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.

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

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 options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Figure 1: QSH state in monolayer graphene in extreme tilted magnetic fields.
Figure 2: Nonlocal two-terminal transport in the QSH regime.
Figure 3: Symmetry-driven quantum phase transition.
Figure 4: Spin-textured edge states of the CAF phase.

References

  1. 1

    Ryu, S., Schnyder, A. P., Furusaki, A. & Ludwig, A. W. W. Topological insulators and superconductors: tenfold way and dimensional hierarchy. N. J. Phys. 12, 065010 (2010)

    Article  Google Scholar 

  2. 2

    Chen, X., Gu, Z.-C., Liu, Z.-X. & Wen, X.-G. Symmetry-protected topological orders in interacting bosonic systems. Science 338, 1604–1606 (2012)

    CAS  ADS  MathSciNet  Article  Google Scholar 

  3. 3

    Hasan, M. Z. & Kane, C. L. Topological insulators. Rev. Mod. Phys. 82, 3045–3067 (2010)

    CAS  ADS  Article  Google Scholar 

  4. 4

    Qi, X.-L. & Zhang, S.-C. Topological insulators and superconductors. Rev. Mod. Phys. 83, 1057–1110 (2011)

    CAS  ADS  Article  Google Scholar 

  5. 5

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

    CAS  ADS  Article  Google Scholar 

  6. 6

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

    CAS  ADS  Article  Google Scholar 

  7. 7

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

    ADS  Article  Google Scholar 

  8. 8

    Du, L., Knez, I., Sullivan, G. & Du, R.-R. Observation of quantum spin Hall states in InAs/GaSb bilayers under broken time-reversal symmetry. Preprint at http://arxiv.org/abs/1306.1925 (2013)

  9. 9

    Abanin, D. A., Lee, P. A. & Levitov, L. S. Spin-filtered edge states and quantum Hall effect in graphene. Phys. Rev. Lett. 96, 176803 (2006)

    ADS  Article  Google Scholar 

  10. 10

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

    CAS  ADS  Article  Google Scholar 

  11. 11

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

    ADS  Article  Google Scholar 

  12. 12

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

    ADS  Article  Google Scholar 

  13. 13

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

    ADS  Article  Google Scholar 

  14. 14

    Kharitonov, M. 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)

    ADS  Article  Google Scholar 

  15. 15

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

    ADS  Article  Google Scholar 

  16. 16

    Kindermann, M. Topological crystalline insulator phase in graphene multilayers. Preprint at http://arxiv.org/abs/1309.1667 (2013)

  17. 17

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

    ADS  Article  Google Scholar 

  18. 18

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

    ADS  Article  Google Scholar 

  19. 19

    Checkelsky, J. G., Li, L. & Ong, N. P. Zero-energy state in graphene in a high magnetic field. Phys. Rev. Lett. 100, 206801 (2008)

    ADS  Article  Google Scholar 

  20. 20

    Yang, K., Das Sarma, S. & MacDonald, A. H. Collective modes and skyrmion excitations in graphene SU(4) quantum Hall ferromagnets. Phys. Rev. B 74, 075423 (2006)

    ADS  Article  Google Scholar 

  21. 21

    Alicea, J. & Fisher, M. P. A. Graphene integer quantum Hall effect in the ferromagnetic and paramagnetic regimes. Phys. Rev. B 74, 075422 (2006)

    ADS  Article  Google Scholar 

  22. 22

    Nomura, K., Ryu, S. & Lee, D.-H. Field-induced Kosterlitz-Thouless transition in the N = 0 Landau level of graphene. Phys. Rev. Lett. 103, 216801 (2009)

    ADS  Article  Google Scholar 

  23. 23

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

    CAS  ADS  Article  Google Scholar 

  24. 24

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

    CAS  ADS  Article  Google Scholar 

  25. 25

    Mazo, V., Huang, C.-W., Shimshoni, E., Carr, S. T. & Fertig, H. A. Superfluid-insulator transition of quantum hall domain walls in bilayer graphene. Preprint at http://arxiv.org/abs/1309.1563. (2013)

  26. 26

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

    CAS  ADS  Article  Google Scholar 

  27. 27

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

    ADS  Article  Google Scholar 

  28. 28

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

    ADS  Article  Google Scholar 

  29. 29

    Abanin, D. A. & Levitov, L. S. Conformal invariance and shape-dependent conductance of graphene samples. Phys. Rev. B 78, 035416 (2008)

    ADS  Article  Google Scholar 

  30. 30

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

    CAS  ADS  Article  Google Scholar 

  31. 31

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

    CAS  ADS  Article  Google Scholar 

  32. 32

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

    CAS  ADS  Article  Google Scholar 

  33. 33

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

    Article  Google Scholar 

  34. 34

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

    ADS  Article  Google Scholar 

  35. 35

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

    CAS  ADS  Article  Google Scholar 

  36. 36

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

    CAS  ADS  Article  Google Scholar 

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

Affiliations

Authors

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.

Corresponding authors

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

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Extended data figures and tables

Extended Data Figure 1 Images of measured devices.

False-colour AFM images of the devices enumerated in Extended Data Table 1. Dashed lines outline the graphene boundary. Black scale bars correspond to 1 μm.

Extended Data Figure 2 Conductance as a function of B, BT and gate voltage for devices A, B and C.

Colouring of lines from blue to red indicates increasing BT, with B as indicated at the top of each panel.

Extended Data Figure 3 Gcnp as a function of B and BT for devices A, B and E.

