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Phonon renormalization in reconstructed MoS2 moiré superlattices

A Publisher Correction to this article was published on 06 April 2021

This article has been updated


In moiré crystals formed by stacking van der Waals materials, surprisingly diverse correlated electronic phases and optical properties can be realized by a subtle change in the twist angle. Here, we discover that phonon spectra are also renormalized in MoS2 twisted bilayers, adding an insight to moiré physics. Over a range of small twist angles, the phonon spectra evolve rapidly owing to ultra-strong coupling between different phonon modes and atomic reconstructions of the moiré pattern. We develop a low-energy continuum model for phonons that overcomes the outstanding challenge of calculating the properties of large moiré supercells and successfully captures the essential experimental observations. Remarkably, simple optical spectroscopy experiments can provide information on strain and lattice distortions in moiré crystals with nanometre-size supercells. The model promotes a comprehensive and unified understanding of the structural, optical and electronic properties of moiré superlattices.

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Fig. 1: Twist-angle-dependent lattice reconstruction in MoS2 TBLs with small twist angles.
Fig. 2: Measured Raman spectra of MoS2 TBLs as a function of twist angle.
Fig. 3: Analysis of the Raman spectra and experimentally observed lattice reconstruction.
Fig. 4: Calculated evolution of phonon modes as a function of twist angle θ.

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All relevant data are available from the authors upon reasonable request.

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All relevant codes are available from the authors upon reasonable request.

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The spectroscopy experiments at the University of Texas at Austin (J.Q.) were primarily funded by the US Department of Energy, Office of Basic Energy Sciences under grant DE-SC0019398 and a grant from the University of Texas. Material preparation was funded by the Welch Foundation via grant F-1662. The collaboration between the X.L., C.-K.S., K.L. and A.H.M. groups is facilitated by the National Science Foundation Materials Research Science and Engineering Centers (MRSEC) under DMR-1720595, which funded J.C. and J.E. partially. L.L. and F.L. acknowledge support by the TU-D doctoral programme of TU Wien, as well as from the Austrian Science Fund (FWF), project I-3827, and L.L. acknowledges additional support from the Austrian Marshall Plan Foundation. We acknowledge discussions with S. Reichardt and the use of facilities and instrumentation supported by the National Science Foundation through the Center for Dynamics and Control of Materials and National Science Foundation MRSEC under cooperative agreement no. DMR-1720595. P.-H.T. and M.-L.L. acknowledge support from the National Natural Science Foundation of China (grant nos 12004377 and 11874350), CAS Key Research Program of Frontier Sciences (grant no. ZDBS-LY-SLH004) and China Postdoctoral Science Foundation (grant no. 2019TQ0317). The PFM work (D.L. and K.L.) was supported by National Science Foundation DMR-2004536 and Welch Foundation grant F-1814. X.L. gratefully acknowledges the support of sample preparations from the Welch Foundation via grant F-1662. K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by the MEXT, Japan, grant no. JPMXP0112101001; JSPS KAKENHI, grant no. JP20H00354; and the CREST(JPMJCR15F3), JST.

Author information




J.Q. led the optical experiments, and M.-L.L., C.-Y.W., W.-T.H., J.E. and J.C. assisted with the experiment. L.L. led the theoretical calculations, and J.Z. contributed to the theoretical discussions. D.L. performed the PFM measurements. J.Q. and C.Y. prepared the TBL samples. T.T. and K.W. provided the hBN sample. J.Q., L.L., F.L. and X.L. wrote the manuscript. X.L., F.L., A.H.M., P.-H.T., K.L. and C.-K.S. supervised the project. All authors discussed the results.

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Correspondence to Ping-Heng Tan or Florian Libisch or Xiaoqin Li.

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Supplementary Figs. 1–15 and Discussions I–XII.

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Quan, J., Linhart, L., Lin, ML. et al. Phonon renormalization in reconstructed MoS2 moiré superlattices. Nat. Mater. (2021).

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