Control of the interlayer twist angle in two-dimensional van der Waals (vdW) heterostructures enables one to engineer a quasiperiodic moiré superlattice of tunable length scale1,2,3,4,5,6,7,8. In twisted bilayer graphene, the simple moiré superlattice band description suggests that the electronic bandwidth can be tuned to be comparable to the vdW interlayer interaction at a ‘magic angle’9, exhibiting strongly correlated behaviour. However, the vdW interlayer interaction can also cause significant structural reconstruction at the interface by favouring interlayer commensurability, which competes with the intralayer lattice distortion10,11,12,13,14,15,16. Here we report atomic-scale reconstruction in twisted bilayer graphene and its effect on the electronic structure. We find a gradual transition from an incommensurate moiré structure to an array of commensurate domains with soliton boundaries as we decrease the twist angle across the characteristic crossover angle, θc ≈ 1°. In the solitonic regime (θ < θc) where the atomic and electronic reconstruction become significant, a simple moiré band description breaks down and the secondary Dirac bands appear. On applying a transverse electric field, we observe electronic transport along the network of one-dimensional topological channels that surround the alternating triangular gapped domains. Atomic and electronic reconstruction at the vdW interface provide a new pathway to engineer the system with continuous tunability.

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We thank Y. Cao and P. Jarillo-Herrero for important discussions. The authors acknowledge the support of the Army Research Office (W911NF-14-1-0247) under the MURI programme. Part of the TEM analysis was supported by the Global Research Laboratory Program (2015K1A1A2033332) through the National Research Foundation of Korea (NRF). P.K. acknowledges partial support from the Gordon and Betty Moore Foundation’s EPiQS Initiative through grant GBMF4543 and the Lloyd Foundation. R.E. acknowledges support from the National Science Foundation Graduate Research Fellowship under grant no. DGE1745303. P.C. acknowledges support from the National Science Foundation under grant no. DMS-1819220. K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by the MEXT, Japan and the CREST (JPMJCR15F3), JST. Nanofabrication was performed at the Center for Nanoscale Systems at Harvard, supported in part by NSF NNIN award ECS-00335765.

Author information


  1. Department of Physics, Harvard University, Cambridge, MA, USA

    • Hyobin Yoo
    • , Rebecca Engelke
    • , Stephen Carr
    • , Shiang Fang
    • , Efthimios Kaxiras
    •  & Philip Kim
  2. Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, MN, USA

    • Kuan Zhang
    •  & Ellad B. Tadmor
  3. Department of Mathematics, University of Kansas, Lawrence, KS, USA

    • Paul Cazeaux
  4. Department of Materials Science and Engineering, University of Michigan, Ann Arbor, MI, USA

    • Suk Hyun Sung
    •  & Robert Hovden
  5. Institute for Quantum Computing and Department of Chemistry, University of Waterloo, Waterloo, Ontario, Canada

    • Adam W. Tsen
  6. National Institute for Materials Science, Ibaraki, Japan

    • Takashi Taniguchi
    •  & Kenji Watanabe
  7. Department of Physics and Astronomy, Seoul National University, Seoul, Republic of Korea

    • Gyu-Chul Yi
  8. Department of Materials Science and Engineering, Seoul National University, Seoul, Republic of Korea

    • Miyoung Kim
  9. School of Mathematics, University of Minnesota, Minneapolis, MN, USA

    • Mitchell Luskin
  10. John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA

    • Efthimios Kaxiras


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H.Y. and P.K. conceived the experiments. H.Y. and R.E. performed the experiments and analysed the data. S.C., S.F. and E.K. performed the density functional theory calculation. K.Z. and E.B.T. conceived and performed the theoretical and FEM analyses. P.C. and M.L. performed mathematical modelling analysis. S.H.S., R.H., A.W.T., G.-C.Y. and M.K. performed TEM data analysis. K.W. and T.T. provided bulk hBN crystals. H.Y., R.E. and P.K. wrote the manuscript. All authors contributed to the overall scientific interpretation and edited the manuscript.

Competing interests

The authors declare no competing interests.

Corresponding author

Correspondence to Philip Kim.

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