Skip to main content

Thank you for visiting 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.

Domino-like stacking order switching in twisted monolayer–multilayer graphene


Atomic reconstruction has been widely observed in two-dimensional van der Waals structures with small twist angles1,2,3,4,5,6,7. This unusual behaviour leads to many novel phenomena, including strong electronic correlation, spontaneous ferromagnetism and topologically protected states1,5,8,9,10,11,12,13,14. Nevertheless, atomic reconstruction typically occurs spontaneously, exhibiting only one single stable state. Using conductive atomic force microscopy, here we show that, for small-angle twisted monolayer–multilayer graphene, there exist two metastable reconstruction states with distinct stacking orders and strain soliton structures. More importantly, we demonstrate that these two reconstruction states can be reversibly switched, and the switching can propagate spontaneously in an unusual domino-like fashion. Assisted by lattice-resolved conductive atomic force microscopy imaging and atomistic simulations, the detailed structure of the strain soliton networks has been identified and the associated propagation mechanism is attributed to the strong mechanical coupling among solitons. The fine structure of the bistable states is critical for understanding the unique properties of van der Waals structures with tiny twists, and the switching mechanism offers a viable means for manipulating their stacking states.

This is a preview of subscription content

Access options

Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: Reversible stacking order switching in twisted monolayer–multilayer graphene.
Fig. 2: Analysis of possible pathway for stacking order switching.
Fig. 3: MD simulation and DFT-based ACQ model calculation results.
Fig. 4: The switching and propagation of stacking order switching.

Data availability

The authors declare that the main data supporting the findings of this study are available within the paper. Extra data are available from the corresponding authors upon reasonable request. Source data are provided with this paper.


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

    CAS  Article  Google Scholar 

  2. Weston, A. et al. Atomic reconstruction in twisted bilayers of transition metal dichalcogenides. Nat. Nanotechnol. 15, 592–597 (2020).

    CAS  Article  Google Scholar 

  3. Kerelsky, A. et al. Maximized electron interactions at the magic angle in twisted bilayer graphene. Nature 572, 95–100 (2019).

    CAS  Article  Google Scholar 

  4. Jin, C. et al. Observation of moiré excitons in WSe2/WS2 heterostructure superlattices. Nature 567, 76–80 (2019).

    CAS  Article  Google Scholar 

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

    CAS  Article  Google Scholar 

  6. Andersen, T. I. et al. Excitons in a reconstructed moiré potential in twisted WSe2/WSe2 homobilayers. Nat. Mater. 20, 480–487 (2021).

    CAS  Article  Google Scholar 

  7. Rosenberger, M. R. et al. Twist angle-dependent atomic reconstruction and moiré patterns in transition metal dichalcogenide heterostructures. ACS Nano 14, 4550–4558 (2020).

    CAS  Article  Google Scholar 

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

    CAS  Google Scholar 

  10. 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 

  11. Sharpe, A. L. et al. Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene. Science 365, 605–608 (2019).

    CAS  Article  Google Scholar 

  12. Xu, S. G. et al. Giant oscillations in a triangular network of one-dimensional states in marginally twisted graphene. Nat. Commun. 10, 4008 (2019).

    CAS  Article  Google Scholar 

  13. Shimazaki, Y. et al. Strongly correlated electrons and hybrid excitons in a moiré heterostructure. Nature 580, 472–477 (2020).

    CAS  Article  Google Scholar 

  14. Walet, N. R. & Guinea, F. The emergence of one-dimensional channels in marginal-angle twisted bilayer graphene. 2D Mater. 7, 015023 (2019).

    Article  CAS  Google Scholar 

  15. Jiang, Y. et al. Charge order and broken rotational symmetry in magic-angle twisted bilayer graphene. Nature 573, 91–95 (2019).

    CAS  Article  Google Scholar 

  16. Xie, Y. et al. Spectroscopic signatures of many-body correlations in magic-angle twisted bilayer graphene. Nature 572, 101–105 (2019).

    CAS  Article  Google Scholar 

  17. Lu, X. et al. Superconductors, orbital magnets and correlated states in magic-angle bilayer graphene. Nature 574, 653–657 (2019).

    CAS  Article  Google Scholar 

  18. Park, J. M., Cao, Y., Watanabe, K., Taniguchi, T. & Jarillo-Herrero, P. Tunable strongly coupled superconductivity in magic-angle twisted trilayer graphene. Nature 590, 249–255 (2021).

    CAS  Article  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    CAS  Article  Google Scholar 

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

    Article  CAS  Google Scholar 

  22. 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 

  23. Cea, T., Walet, N. R. & Guinea, F. Twists and the electronic structure of graphitic materials. Nano Lett. 19, 8683–8689 (2019).

    CAS  Article  Google Scholar 

  24. Tsim, B., Nam, N. N. T. & Koshino, M. Perfect one-dimensional chiral states in biased twisted bilayer graphene. Phys. Rev. B 101, 125409 (2020).

    CAS  Article  Google Scholar 

  25. Zhang, S. et al. Abnormal conductivity in low-angle twisted bilayer graphene. Sci. Adv. 6, eabc5555 (2020).

    Article  Google Scholar 

  26. 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 

  27. Gong, L. et al. Reversible loss of Bernal stacking during the deformation of few-layer graphene in nanocomposites. ACS Nano 7, 7287–7294 (2013).

