sweep is shown in blue (red), as indicated by the arrows.

Extended Data Fig. 8 Temperature dependence of the quantum Hall states at B = 0.5 T.

Map of the conductance as a function of density and electric field for various temperatures. The dashed lines in the top left images indicate the position of the linecuts shown in Fig. 4 in the main manuscript.

Extended Data Table 1 Classification of the five competing broken symmetry ground states in bilayer graphene at n = E⊥ = B = 0
Full size table

Supplementary information

Rights and permissions

Reprints and Permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Geisenhof, F.R., Winterer, F., Seiler, A.M. et al. Quantum anomalous Hall octet driven by orbital magnetism in bilayer graphene. Nature 598, 53–58 (2021). https://doi.org/10.1038/s41586-021-03849-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41586-021-03849-w

This article is cited by

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Advanced 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