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.
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McCann, E. Asymmetry gap in the electronic band structure of bilayer graphene. Phys. Rev. B 74, 161403 (2006)
Castro, E. V. et al. Biased bilayer graphene: semiconductor with a gap tunable by the electric field effect. Phys. Rev. Lett. 99, 216802 (2007)
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)
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)
Zhang, Y. B. et al. Direct observation of a widely tunable bandgap in bilayer graphene. Nature 459, 820–823 (2009)
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)
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)
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)
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)
Yan, J. & Fuhrer, M. S. Charge transport in dual gated bilayer graphene with Corbino geometry. Nano Lett. 10, 4521–4525 (2010)
Martin, I., Blanter, Y. M. & Morpurgo, A. F. Topological confinement in bilayer graphene. Phys. Rev. Lett. 100, 036804 (2008)
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)
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)
Keilmann, F. & Hillenbrand, R. Near-field microscopy by elastic light scattering from a tip. Phil. Trans. R. Soc. A 362, 787–805 (2004)
Chen, J. N. et al. Optical nano-imaging of gate-tunable graphene plasmons. Nature 487, 77–81 (2012)
Fei, Z. et al. Gate-tuning of graphene plasmons revealed by infrared nano-imaging. Nature 487, 82–85 (2012)
Novoselov, K. S. et al. Unconventional quantum Hall effect and Berry's phase of 2π in bilayer graphene. Nature Phys. 2, 177–180 (2006)
Kane, C. L. & Mele, E. J. Quantum spin Hall effect in graphene. Phys. Rev. Lett. 95, 226801 (2005)
Konig, M. et al. Quantum spin hall insulator state in HgTe quantum wells. Science 318, 766–770 (2007)
Wen, X. G. Symmetry-protected topological phases in noninteracting fermion systems. Phys. Rev. B 85, 085103 (2012)
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)
Velasco, J. et al. Transport spectroscopy of symmetry-broken insulating states in bilayer graphene. Nature Nanotechnol. 7, 156–160 (2012)
Maher, P. et al. Evidence for a spin phase transition at charge neutrality in bilayer graphene. Nature Phys. 9, 154–158 (2013)
Alden, J. S. et al. Strain solitons and topological defects in bilayer graphene. Proc. Natl Acad. Sci. USA 110, 11256–11260 (2013)
Butz, B. et al. Dislocations in bilayer graphene. Nature 505, 533–537 (2013)
Min, H. K. & MacDonald, A. H. Electronic structure of multilayer graphene. Prog. Theor. Phys. 176 (Suppl.). 227–252 (2008)
Lui, C. H. et al. Imaging stacking order in few-layer graphene. Nano Lett. 11, 164–169 (2011)
Datta, S. Electronic Transport in Mesoscopic Systems Ch. 2 (Cambridge Univ. Press, 1995)
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)
Wang, L. et al. One-dimensional electrical contact to a two-dimensional material. Science 342, 614–617 (2013)
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)
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)
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.
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.
a–d, Gate-dependent resistance R for three bilayer graphene devices with one domain wall (a–c) 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 a–c (∼8 kΩ in d). The dashed lines indicate the saturated conductance values. e–h, 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).
Data in left panels are from one graphene flake, data in right panels are from another. a–d, 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. e–h, 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.
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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
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