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Anomalous optical excitations from arrays of whirlpooled lattice distortions in moiré superlattices

Abstract

Moiré superlattices formed by stacking two-dimensional crystals have reinvigorated the pursuit for emergent functionalities of engineered superlattices. Unique optical characteristics can be realized from the interplay between the electronic excitations and the atomic rearrangements owing to their intrinsic softness. Although large-scale reconstructions have been identified at small twist angles, they have been treated as being rigid at large twist angles. Here, we report that moiré superlattices made from single layers of MoS2 and WSe2 exhibit a pair of torsional strains with opposite chirality irrespective of the twist angle. The whirlpool-shaped periodic lattice distortions introduce fuzziness in the Raman spectra and universal redshifts to the intralayer excitons for all twist angles. We show that both of these modulations become weaker as the twist angle increases but do not disappear, whereas they are turned off when the constituent layers are not tightly coupled, thus establishing an essential structure–property relationship for moiré superlattices.

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Fig. 1: MoS2/WSe2 heterostructure.
Fig. 2: Twist-angle dependence of Raman spectra.
Fig. 3: Out-of-plane and in-plane distortions.
Fig. 4: SAED pattern obtained from a heterostructure.
Fig. 5: Twist-angle-dependent exciton energy shift in a heterostructure.

Data availability

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

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Acknowledgements

This work was supported by the National Research Foundation (NRF) grant funded by the Korean government (MSIT) (2019R1A2C3006189, 2017R1A5A1014862, SRC program: vdWMRC center and 2021R1C1C1010924). Y.-W.S. was partly supported by a KIAS individual grant (no. CG031509). E.K. was supported by a KIAS individual grant (no. CG075002). Computations were supported by the CAC of KIAS.

Author information

Authors and Affiliations

Authors

Contributions

H.C. and J.K. conceived the experiment. J.K. prepared the samples and carried out optical measurements. J.J., M.K. and H.Y. carried out the TEM analysis. The spectroscopic data were analysed by H.C. and J.K. Theoretical analyses were done by E.K. and Y.-W.S. All the authors discussed the results and wrote the manuscript together.

Corresponding authors

Correspondence to Hyobin Yoo, Young-Woo Son or Hyeonsik Cheong.

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Competing interests

The authors declare no competing interests.

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Peer review information

Nature Materials thanks Kristiaan De Greve, Ado Jorio and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Twist-angle dependence of Raman spectra.

Compilation of Raman spectra for all samples measured.

Source data

Extended Data Fig. 2 Twist-angle dependence of ILB and force constant.

Twist-angle dependence of the ILB mode frequency (a) and force constant between MoS2 and WSe2 layers (b).

Source data

Extended Data Fig. 3 In-plane displacement vector dv (red arrows) of the atoms in MoS2 of the model HS with respect to the twist angle.

The pink circle and red circle denote S and Mo atoms, respectively. The magnitude of dv (length of the red arrow) is enlarged from one hundred times to three hundred times as indicated.

Source data

Extended Data Fig. 4 Electron diffraction and DF analysis of the lattice modulation.

a, SAED pattern of a MoS2/WSe2 HS with a twist angle of 1.0°. b,d,f, g = \(11\bar 20\), \(\bar 12\bar 10\), \(\bar 2110\) DF images obtained by selecting electron diffraction peaks marked with dashed squares in a. c,e,g are fast-Fourier-transforms (FFT) of the DF images shown in b,d,f, respectively. The peaks marked with black dashed circles in FFTs correspond to the frequency component of 0.25 nm−1. Such frequency is associated with the moiré fringe obtained by simply interfering two sets of {\(11\bar 20\)} planes of MoS2 and WSe2 twisted with 1.0°. The other set of peaks marked with red dashed circles correspond to the frequency of 0.14 nm−1 that are associated with the periodic structures visualized due to the lattice modulation at the interface.

Supplementary information

Supplementary Information

Supplementary Figs. 1–17, Tables 1–3 and Note 1.

Source data

Source Data Fig. 1

Spectra.

Source Data Fig. 2

Spectra and spectral parameters extracted from spectra.

Source Data Fig. 3

Calculation results.

Source Data Fig. 5

Spectra and spectral parameters extracted from spectra.

Source Data Extended Data Fig. 1

Spectra.

Source Data Extended Data Fig. 2

Spectral parameters extracted from spectra.

Source Data Extended Data Fig. 3

Calculation results.

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Kim, J., Ko, E., Jo, J. et al. Anomalous optical excitations from arrays of whirlpooled lattice distortions in moiré superlattices. Nat. Mater. (2022). https://doi.org/10.1038/s41563-022-01240-2

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