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Deep moiré potentials in twisted transition metal dichalcogenide bilayers


In twisted bilayers of semiconducting transition metal dichalcogenides, a combination of structural rippling and electronic coupling gives rise to periodic moiré potentials that can confine charged and neutral excitations1,2,3,4,5. Here we show that the moiré potential in these bilayers at small angles is unexpectedly large, reaching values above 300 meV for the valence band and 150 meV for the conduction band—an order of magnitude larger than theoretical estimates based on interlayer coupling alone. We further demonstrate that the moiré potential is a non-monotonic function of moiré wavelength, reaching a maximum at a moiré period of ~13 nm . This non-monotonicity coincides with a change in the structure of the moiré pattern from a continuous variation of stacking order at small moiré wavelengths to a one-dimensional soliton-dominated structure at large moiré wavelengths. We show that the in-plane structure of the moiré pattern is captured by a continuous mechanical relaxation model, and find that the moiré structure and internal strain, rather than the interlayer coupling, are the dominant factors in determining the moiré potential. Our results demonstrate the potential of using precision moiré structures to create deeply trapped carriers or excitations for quantum electronics and opto-electronics.

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Fig. 1: Structure of twisted heterobilayer WSe2/MoSe2.
Fig. 2: Spectroscopic properties of moiré patterns of different wavelengths.
Fig. 3: Spectroscopic imaging of conduction and valence band edges.
Fig. 4: Quantifying the moiré potential.

Data availability

Data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request. Source data are provided with this paper.


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We thank S. Carr and E. Kaxiras for providing the GSFE function for relaxation calculations. We thank C. Dean, L. Fu, M. Jain, I. Maiti, Q. Shi and Y. Zhang for useful discussions. 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). STM experiments were supported by the Air Force Office of Scientific Research via grant no. FA9550-16-1-0601 (S.S. and A.N.P.). 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). D.H. was supported by a grant from the Simons Foundation (579913). DFT calculations were performed with the support of the National Natural Science Foundation of China (grants nos. 11774084 and U19A2090, to M.C.).

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Authors and Affiliations



S.S. performed STM experiments, assisted by S.L. D.H. performed relaxation calculations. W.W. performed SHG experiments. M.C. performed DFT calculations. J.H., W.Y., D.N.B., X.Z. and A.N.P. provided advice. Data analysis and manuscript preparation were performed by S.S. and A.N.P. with input from all coauthors.

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Correspondence to Abhay N. Pasupathy.

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The authors declare no competing interests.

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Peer review information Nature Physics thanks Brian LeRoy and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary information

Supplementary Information

Supplementary discussion.

Source data

Source Data Fig. 2

Source data of spectroscopy for different moiré wavelengths.

Source Data Fig. 3

Source data of the position of the band edges.

Source Data Fig. 4

Source data for the moiré potential as a function of moiré wavelength, strain tensor components and maximal shear strain as a function of moiré wavelength.

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Shabani, S., Halbertal, D., Wu, W. et al. Deep moiré potentials in twisted transition metal dichalcogenide bilayers. Nat. Phys. 17, 720–725 (2021).

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