Imaging moiré flat bands in three-dimensional reconstructed WSe2/WS2 superlattices


Moiré superlattices in transition metal dichalcogenide (TMD) heterostructures can host novel correlated quantum phenomena due to the interplay of narrow moiré flat bands and strong, long-range Coulomb interactions1,2,3,4,5,6,7,8,9. However, microscopic knowledge of the atomically reconstructed moiré superlattice and resulting flat bands is still lacking, which is critical for fundamental understanding and control of the correlated moiré phenomena. Here we quantitatively study the moiré flat bands in three-dimensional (3D) reconstructed WSe2/WS2 moiré superlattices by comparing scanning tunnelling spectroscopy (STS) of high-quality exfoliated TMD heterostructure devices with ab initio simulations of TMD moiré superlattices. A strong 3D buckling reconstruction accompanied by large in-plane strain redistribution is identified in our WSe2/WS2 moiré heterostructures. STS imaging demonstrates that this results in a remarkably narrow and highly localized K-point moiré flat band at the valence band edge of the heterostructure. A series of moiré flat bands are observed at different energies that exhibit varying degrees of localization. Our observations contradict previous simplified theoretical models but agree quantitatively with ab initio simulations that fully capture the 3D structural reconstruction. Our results reveal that the strain redistribution and 3D buckling in TMD heterostructures dominate the effective moiré potential and the corresponding moiré flat bands at the Brillouin zone K points.

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Fig. 1: Aligned WSe2/WS2 heterostructure.
Fig. 2: Moiré superlattice reconstruction.
Fig. 3: STS measurement of moiré-induced flat bands.
Fig. 4: Ab initio calculations of the electronic structure in reconstructed moiré superlattice.

Data availability

The data supporting the findings of this study are included in the main text and in the Supplementary Information files, and are also available at


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This work was supported by the Director, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division of the US Department of Energy under the van der Waals heterostructure program (KCWF16), contract number DE-AC02-05CH11231 (device electrode preparation, STM spectroscopy, DFT calculations and theoretical analysis). Support was also provided by the US Army Research Office under MURI award W911NF-17-1-0312 (device layer transfer), and by the National Science Foundation Awards DMR-1807233 (surface preparation) and DMR-1926004 (GW calculations). S.T. acknowledges support from DOE-SC0020653, NSF DMR 1552220, DMR 1904716 and NSF CMMI 1933214 for WSe2 and WS2 bulk crystal growth and analysis. K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by the MEXT, Japan, grant number JPMXP0112101001, JSPS KAKENHI grant number JP20H00354 and the CREST(JPMJCR15F3), JST for bulk hBN crystal growth and analysis. E.C.R. acknowledges support from the Department of Defense (DoD) through the National Defense Science & Engineering Graduate Fellowship (NDSEG) Program. S.L. acknowledges support from Kavli ENSI Heising Simons Junior Fellowship. M.H.N. thanks S. Kundu and M. Jain for their implementation of noncollinear wavefunction plotting in Siesta. Computational resources were provided by Cori at National Energy Research Scientific Computing Center (NERSC), which is supported by the Office of Science of the US Department of Energy under contract no. DE-AC02-05CH11231, Stampede2 at the Texas Advanced Computing Center (TACC) through Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation under grant no. ACI-1053575 and Frontera at TACC, which is supported by the National Science Foundation under grant no. OAC-1818253.

Author information




M.F.C., F.W. and S.L. conceived the project, and S.G.L. supervised the theoretical calculations. H.L. and S.L. performed the STM measurements, and M.H.N. carried out the DFT and GW calculations. H.L., J.X., X.L., J.W., W.Z., S.Z. and S.K. fabricated the heterostructure device. E.R. and D.W. performed the second harmonic generation measurements. K.Y., M.B. and S.T. grew WSe2 and WS2 crystals. K.W. and T.T. grew the hBN single crystal. All authors discussed the results and wrote the manuscript.

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Correspondence to Shaowei Li or Steven G. Louie or Feng Wang or Michael F. Crommie.

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Peer review information Nature Materials thanks Andrea Young and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary information

Supplementary Information

Materials and Methods and Supplementary Figs. 1–13.

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Li, H., Li, S., Naik, M.H. et al. Imaging moiré flat bands in three-dimensional reconstructed WSe2/WS2 superlattices. Nat. Mater. (2021).

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