Letter | Published:

Tunable symmetry breaking and helical edge transport in a graphene quantum spin Hall state

Nature volume 505, pages 528532 (23 January 2014) | Download Citation

Abstract

Low-dimensional electronic systems have traditionally been obtained by electrostatically confining electrons, either in heterostructures or in intrinsically nanoscale materials such as single molecules, nanowires and graphene. Recently, a new method has emerged with the recognition that symmetry-protected topological (SPT) phases1,2, which occur in systems with an energy gap to quasiparticle excitations (such as insulators or superconductors), can host robust surface states that remain gapless as long as the relevant global symmetry remains unbroken. The nature of the charge carriers in SPT surface states is intimately tied to the symmetry of the bulk, resulting in one- and two-dimensional electronic systems with novel properties. For example, time reversal symmetry endows the massless charge carriers on the surface of a three-dimensional topological insulator with helicity, fixing the orientation of their spin relative to their momentum3,4. Weakly breaking this symmetry generates a gap on the surface5, resulting in charge carriers with finite effective mass and exotic spin textures6. Analogous manipulations have yet to be demonstrated in two-dimensional topological insulators, where the primary example of a SPT phase is the quantum spin Hall state7,8. Here we demonstrate experimentally that charge-neutral monolayer graphene has a quantum spin Hall state9,10 when it is subjected to a very large magnetic field angled with respect to the graphene plane. In contrast to time-reversal-symmetric systems7, this state is protected by a symmetry of planar spin rotations that emerges as electron spins in a half-filled Landau level are polarized by the large magnetic field. The properties of the resulting helical edge states can be modulated by balancing the applied field against an intrinsic antiferromagnetic instability11,12,13, which tends to spontaneously break the spin-rotation symmetry. In the resulting canted antiferromagnetic state, we observe transport signatures of gapped edge states, which constitute a new kind of one-dimensional electronic system with a tunable bandgap and an associated spin texture14.

Access optionsAccess options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

References

  1. 1.

    , , & Topological insulators and superconductors: tenfold way and dimensional hierarchy. N. J. Phys. 12, 065010 (2010)

  2. 2.

    , , & Symmetry-protected topological orders in interacting bosonic systems. Science 338, 1604–1606 (2012)

  3. 3.

    & Topological insulators. Rev. Mod. Phys. 82, 3045–3067 (2010)

  4. 4.

    & Topological insulators and superconductors. Rev. Mod. Phys. 83, 1057–1110 (2011)

  5. 5.

    et al. Massive Dirac fermion on the surface of a magnetically doped topological insulator. Science 329, 659–662 (2010)

  6. 6.

    et al. Hedgehog spin texture and Berry’s phase tuning in a magnetic topological insulator. Nature Phys. 8, 616–622 (2012)

  7. 7.

    et al. Quantum spin Hall insulator state in HgTe quantum wells. Science 318, 766–770 (2007)

  8. 8.

    , , & Observation of quantum spin Hall states in InAs/GaSb bilayers under broken time-reversal symmetry. Preprint at (2013)

  9. 9.

    , & Spin-filtered edge states and quantum Hall effect in graphene. Phys. Rev. Lett. 96, 176803 (2006)

  10. 10.

    & Luttinger liquid at the edge of undoped graphene in a strong magnetic field. Phys. Rev. Lett. 97, 116805 (2006)

  11. 11.

    Theory of integer quantum Hall effect in graphene. Phys. Rev. B 75, 165411 (2007)

  12. 12.

    & Theory of the magnetic-field-induced insulator in neutral graphene sheets. Phys. Rev. B 80, 235417 (2009)

  13. 13.

    Phase diagram for the ν = 0 quantum Hall state in monolayer graphene. Phys. Rev. B 85, 155439 (2012)

  14. 14.

    Edge excitations of the canted antiferromagnetic phase of the ν = 0 quantum Hall state in graphene: a simplified analysis. Phys. Rev. B 86, 075450 (2012)

  15. 15.

    et al. Topological crystalline insulators in the SnTe material class. Nature Commun. 3, 982 (2012)

  16. 16.

    Topological crystalline insulator phase in graphene multilayers. Preprint at (2013)

  17. 17.

    et al. Intrinsic and Rashba spin-orbit interactions in graphene sheets. Phys. Rev. B 74, 165310 (2006)

  18. 18.

    Condensed-matter simulation of a three-dimensional anomaly. Phys. Rev. Lett. 53, 2449–2452 (1984)

  19. 19.

    , & Zero-energy state in graphene in a high magnetic field. Phys. Rev. Lett. 100, 206801 (2008)

  20. 20.

    , & Collective modes and skyrmion excitations in graphene SU(4) quantum Hall ferromagnets. Phys. Rev. B 74, 075423 (2006)

  21. 21.

