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.

Topological valley transport at bilayer graphene domain walls

Abstract

Electron valley, a degree of freedom that is analogous to spin, can lead to novel topological phases in bilayer graphene. A tunable bandgap can be induced in bilayer graphene by an external electric field1,2,3,4,5, and such gapped bilayer graphene is predicted to be a topological insulating phase protected by no-valley mixing symmetry, featuring quantum valley Hall effects and chiral edge states6,7,8,9. Observation of such chiral edge states, however, is challenging because inter-valley scattering is induced by atomic-scale defects at real bilayer graphene edges10. Recent theoretical work11,12,13 has shown that domain walls between AB- and BA-stacked bilayer graphene can support protected chiral edge states of quantum valley Hall insulators. Here we report an experimental observation of ballistic (that is, with no scattering of electrons) conducting channels at bilayer graphene domain walls. We employ near-field infrared nanometre-scale microscopy (nanoscopy)14,15,16 to image in situ bilayer graphene layer-stacking domain walls on device substrates, and we fabricate dual-gated field effect transistors based on the domain walls. Unlike single-domain bilayer graphene, which shows gapped insulating behaviour under a vertical electrical field, bilayer graphene domain walls feature one-dimensional valley-polarized conducting channels with a ballistic length of about 400 nanometres at 4 kelvin. Such topologically protected one-dimensional chiral states at bilayer graphene domain walls open up opportunities for exploring unique topological phases and valley physics in graphene.

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: Imaging AB-BA domain walls in exfoliated bilayer graphene.
Figure 2: Infrared nanoscopy images of domains and domain walls in exfoliated mono-, bi- and trilayer graphene.
Figure 3: Dual-gated field-effect transistor devices on bilayer graphene with AB-BA domain walls and their electrical transport properties.
Figure 4: Conductivity of topologically protected chiral modes at AB-BA domain walls.

References

  1. 1

    McCann, E. Asymmetry gap in the electronic band structure of bilayer graphene. Phys. Rev. B 74, 161403 (2006)

    ADS  Article  Google Scholar 

  2. 2

    Castro, E. V. et al. Biased bilayer graphene: semiconductor with a gap tunable by the electric field effect. Phys. Rev. Lett. 99, 216802 (2007)

    ADS  Article  Google Scholar 

  3. 3

    Min, H. K., Sahu, B., Banerjee, S. K. & MacDonald, A. H. Ab initio theory of gate induced gaps in graphene bilayers. Phys. Rev. B 75, 155115 (2007)

    ADS  Article  Google Scholar 

  4. 4

    Oostinga, J. B., Heersche, H. B., Liu, X. L., Morpurgo, A. F. & Vandersypen, L. M. K. Gate-induced insulating state in bilayer graphene devices. Nature Mater. 7, 151–157 (2008)

    ADS  CAS  Article  Google Scholar 

  5. 5

    Zhang, Y. B. et al. Direct observation of a widely tunable bandgap in bilayer graphene. Nature 459, 820–823 (2009)

    ADS  CAS  Article  Google Scholar 

  6. 6

    Yao, W., Yang, S. A. & Niu, Q. Edge states in graphene: from gapped flat-band to gapless chiral modes. Phys. Rev. Lett. 102, 096801 (2009)

    ADS  Article  Google Scholar 

  7. 7

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

    ADS  Article  Google Scholar 

  8. 8

    Castro Neto, A. H., Guinea, F., Peres, N. M. R., Novoselov, K. S. & Geim, A. K. The electronic properties of graphene. Rev. Mod. Phys. 81, 109 (2009)

    ADS  CAS  Article  Google Scholar 

  9. 9

    Jung, J., Zhang, F., Qiao, Z. H. & MacDonald, A. H. Valley-Hall kink and edge states in multilayer graphene. Phys. Rev. B 84, 075418 (2011)

    ADS  Article  Google Scholar 

  10. 10

    Yan, J. & Fuhrer, M. S. Charge transport in dual gated bilayer graphene with Corbino geometry. Nano Lett. 10, 4521–4525 (2010)

