Atomic and electronic reconstruction at the van der Waals interface in twisted bilayer graphene


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.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: Atomic-scale reconstruction in TBG with a controlled twist angle.
Fig. 2: Electronic reconstruction in TBG.
Fig. 3: Transport properties of BLG with a controlled twist angle.

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.


  1. 1.

    Li, G. et al. Observation of Van Hove singularities in twisted graphene layers. Nat. Phys. 6, 109–113 (2010).

    Article  Google Scholar 

  2. 2.

    Ponomarenko, L. et al. Cloning of Dirac fermions in graphene superlattices. Nature 497, 594–597 (2013).

    CAS  Article  Google Scholar 

  3. 3.

    Dean, C. R. et al. Hofstadter’s butterfly and the fractal quantum Hall effect in moiré superlattices. Nature 497, 598–602 (2013).

    CAS  Article  Google Scholar 

  4. 4.

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

    CAS  Article  Google Scholar 

  5. 5.

    Cao, Y. et al. Superlattice-induced insulating states and valley-protected orbits in twisted bilayer graphene. Phys. Rev. Lett. 117, 116804 (2016).

    CAS  Article  Google Scholar 

  6. 6.

    Kim, K. et al. Tunable moiré bands and strong correlations in small-twist-angle bilayer graphene. Proc. Natl Acad. Sci. USA 114, 3364–3369 (2017).

    CAS  Article  Google Scholar 

  7. 7.

    Cao, Y. et al. Unconventional superconductivity in magic-angle graphene superlattices. Nature 556, 43–50 (2018).

    CAS  Article  Google Scholar 

  8. 8.

    Cao, Y. et al. Correlated insulator behaviour at half-filling in magic-angle graphene superlattices. Nature 556, 80–84 (2018).

    CAS  Article  Google Scholar 

  9. 9.

    Bistritzer, R. & MacDonald, A. H. Moiré bands in twisted double-layer graphene. Proc. Natl Acad. Sci. USA 108, 12233–12237 (2011).

    CAS  Article  Google Scholar 

  10. 10.

    Woods, C. et al. Commensurate–incommensurate transition in graphene on hexagonal boron nitride. Nat. Phys. 10, 451–456 (2014).

    CAS  Article  Google Scholar 

  11. 11.

    Kim, N. Y. et al. Evidence of local commensurate state with lattice match of graphene on hexagonal boron nitride. ACS Nano 11, 7084–7090 (2017).

    CAS  Article  Google Scholar 

  12. 12.

    Van Wijk, M., Schuring, A., Katsnelson, M. & Fasolino, A. Relaxation of moiré patterns for slightly misaligned identical lattices: graphene on graphite. 2D Materials 2, 034010 (2015).

    Article  Google Scholar 

  13. 13.

    Dai, S., Xiang, Y. & Srolovitz, D. J. Twisted bilayer graphene: moiré with a twist. Nano Lett. 16, 5923–5927 (2016).

    CAS  Article  Google Scholar 

  14. 14.

    Nam, N. N. T. & Koshino, M. Lattice relaxation and energy band modulation in twisted bilayer graphene. Phys. Rev. B 96, 075311 (2017).

    Article  Google Scholar 

  15. 15.

    Gargiulo, F. & Yazyev, O. V. Structural and electronic transformation in low-angle twisted bilayer graphene. 2D Materials 5, 015019 (2018).

    Article  Google Scholar 

  16. 16.

    Zhang, K. & Tadmor, E. B. Structural and electron diffraction scaling of twisted graphene bilayers. J. Mech. Phys. Solids 112, 225–238 (2018).

    Article  Google Scholar 

  17. 17.

    Koma, A. Van der Waals epitaxy—a new epitaxial growth method for a highly lattice-mismatched system. Thin Solid Films 216, 72–76 (1992).

    CAS  Article  Google Scholar 

  18. 18.

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

    CAS  Article  Google Scholar 

  19. 19.

    Lin, J. et al. AC/AB stacking boundaries in bilayer graphene. Nano Lett. 13, 3262–3268 (2013).

    CAS  Article  Google Scholar 

  20. 20.

    Butz, B. et al. Dislocations in bilayer graphene. Nature 505, 533–537 (2014).

    CAS  Article  Google Scholar 

  21. 21.

    Yuk, J. M. et al. Superstructural defects and superlattice domains in stacked graphene. Carbon 80, 755–761 (2014).

    CAS  Article  Google Scholar 

  22. 22.

    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).

    CAS  Article  Google Scholar 

  23. 23.

    Vaezi, A., Liang, Y., 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 

  24. 24.

    Ju, L. et al. Topological valley transport at bilayer graphene domain walls. Nature 520, 650–655 (2015).

    CAS  Article  Google Scholar 

  25. 25.

    Huang, S. et al. Topologically protected helical states in minimally twisted bilayer graphene. Phys. Rev. Lett. 121, 037702 (2018).