    & Graphene integer quantum Hall effect in the ferromagnetic and paramagnetic regimes. Phys. Rev. B 74, 075422 (2006)

  22. 22.

    , & Field-induced Kosterlitz-Thouless transition in the N = 0 Landau level of graphene. Phys. Rev. Lett. 103, 216801 (2009)

  23. 23.

    et al. Spin and valley quantum Hall ferromagnetism in graphene. Nature Phys. 8, 550–556 (2012)

  24. 24.

    et al. Evidence for a spin phase transition at charge neutrality in bilayer graphene. Nature Phys. 9, 154–158 (2013)

  25. 25.

    , , , & Superfluid-insulator transition of quantum hall domain walls in bilayer graphene. Preprint at . (2013)

  26. 26.

    et al. Nonlocal transport in the quantum spin Hall state. Science 325, 294–297 (2009)

  27. 27.

    et al. Single valley Dirac fermions in zero-gap HgTe quantum wells. Nature Phys. 7, 418–422 (2011)

  28. 28.

    et al. Quantum spin Hall effect in a transition metal oxide Na2IrO3. Phys. Rev. Lett. 102, 256403 (2009)

  29. 29.

    & Conformal invariance and shape-dependent conductance of graphene samples. Phys. Rev. B 78, 035416 (2008)

  30. 30.

    et al. Giant Rashba splitting in graphene due to hybridization with gold. Nature Commun. 3, 1232 (2012)

  31. 31.

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

  32. 32.

    et al. Boron nitride substrates for high-quality graphene electronics. Nature Nanotechnol. 5, 722–726 (2010)

  33. 33.

    et al. Scanning gate microscopy on graphene: charge inhomogeneity and extrinsic doping. Nanotechnology 22, 295705 (2011)

  34. 34.

    et al. Mechanical cleaning of graphene. Appl. Phys. Lett. 100, 073110 (2012)

  35. 35.

    et al. Single-electron capacitance spectroscopy of discrete quantum levels. Phys. Rev. Lett. 68, 3088–3091 (1992)

  36. 36.

    , & Capacitance measurements of a quantized two-dimensional electron gas in the regime of the quantum Hall effect. Phys. Rev. B 31, 6597–6608 (1985)

Download references

Acknowledgements

We acknowledge discussions with D. Abanin, A. Akhmerov, C. Beenakker, L. Brey, L. Fu, M. Kharitonov, L. Levitov, P. Lee and J. Sau. B.H. and R.C.A. were funded by the BES Program of the Office of Science of the US DOE, contract no. FG02-08ER46514, and the Gordon and Betty Moore Foundation, through grant GBMF2931. J.D.S.-Y, and P.J.-H. were primarily supported by the US DOE, BES Office, Division of Materials Sciences and Engineering, under award DE-SC0001819. Early fabrication feasibility studies were supported by NSF Career Award no. DMR-0845287 and the ONR GATE MURI. This work made use of the MRSEC Shared Experimental Facilities supported by the NSF under award no. DMR-0819762 and of Harvard’s CNS, supported by the NSF under grant no. ECS-0335765. Some measurements were performed at the National High Magnetic Field Laboratory, which is supported by NSF Cooperative Agreement DMR-0654118, the State of Florida and the DOE. A.F.Y. acknowledges the support of the Pappalardo Fellowship in Physics.

Author information

Author notes

    • A. F. Young
    • , J. D. Sanchez-Yamagishi
    •  & B. Hunt

    These authors contributed equally to this work.

Affiliations

  1. Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

    • A. F. Young
    • , J. D. Sanchez-Yamagishi
    • , B. Hunt
    • , S. H. Choi
    • , R. C. Ashoori
    •  & P. Jarillo-Herrero
  2. Advanced Materials Laboratory, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan

    • K. Watanabe
    •  & T. Taniguchi

Authors

  1. Search for A. F. Young in:

  2. Search for J. D. Sanchez-Yamagishi in:

  3. Search for B. Hunt in:

  4. Search for S. H. Choi in:

  5. Search for K. Watanabe in:

  6. Search for T. Taniguchi in:

  7. Search for R. C. Ashoori in:

  8. Search for P. Jarillo-Herrero in:

Contributions

A.F.Y. and J.D.S.-Y. had the idea for the experiment. J.D.S.-Y. and S.H.C. fabricated the samples. A.F.Y., J.D.S.-Y. and B.H. performed the experiments, analysed the data and wrote the paper. T.T. and K.W. grew the crystals of hexagonal boron nitride. R.C.A. and P.J.-H. advised on experiments, data analysis and writing the paper.

Competing interests

The authors declare no competing financial interests.

Corresponding authors

Correspondence to A. F. Young or J. D. Sanchez-Yamagishi or B. Hunt.

Extended data

About this article

Publication history

Received

Accepted

Published

DOI

https://doi.org/10.1038/nature12800

Further reading

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.