    ADS  CAS  Article  Google Scholar 

  11. 11

    Martin, I., Blanter, Y. M. & Morpurgo, A. F. Topological confinement in bilayer graphene. Phys. Rev. Lett. 100, 036804 (2008)

    ADS  Article  Google Scholar 

  12. 12

    Zhang, F., MacDonald, A. H. & Mele, E. J. Valley Chern numbers and boundary modes in gapped bilayer graphene. Proc. Natl Acad. Sci. USA 110, 10546–10551 (2013)

    ADS  CAS  Article  Google Scholar 

  13. 13

    Vaezi, A., Liang, Y. F., Ngai, D. H., Yang, L. & Kim, E. A. Topological edge states at a tilt boundary in gated multilayer graphene. Phys. Rev. X 3, 021018 (2013)

    Google Scholar 

  14. 14

    Keilmann, F. & Hillenbrand, R. Near-field microscopy by elastic light scattering from a tip. Phil. Trans. R. Soc. A 362, 787–805 (2004)

    ADS  CAS  Article  Google Scholar 

  15. 15

    Chen, J. N. et al. Optical nano-imaging of gate-tunable graphene plasmons. Nature 487, 77–81 (2012)

    ADS  CAS  Article  Google Scholar 

  16. 16

    Fei, Z. et al. Gate-tuning of graphene plasmons revealed by infrared nano-imaging. Nature 487, 82–85 (2012)

    ADS  CAS  Article  Google Scholar 

  17. 17

    Novoselov, K. S. et al. Unconventional quantum Hall effect and Berry's phase of 2π in bilayer graphene. Nature Phys. 2, 177–180 (2006)

    ADS  Article  Google Scholar 

  18. 18

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

    ADS  CAS  Article  Google Scholar 

  19. 19

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

    ADS  Article  Google Scholar 

  20. 20

    Wen, X. G. Symmetry-protected topological phases in noninteracting fermion systems. Phys. Rev. B 85, 085103 (2012)

    ADS  Article  Google Scholar 

  21. 21

    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)

    ADS  CAS  Article  Google Scholar 

  22. 22

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

    ADS  CAS  Article  Google Scholar 

  23. 23

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

    ADS  CAS  Article  Google Scholar 

  24. 24

    Alden, J. S. et al. Strain solitons and topological defects in bilayer graphene. Proc. Natl Acad. Sci. USA 110, 11256–11260 (2013)

    ADS  CAS  Article  Google Scholar 

  25. 25

    Butz, B. et al. Dislocations in bilayer graphene. Nature 505, 533–537 (2013)

    ADS  Article  Google Scholar 

  26. 26

    Min, H. K. & MacDonald, A. H. Electronic structure of multilayer graphene. Prog. Theor. Phys. 176 (Suppl.). 227–252 (2008)

    CAS  Article  Google Scholar 

  27. 27

    Lui, C. H. et al. Imaging stacking order in few-layer graphene. Nano Lett. 11, 164–169 (2011)

    ADS  CAS  Article  Google Scholar 

  28. 28

    Datta, S. Electronic Transport in Mesoscopic Systems Ch. 2 (Cambridge Univ. Press, 1995)

    Book  Google Scholar 

  29. 29

    Gorbachev, R. V., Tikhonenko, F. V., Mayorov, A. S., Horsell, D. W. & Savchenko, A. K. Weak localization in bilayer graphene. Phys. Rev. Lett. 98, 176805 (2007)

    ADS  CAS  Article  Google Scholar 

  30. 30

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

    ADS  CAS  Article  Google Scholar 

  31. 31

    Lopes dos Santos, J. M. B., Peres, N. M. R. & Castro Neto, A. H. Graphene bilayer with a twist: electronic structure. Phys. Rev. Lett. 99, 256802 (2007)

    ADS  CAS  Article  Google Scholar 

  32. 32

    Mak, K. F., Sfeir, M. Y., Misewich, J. A. & Heinz, T. F. The evolution of electronic structure in few-layer graphene revealed by optical spectroscopy. Proc. Natl Acad. Sci. USA 107, 14999–15004 (2010)

