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Deep moiré potentials in twisted transition metal dichalcogenide bilayers

Nature Physics volume 17, pages 720–725 (2021)Cite this article

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Abstract

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.

References

  1. Seyler, K. L. et al. Signatures of moiré-trapped valley excitons in MoSe2/WSe2 heterobilayers. Nature 567, 66–70 (2019).

    Article  ADS  Google Scholar 

  2. Wu, F. et al. Theory of optical absorption by interlayer excitons in transition metal dichalcogenide heterobilayers. Phys. Rev. B 97, 035306 (2018).

    Article  ADS  Google Scholar 

  3. Tran, K. et al. Evidence for moiré excitons in van der Waals heterostructures. Nature 567, 71–75 (2019).

    Article  ADS  Google Scholar 

  4. Wang, L. et al. Correlated electronic phases in twisted bilayer transition metal dichalcogenides. Nat. Mater. 19, 861–866 (2020).

    Article  Google Scholar 

  5. Wang, J. et al. Excitonic phase transitions in MoSe2/WSe2 heterobilayers. Preprint at https://arxiv.org/pdf/2001.03812.pdf (2020).

  6. Regan, E. C. et al. Mott and generalized Wigner crystal states in WSe2/WS2 moiré superlattices. Nature 579, 359–363 (2020).

    Article  ADS  Google Scholar 

  7. Wang, Z. et al. Evidence of high-temperature exciton condensation in two-dimensional atomic double layers. Nature 574, 76–80 (2019).

    Article  ADS  Google Scholar 

  8. Wu, F. et al. Hubbard model physics in transition metal dichalcogenide moiré bands. Phys. Rev. Lett. 121, 026402 (2018).

    Article  ADS  Google Scholar 

  9. Zhang, Y. et al. Moiré quantum chemistry: charge transfer in transition metal dichalcogenide superlattices. Phys. Rev. B 102, 201115 (2020).

    Article  ADS  Google Scholar 

  10. Yu, H. et al. Moiré excitons: from programmable quantum emitter arrays to spin–orbit-coupled artificial lattices. Sci. Adv. 3, e1701696 (2017).

    Article  ADS  Google Scholar 

  11. Ruiz-Tijerina, D. A. et al. Interlayer hybridization and moiré superlattice minibands for electrons and excitons in heterobilayers of transition-metal dichalcogenides. Phys. Rev. B 99, 125424 (2019).

    Article  ADS  Google Scholar 

  12. Geng, W. et al. Moiré potential, lattice corrugation and band gap spatial variation in a twist-free MoTe22/MoS2 heterobilayer. J. Phys. Chem. Lett. 11, 2637–2646 (2020).

    Article  Google Scholar 

  13. Zhang, C. et al. Interlayer couplings, moiré patterns, and 2D electronic superlattices in MoS2/WSe2 hetero-bilayers. Sci. Adv. 3, e1601459 (2017).

    Article  ADS  Google Scholar 

  14. Pan, Y. et al. Quantum-confined electronic states arising from the moiré pattern of MoS2-WSe2 heterobilayers. Nano Lett. 18, 1849–1855 (2018).

    Article  ADS  Google Scholar 

  15. Zhang, Z. et al. Flat bands in twisted bilayer transition metal dichalcogenides. Nat. Phys. 16, 1093–1096 (2020).

    Article  Google Scholar 

  16. Li, H. et al. Imaging moiré flat bands in 3D reconstructed WSe2/WS2 superlattices. Preprint at https://arxiv.org/pdf/2007.06113.pdf (2020).

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

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  19. Halbertal, D. et al. Moiré metrology of energy landscapes in van der Waals heterostructures. Nat. Commun. 12, 242 (2021).

    Article  Google Scholar 

  20. Maity, I. et al. Reconstruction of moiré lattices in twisted transition metal dichalcogenide bilayers. Preprint at https://arxiv.org/pdf/1912.08702.pdf (2019).

  21. Enaldiev, V. et al. Stacking domains and dislocation networks in marginally twisted bilayers of transition metal dichalcogenides. Phys. Rev. Lett. 124, 206101 (2020).

    Article  ADS  Google Scholar 

  22. Edelberg, D. et al. Tunable strain soliton networks confine electrons in van der Waals materials. Nat. Phys. 16, 1097–1102 (2020).

    Article  Google Scholar 

  23. Bai, Y. et al. Excitons in strain-induced one-dimensional moiré potentials at transition metal dichalcogenide heterojunctions. Nat. Mater. 19, 1068–1073 (2020).

    Article  ADS  Google Scholar 

  24. Naik, M. H. et al. Ultraflatbands and shear solitons in moiré patterns of twisted bilayer transition metal dichalcogenides. Phys. Rev. Lett. 121, 266401 (2018).

    Article  ADS  Google Scholar 

  25. Wilson, N. R. et al. Determination of band offsets, hybridization and exciton binding in 2D semiconductor heterostructures. Sci. Adv. 3, e1601832 (2017).

    Article  ADS  Google Scholar 

  26. Edelberg, D. et al. Approaching the intrinsic limit in transition metal diselenides via point defect control. Nano Lett. 19, 4371–4379 (2018).

    Article  ADS  Google Scholar 

  27. Kresse, G. et al. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169–11186 (1996).

    Article  ADS  Google Scholar 

  28. Kresse, G. et al. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 59, 1758–1775 (1999).

    Article  ADS  Google Scholar 

  29. Perdew, J. P. et al. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).

    Article  ADS  Google Scholar 

  30. Klimeš, J. et al. Van der Waals density functionals applied to solids. Phys. Rev. B 83, 195131 (2011).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  32. Grimme, S. et al. A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu. J. Chem. Phys. 132, 154104 (2010).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

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

  1. Department of Physics, Columbia University, New York, NY, USA

    Sara Shabani, Dorri Halbertal, D. N. Basov & Abhay N. Pasupathy

  2. Department of Chemistry, Columbia University, New York, NY, USA

    Wenjing Wu & Xiaoyang Zhu

  3. School of Physics and Electronics, Hunan Normal University, Key Laboratory for Matter Microstructure and Function of Hunan Province, Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control of Ministry of Education, Changsha, Hunan, China

    Mingxing Chen

  4. Department of Mechanical Engineering, Columbia University, New York, NY, USA

    Song Liu & James Hone

  5. Department of Physics and Center of Theoretical and Computational Physics, University of Hong Kong, Hong Kong, China

    Wang Yao

Authors
  1. Sara Shabani
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Contributions

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.

Corresponding author

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). https://doi.org/10.1038/s41567-021-01174-7

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