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Visualization of moiré superlattices


Moiré superlattices in van der Waals heterostructures have given rise to a number of emergent electronic phenomena due to the interplay between atomic structure and electron correlations. Indeed, electrons in these structures have been recently found to exhibit a number of emergent properties that the individual layers themselves do not exhibit. This includes superconductivity1,2, magnetism3, topological edge states4,5, exciton trapping6 and correlated insulator phases7. However, the lack of a straightforward technique to characterize the local structure of moiré superlattices has thus far impeded progress in the field. In this work we describe a simple, room-temperature, ambient method to visualize real-space moiré superlattices with sub-5-nm spatial resolution in a variety of twisted van der Waals heterostructures including, but not limited to, conducting graphene, insulating boron nitride and semiconducting transition metal dichalcogenides. Our method uses piezoresponse force microscopy, an atomic force microscope modality that locally measures electromechanical surface deformation. We find that all moiré superlattices, regardless of whether the constituent layers have inversion symmetry, exhibit a mechanical response to out-of-plane electric fields. This response is closely tied to flexoelectricity wherein electric polarization and electromechanical response is induced through strain gradients present within moiré superlattices. Therefore, moiré superlattices of two-dimensional materials manifest themselves as an interlinked network of polarized domain walls in a non-polar background matrix.

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Fig. 1: Stacking order domains in twisted bilayer graphene and visualization by PFM.
Fig. 2: Examples of PFM imaging of moiré superlattices in various vdW heterostructures.
Fig. 3: PFM imaging modes, cantilever dynamics and the resulting effects on contrast in tBLG.
Fig. 4: Strain-gradient and curvature induced polarization.

Data availability

Data is available from the corresponding author upon request.


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This work is supported by the Programmable Quantum Materials (Pro-QM) programme at Columbia University, an Energy Frontier Research Center established by the Department of Energy (grant no. DE-SC0019443). L.J.M. acknowledges support from the Swiss National Science Foundation (grant no. P400P2_186744). Synthesis of MoSe2 and WSe2 was supported by the National Science Foundation Materials Research Science and Engineering Centers programme through Columbia in the Center for Precision Assembly of Superstratic and Superatomic Solids (DMR-1420634). The Flatiron Institute is a division of the Simons Foundation. C.E.D. acknowledges support from the National Science Foundation under grant no. DMR-1918455. M.S. and K.S. acknowledge the support of the European Research Council under the European Union’s Horizon 2020 research and innovation programme (grant agreement no. 724529), Ministerio de Economia, Industria y Competitividad through grant nos. MAT2016-77100-C2-2-P and SEV-2015-0496, and the Generalitat de Catalunya (grant no. 2017SGR 1506). We thank D. Griffin and T. Walsh from Oxford Instruments Asylum Research for confirmation of PFM results.

Author information




L.J.M. conceived the concept of the study and initiated the first PFM experiments. A.K., N.R.F., E.-M.S., A.G., Y.Z., S.L.M., W.W., Y.B. and L.Z. provided additional samples and experimental results. K.S., M.S. and C.E.D performed theoretical calculations and simulations. K.W. and T.T. provided hBN crystals. J.H., X.Z., D.N.B., C.D., C.E.D. and A.N.P. advised. L.J.M and A.N.P. wrote the manuscript with assistance from all authors.

Corresponding author

Correspondence to Abhay N. Pasupathy.

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Extended data

Extended Data Fig. 1 Example of large-scale mapping of moiré superlattice.

A lateral PFM image for a scan of 8 × 8 µm2; topography (a), phase (b) and amplitude (c) demonstrating that this technique can be used to observe the moiré across length scales that span orders of magnitude. Note the huge variation in moiré wavelength from ~500 to ~50 nm and presence of large strains.

Extended Data Fig. 2 Example of mapping of two co-existing moiré superlattices.

Amplitude (a) and phase (b) images clearly show a strained moiré superlattice due to the twisted bilayer of graphene with wavelength \(\lambda _m^{tBLG}\sim 70\,{\mathrm{nm}}\) and a second smaller wavelength related to the bottom layer of graphene with the hBN flake of \(\lambda _m^{SLG}\sim 4.5\,{\mathrm{nm}}\).

Supplementary information

Supplementary Information

Supplementary sections 1–7, Figs. 1–7 and refs. 1 and 2.

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McGilly, L.J., Kerelsky, A., Finney, N.R. et al. Visualization of moiré superlattices. Nat. Nanotechnol. 15, 580–584 (2020).

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