Correspondingly higher values of BT are required to induce the transition for higher values of B. For device A, the curves correspond to B = 0.75, 1, 1.2, 1.4, 1.6, 2, 2.5, 3, 3.5 and 4 T (blue to red). For device B, the curves correspond to B = 1, 1.5, 2, 2.5, 3 and 3.5 T (blue to red). For device E, the curves correspond to B = 0.9, 1, 1.1, 1.2, 1.3, 1.4 and 1.5 T (blue to red).

Extended Data Figure 4 Nonlocal measurements for device C in the QSH and CAF regimes.

In the main text, evidence for conduction via edge states in the QSH and CAF regimes is provided by non-local transport measurements in device A (Figs 2b and 4b). Owing to conduction through counterpropagating edge states, interrupting an edge with a floating contact decreases the two-terminal conductance much more than would be expected in a diffusive transport model. Here we provide an additional example of this behaviour for device C. a, Schematic of distinct two-terminal measurement topologies with different numbers of floating contacts (open circles). b, QSH regime, B = 2.7 T and BT = 45 T. c, CAF regime, B = 5.9 T and BT = 45 T. Curves are colour-coded according to the measurement schematics, as in the main text. Owing to a small gate leak in one of the contacts, these specific non-local measurements underestimate the conductance by a scale factor that was adjusted for by fitting the ν = −1 plateau to a conductance of e2/h.

Extended Data Figure 5 Double conductance peaks in seven different devices.

A generic feature of the intermediate regime between the insulating and metallic QSH regimes is the appearance of double conductance peaks close to ν = 0. The figure shows two-terminal conductance versus back-gate voltage, VG. Purely perpendicular magnetic field only (BT = B, black lines) results in an insulating state at ν = 0. Increasing the total magnetic field while keeping the perpendicular component constant (BT > B, red lines), induces a transition to the CAF with an associated double conductance peak feature. Devices are ordered from left to right by descending aspect ratio.

Extended Data Figure 6 Temperature dependence of the charge-neutrality point conductivity for device B.

ac, Gate sweeps for device B at constant B = 2.5 T and BT = 2.5 (a), 26.5 (b) and 34.5 T (c). d, Conductance at the charge-neutrality point as a function of temperature for the data in ac. A clear insulating dependence (∂G/∂T > 0) is observed for B = BT. With increased BT, in the intermediate regime, the double conductance peaks between ν = 0 and ν = ±1 have a weakly metallic temperature dependence (∂G/∂T < 0) whereas Gcnp is very weakly insulating. In the QSH regime (BTB), where the conduction is along edge channels, the temperature dependence at ν = 0 is metallic.

Extended Data Figure 7 Schematic diagram of the capacitance bridge-on-a-chip in a tilted magnetic field.

The magnetic field points up in the diagram. Beige: sample stage, showing axis of rotation (red arrows). Purple: graphene sample mount. Blue: transistor mount with 90° bend. The HEMT is mounted on the face angled at 90° to the graphene sample mount and with the plane of its 2D conduction channel perpendicular to the sample-stage axis of rotation. A single wire bond connects the two mounts, from the graphite back gate to the balance point of the capacitance bridge. The transistor is gated by applying VG to the balance point/graphite back gate through a 100-MΩ chip resistor. Combined with the total capacitance of the balance point to ground (3 pF), this sets the low-frequency cut-off for the measurement at 1 kHz. The density of electrons in the graphene sample is determined by the d.c. voltage difference between the graphene sample and the graphite back gate, namely by Vs − VG. In the main text, this is compensated for and all capacitance measurements are shown as functions of the graphite gate voltage relative to grounded graphene. All components shown in black are at room temperature.

Extended Data Figure 8 Tilted-field magnetotransport in zero-field insulating monolayer graphene.

In a fraction of devices with the same geometry as those discussed in the main text, we find that, rather than a conductivity of e2/h at charge neutrality, these devices instead have insulating behaviour at the charge-neutrality point at zero applied magnetic field. We ascribe this insulating behaviour to the opening of a bandgap at the charge-neutrality point owing to the effect of an aligned hBN substrate31. The top panel shows the resistance of the device in zero magnetic field. This device has a resistance of 825 kΩ at the charge-neutrality point in zero magnetic field and at T = 0.3 K. As with the devices described in the main text, the insulating state becomes stronger in a perpendicular magnetic field. In the bottom panel, solid lines are gate sweeps at constant B = 1, 2 and 3 T and BT = B. Dashed lines are for the corresponding sequence with B = 1, 2 and 3 T but BT = 45 T. Data taken at 0.3 K. Semiconducting graphene samples do not show any sign of QSH-type physics, at least up to 45 T. Even for B = 1 T and BT = 45 T, the conductance at the charge-neutrality point increases only slightly, from 0.02e2/h with zero in-plane field to 0.14e2/h with BT = 45 T. This is understandable, because, even neglecting interaction effects, closing a moiré-induced band gap of Δ = 10 meV requires a Zeeman field of nearly Δ/B ≈ 85 T. We note that in these samples, the ground state at BT = B may not be an antiferromagnet.

Extended Data Table 1 Physical parameters of measured devices

PowerPoint slides

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Young, A., Sanchez-Yamagishi, J., Hunt, B. et al. Tunable symmetry breaking and helical edge transport in a graphene quantum spin Hall state. Nature 505, 528–532 (2014). https://doi.org/10.1038/nature12800

Download citation

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.

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