    CAS  Article  Google Scholar 

  28. Li, H. et al. Global control of stacking-order phase transition by doping and electric field in few-layer graphene. Nano Lett. 20, 3106–3112 (2020).

    CAS  Article  Google Scholar 

  29. Jiang, L. et al. Manipulation of domain-wall solitons in bi- and trilayer graphene. Nat. Nanotechnol. 13, 204–208 (2018).

    CAS  Article  Google Scholar 

  30. Geisenhof, F. R. et al. Anisotropic strain-induced soliton movement changes stacking order and band structure of graphene multilayers: implications for charge transport. ACS Appl. Nano Mater. 2, 6067–6075 (2019).

    CAS  Article  Google Scholar 

  31. Schweizer, P., Dolle, C. & Spiecker, E. In situ manipulation and switching of dislocations in bilayer graphene. Sci. Adv. 4, eaat4712 (2018).

    CAS  Article  Google Scholar 

  32. Yankowitz, M. et al. Electric field control of soliton motion and stacking in trilayer graphene. Nat. Mater. 13, 786–789 (2014).

    CAS  Article  Google Scholar 

  33. Hou, Y. et al. Preparation of twisted bilayer graphene via the wetting transfer method. ACS Appl. Mater. Interfaces. 12, 40958–40967 (2020).

    CAS  Article  Google Scholar 

  34. Zhang, S. et al. Tuning local electrical conductivity via fine atomic scale structures of two-dimensional interfaces. Nano Lett. 18, 6030–6036 (2018).

    CAS  Article  Google Scholar 

  35. Song, A. et al. Modeling atomic-scale electrical contact quality across two-dimensional interfaces. Nano Lett. 19, 3654–3662 (2019).

    CAS  Article  Google Scholar 

  36. Bao, W. et al. Stacking-dependent band gap and quantum transport in trilayer graphene. Nat. Phys. 7, 948–952 (2011).

    CAS  Article  Google Scholar 

  37. Qin, Q. et al. Recoverable plasticity in penta-twinned metallic nanowires governed by dislocation nucleation and retraction. Nat. Commun. 6, 5983 (2015).

    CAS  Article  Google Scholar 

  38. Kondo, S., Mitsuma, T., Shibata, N. & Ikuhara, Y. Direct observation of individual dislocation interaction processes with grain boundaries. Sci. Adv. 2, e1501926 (2016).

    Article  CAS  Google Scholar 

  39. Hou, Y. et al. Evaluation local strain of twisted bilayer graphene via moiré pattern. Opt. Lasers Eng. 152, 106946 (2022).

    Article  Google Scholar 

  40. Brenner, D. W. et al. A second-generation reactive empirical bond order (REBO) potential energy expression for hydrocarbons. J. Phys. Condens. Matter 14, 783–802 (2002).

    CAS  Article  Google Scholar 

  41. Ouyang, W., Mandelli, D., Urbakh, M. & Hod, O. Nanoserpents: graphene nanoribbon motion on two-dimensional hexagonal materials. Nano Lett. 18, 6009–6016 (2018).

    CAS  Article  Google Scholar 

  42. Gadelha, A. C. et al. Localization of lattice dynamics in low-angle twisted bilayer graphene. Nature 590, 405–409 (2021).

    CAS  Article  Google Scholar 

  43. Lamparski, M., Van Troeye, B. & Meunier, V. Soliton signature in the phonon spectrum of twisted bilayer graphene. 2D Mater. 7, 025050 (2020).

    CAS  Article  Google Scholar 

Download references


We acknowledge the financial support from the National Natural Science Foundation of China (grant nos 12025203 (Q.L.), 11921002 (X.-Q.F.), 51935006 (T.M.), 11890671 (Q.L.), 51705017 (L.G.) and 11890682 (L.L.)), the State Key Laboratory of Tribology at Tsinghua University (grant no. SKLT2022A01 (Q.L.)), the Strategic Priority Research Program of Chinese Academy of Sciences (grant no. XDB36000000 (L.L.)), China National Postdoctoral Program for Innovative Talents (BX2021163 (S.Z.)) and the Shuimu Tsinghua Scholar program of Tsinghua University (S.Z.). Computations were carried out on the ‘Explorer 100’ cluster system of Tsinghua National Laboratory for Information Science and Technology.

Author information

Authors and Affiliations



Q.L. conceived the project. S.Z. performed the c-AFM and STM experiments and carried out the strain and structural switching analyses. Q.X. and T.M. carried out the MD simulations. Y.H., M.Z. and L.L. prepared the twisted graphene samples. A.S., Y.M., L.G. and T.M. carried out the first-principles calculations. S.Z., Q.X., A.S., L.G., T.M., X.-Q.F. and Q.L. wrote the paper. All authors analysed and discussed the results and approved the manuscript.

Corresponding authors

Correspondence to Tianbao Ma, Xi-Qiao Feng or Qunyang Li.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Materials thanks Vincent Meunier and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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 Figs. 1–24.

Source data

Source Data Fig. 1

Raw data for Fig. 1c,d.

Source Data Fig. 2

Raw data for Fig. 2c.

Source Data Fig. 3

Raw data for Fig. 3b,c.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Zhang, S., Xu, Q., Hou, Y. et al. Domino-like stacking order switching in twisted monolayer–multilayer graphene. Nat. Mater. 21, 621–626 (2022).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

Further reading


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