    ADS  Article  Google Scholar 

Download references

Acknowledgements

We thank Y. Ye and H. Zhu for their help on electron-beam lithography, Y. Zeng and H. Chang for help with device fabrication, and M. Raschke for help with near-field infrared techniques. The optical and electrical measurements were supported by the Office of Basic Energy Science, Department of Energy under contract numbers DE-SC0003949 (Early Career Award), DE-AC02-05CH11231 (Materials Science Division SP2 programme and the Laboratory Directed Research and Development Program of Lawrence Berkeley National Laboratory). Device fabrication was supported by the Office of Naval Research (award N00014-13-1-0464). F.W. acknowledges support from a David and Lucile Packard fellowship. The Advanced Light Source is supported by the Director, Office of Science, Office of Basic Energy Sciences, of the US Department of Energy under contract number DE-AC02-05CH11231.

Author information

Affiliations

Authors

Contributions

F.W., L.J. and Z.S conceived the experiment, Z.S., C.J., H.A.B. and M.C.M. performed the near-field infrared nanoscopy and optical measurements, L.J., Y.L. and J.V. fabricated the dual-gated field-effect transistor devices, L.J., N.N. and C.O.-A. did the electrical transport measurements. F.W., J.A. and A.Z. supervised the project. All authors discussed the results and wrote the paper.

Corresponding author

Correspondence to Feng Wang.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Extended data figures and tables

Extended Data Figure 1 Electrical transport of dual-gated bilayer graphene devices with (left) and without (right) AB-BA domain walls.

ad, Gate-dependent resistance R for three bilayer graphene devices with one domain wall (ac) and one with two domain walls (d) at 4.2 K. The backgate voltage Vbg is varied from 0 V to 140 V with a step of 10 V, and the top gate voltage Vtg is swept continuously. The resistance peak in each trace corresponds to a CNP. The resistance at the CNP first increases and then saturates at 14 kΩ in ac (8 kΩ in d). The dashed lines indicate the saturated conductance values. eh, Gate-dependent resistance of four reference bilayer graphene devices without domain walls. The resistance at the CNP increases continuously at high Vbg owing to the opening of a bandgap, and reaches values much higher than that of corresponding devices with bilayer graphene domain walls (indicated by the dashed line).

Extended Data Figure 2 Length dependence of electrical transport of AB-BA domain walls.

Data in left panels are from one graphene flake, data in right panels are from another. ad, Gate-dependent resistance for four bilayer graphene devices fabricated on a long domain wall with channel lengths of 200 nm, 400 nm, 600 nm and 800 nm (defined by the top gate width), respectively. eh, Gate-dependent resistance for four bilayer graphene devices fabricated on another long domain wall with channel lengths of 200 nm, 400 nm, 600 nm and 800 nm respectively. The backgate voltage Vbg is varied from 0 to −140 V with a step of 10 V, and the top gate voltage Vtg is swept continuously. The resistance peak in each trace corresponds to a CNP. The resistance at the CNP first increases as the bandgap is opened in the bulk and then saturates at high Vbg, where the electrical transport is dominated by one-dimensional channels along the domain wall.

Extended Data Figure 3 Temperature-dependent electrical transport through bulk bilayer graphene and through the AB-BA domain wall.

The CNP resistance (Vbg = −140 V) of a bilayer graphene device without a domain wall (NDW, black line) increases by over 300 kΩ (2.5 times) as the temperature is decreased from 50 K to 1.8 K. In contrast, the CNP resistance (Vbg = −140 V) of a bilayer graphene device with domain wall (red line, the same device as in Extended Data Fig. 2c) increases by only 5 kΩ (50%) at the same temperature. The much weaker temperature dependence of the domain wall resistance arises from a metallic one-dimensional conducting channel.

PowerPoint slides

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Ju, L., Shi, Z., Nair, N. et al. Topological valley transport at bilayer graphene domain walls. Nature 520, 650–655 (2015). https://doi.org/10.1038/nature14364

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