    CAS  Article  Google Scholar 

  26. 26.

    San-Jose, P. & Prada, E. Helical networks in twisted bilayer graphene under interlayer bias. Phys. Rev. B 88, 121408 (2013).

    Article  Google Scholar 

  27. 27.

    Anđelković, M., Covaci, L. & Peeters, F. M. DC conductivity of twisted bilayer graphene: Angle-dependent transport properties and effects of disorder. Phys. Rev. Mater. 2, 034004 (2018).

    Article  Google Scholar 

  28. 28.

    Li, J. et al. Gate-controlled topological conducting channels in bilayer graphene. Nat. Nanotechnol. 11, 1060–1065 (2016).

    CAS  Article  Google Scholar 

  29. 29.

    Rickhaus, P. et al. Transport through a network of topological channels in twisted bilayer graphene. Nano Lett. 18, 6725–6730 (2018).

    CAS  Article  Google Scholar 

  30. 30.

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

    Article  Google Scholar 

  31. 31.

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

    Article  Google Scholar 

  32. 32.

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

    CAS  Article  Google Scholar 

  33. 33.

    Dos Santos, J. L., Peres, N. & Neto, A. C. Graphene bilayer with a twist: Electronic structure. Phys. Rev. Lett. 99, 256802 (2007).

    Article  Google Scholar 

  34. 34.

    Sanchez-Yamagishi, J. D. et al. Quantum Hall effect, screening, and layer-polarized insulating states in twisted bilayer graphene. Phys. Rev. Lett. 108, 076601 (2012).

    Article  Google Scholar 

  35. 35.

    Hofstadter, D. R. Energy levels and wave functions of Bloch electrons in rational and irrational magnetic fields. Phys. Rev. B 14, 2239–2249 (1976).

    CAS  Article  Google Scholar 

  36. 36.

    Brown, L. et al. Twinning and twisting of tri- and bilayer graphene. Nano Lett. 12, 1609–1615 (2012).

    CAS  Article  Google Scholar 

  37. 37.

    Zhang, K. & Tadmor, E. B. Energy and moiré patterns in 2D bilayers in translation and rotation: A study using an efficient discrete-continuum interlayer potential. Extreme Mech. Lett. 14, 16–22 (2017).

    Article  Google Scholar 

  38. 38.

    Zhang, K. & Arroyo, M. Understanding and strain-engineering wrinkle networks in supported graphene through simulations. J. Mech. Phys. Solids 72, 61–74 (2014).

    CAS  Article  Google Scholar 

  39. 39.

    Zhang, K. & Arroyo, M. Coexistence of wrinkles and blisters in supported graphene. Extreme Mech. Lett. 14, 23–30 (2017).

    Article  Google Scholar 

  40. 40.

    Kolmogorov, A. N. & Crespi, V. H. Registry-dependent interlayer potential for graphitic systems. Phys. Rev. B 71, 235415 (2005).

    Article  Google Scholar 

  41. 41.

    Fang, S. & Kaxiras, E. Electronic structure theory of weakly interacting bilayers. Phys. Rev. B 93, 235153 (2016).

    Article  Google Scholar 

  42. 42.

    Carr, S., Fang, S., Jarillo-Herrero, P. & Kaxiras, E. Pressure dependence of the magic twist angle in graphene superlattices. Phys. Rev. B 98, 085144 (2018).

    CAS  Article  Google Scholar 

  43. 43.

    Massatt, D., Carr, S., Luskin, M. & Ortner, C. Incommensurate heterostructures in momentum space. Multiscale Model. Simul. 16, 429–451 (2018).

    Article  Google Scholar 

  44. 44.

    Lehmann, G. & Taut, M. On the numerical calculation of the density of states and related properties. Phys. Status Solidi b 54, 469–477 (1972).

    CAS  Article  Google Scholar 

  45. 45.

    Carr, S. et al. Relaxation and domain formation in incommensurate two-dimensional heterostructures. Phys. Rev. B 98, 224102 (2018).

    CAS  Article  Google Scholar 

  46. 46.

    Zhou, S., Han, J., Dai, S., Sun, J. & Srolovitz, D. J. van der Waals bilayer energetics: Generalized stacking-fault energy of graphene, boron nitride, and graphene/boron nitride bilayers. Phys. Rev. B 92, 155438 (2015).

    Article  Google Scholar 

  47. 47.

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

    CAS  Article  Google Scholar 

Download references


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




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.

Corresponding author

Correspondence to Philip Kim.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary Figures 1–10, Supplementary References 1–19

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Yoo, H., Engelke, R., Carr, S. et al. Atomic and electronic reconstruction at the van der Waals interface in twisted bilayer graphene. Nat. Mater. 18, 448–453 (2019).

Download citation

Further reading


Sign up for the Nature Briefing newsletter for a daily update on COVID-19 science.
Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing