Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Phonon renormalization in reconstructed MoS2 moiré superlattices

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

This article has been updated

Abstract

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.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

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.

Data availability

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

Code availability

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

Change history

References

  1. 1.

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

    Google Scholar 

  2. 2.

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

    CAS  Google Scholar 

  3. 3.

    Kim, K. et al. van der Waals heterostructures with high accuracy rotational alignment. Nano Lett. 16, 1989–1995 (2016).

    CAS  Google Scholar 

  4. 4.

    Cao, Y. et al. Unconventional superconductivity in magic-angle graphene superlattices. Nature 556, 43–50 (2018).

    CAS  Google Scholar 

  5. 5.

    Yankowitz, M. et al. Tuning superconductivity in twisted bilayer graphene. Science 363, 1059–1064 (2019).

    CAS  Google Scholar 

  6. 6.

    Sharpe, A. L. et al. Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene. Science 365, 605–608 (2019).

    CAS  Google Scholar 

  7. 7.

    Serlin, M. et al. Intrinsic quantized anomalous hall effect in a moiré heterostructure. Science 367, 900–903 (2020).

    CAS  Google Scholar 

  8. 8.

    Cao, Y. et al. Correlated insulator behaviour at half-filling in magic-angle graphene superlattices. Nature 556, 80–84 (2018).

    CAS  Google Scholar 

  9. 9.

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

    CAS  Google Scholar 

  10. 10.

    Tang, Y. et al. Simulation of Hubbard model physics in WSe2/WS2 moiré superlattices. Nature 579, 353–358 (2020).

    CAS  Google Scholar 

  11. 11.

    Shimazaki, Y. et al. Strongly correlated electrons and hybrid excitons in a moiré heterostructure. Nature 580, 472–477 (2020).

    CAS  Google Scholar 

  12. 12.

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

    CAS  Google Scholar 

  13. 13.

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

    CAS  Google Scholar 

  14. 14.

    Gadelha, A. C. et al. Localization of lattice dynamics in low-angle twisted bilayer graphene. Nature 590, 405–409 (2021).

    CAS  Google Scholar 

  15. 15.

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

    CAS  Google Scholar 

  16. 16.

    Sushko, A. et al. High resolution imaging of reconstructed domains and moiré patterns in functional van der Waals heterostructure devices. Preprint at https://arXiv.org/abs/1912.07446 (2019).

  17. 17.

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

    CAS  Google Scholar 

  18. 18.

    McGilly, L. J. et al. Visualization of moiré superlattices. Nat. Nanotechnol. 15, 580–584 (2020).

    CAS  Google Scholar 

  19. 19.

    Jung, J., DaSilva, A. M., MacDonald, A. H. & Adam, S. Origin of band gaps in graphene on hexagonal boron nitride. Nat. Commun. 6, 6308 (2015).

    CAS  Google Scholar 

  20. 20.

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

    CAS  Google Scholar 

  21. 21.

    Yoo, H. et al. Atomic and electronic reconstruction at the van der Waals interface in twisted bilayer graphene. Nat. Mater. 18, 448–453 (2019).

    CAS  Google Scholar 

  22. 22.

    Zhang, K. & Tadmor, E. B. Structural and electron diffraction scaling of twisted graphene bilayers. J. Mech. Phys. Solids 112, 225–238 (2018).

    Google Scholar 

  23. 23.

    Alden, J. S. et al. Strain solitons and topological defects in bilayer graphene. Proc. Natl Acad. Sci. USA 110, 11256–11260 (2013).

    CAS  Google Scholar 

  24. 24.

    Huang, S. et al. Low-frequency interlayer Raman modes to probe interface of twisted bilayer MoS2. Nano Lett. 16, 1435–1444 (2016).

    CAS  Google Scholar 

  25. 25.

    Nam, N. N. & Koshino, M. Lattice relaxation and energy band modulation in twisted bilayer graphene. Phys. Rev. B 96, 075311 (2017).

    Google Scholar 

  26. 26.

    Molina-Sánchez, A. & Wirtz, L. Phonons in single-layer and few-layer MoS2 and WS2. Phys. Rev. B 84, 155413 (2011).

    Google Scholar 

  27. 27.

    Tan, P. et al. The shear mode of multilayer graphene. Nat. Mater. 11, 294–300 (2012).

    CAS  Google Scholar 

  28. 28.

    Zhang, X. et al. Raman spectroscopy of shear and layer breathing modes in multilayer MoS2. Phys. Rev. B 87, 115413 (2013).

    Google Scholar 

  29. 29.

    Zhao, Y. et al. Interlayer breathing and shear modes in few-trilayer MoS2 and WSe2. Nano Lett. 13, 1007–1015 (2013).

    CAS  Google Scholar 

  30. 30.

    Lin, M.-L. et al. Cross-dimensional electron-phonon coupling in van der Waals heterostructures. Nat. Commun. 10, 2419 (2019).

    Google Scholar 

  31. 31.

    Lee, C. et al. Anomalous lattice vibrations of single- and few-layer MoS2. ACS Nano 4, 2695–2700 (2010).

    CAS  Google Scholar 

  32. 32.

    Verble, J. L. & Wieting, T. J. Lattice mode degeneracy in MoS2 and other layer compounds. Phys. Rev. Lett. 25, 362–364 (1970).

    CAS  Google Scholar 

  33. 33.

    Li, H. et al. From bulk to monolayer MoS2: evolution of Raman scattering. Adv. Funct. Mater. 22, 1385–1390 (2012).

    CAS  Google Scholar 

  34. 34.

    Puretzky, A. A. et al. Twisted MoSe2 bilayers with variable local stacking and interlayer coupling revealed by low-frequency Raman spectroscopy. ACS Nano 10, 2736–2744 (2016).

    CAS  Google Scholar 

  35. 35.

    Holler, J. et al. Low-frequency Raman scattering in WSe2–MoSe2 heterobilayers: evidence for atomic reconstruction. Appl. Phys. Lett. 117, 013104 (2020).

    Google Scholar 

  36. 36.

    Liao, M. et al. Precise control of the interlayer twist angle in large scale MoS2 homostructures. Nat. Commun. 11, 2153 (2020).

    CAS  Google Scholar 

  37. 37.

    Debnath, R. et al. Evolution of high-frequency Raman modes and their doping dependence in twisted bilayer MoS2. Nanoscale 12, 17272–17280 (2020).

    CAS  Google Scholar 

  38. 38.

    Cuscó, R., Gil, B., Cassabois, G. & Artús, L. Temperature dependence of Raman-active phonons and anharmonic interactions in layered hexagonal BN. Phys. Rev. B 94, 155435 (2016).

    Google Scholar 

  39. 39.

    Lee, J.-U. et al. Strain-shear coupling in bilayer MoS2. Nat. Commun. 8, 1370 (2017).

    Google Scholar 

  40. 40.

    Wang, Y., Cong, C., Qiu, C. & Yu, T. Raman spectroscopy study of lattice vibration and crystallographic orientation of monolayer MoS2 under uniaxial strain. Small 9, 2857–2861 (2013).

    CAS  Google Scholar 

  41. 41.

    Lin, M.-L. et al. Moiré phonons in twisted bilayer MoS2. ACS Nano 12, 8770–8780 (2018).

    CAS  Google Scholar 

  42. 42.

    Koshino, M. & Son, Y.-W. Moiré phonons in twisted bilayer graphene. Phys. Rev. B 100, 075416 (2019).

    CAS  Google Scholar 

  43. 43.

    Campos-Delgado, J., Cançado, L. G., Achete, C. A., Jorio, A. & Raskin, J.-P. Raman scattering study of the phonon dispersion in twisted bilayer graphene. Nano Res. 6, 269–274 (2013).

    CAS  Google Scholar 

  44. 44.

    He, R. et al. Observation of low energy Raman modes in twisted bilayer graphene. Nano Lett. 13, 3594–3601 (2013).

    CAS  Google Scholar 

  45. 45.

    Cocemasov, A. I., Nika, D. L. & Balandin, A. A. Phonons in twisted bilayer graphene. Phys. Rev. B 88, 035428 (2013).

    Google Scholar 

  46. 46.

    Jorio, A. & Cançado, L. G. Raman spectroscopy of twisted bilayer graphene. Solid State Commun. 175, 3–12 (2013).

    Google Scholar 

  47. 47.

    Maity, I., Naik, M. H., Maiti, P. K., Krishnamurthy, H. & Jain, M. Phonons in twisted transition-metal dichalcogenide bilayers: ultrasoft phasons and a transition from a superlubric to a pinned phase. Phys. Rev. Res. 2, 013335 (2020).

    CAS  Google Scholar 

  48. 48.

    Cocemasov, A. I., Nika, D. L. & Balandin, A. A. Phonons in twisted bilayer graphene. Phys. Rev. B 88, 035428 (2013).

    Google Scholar 

  49. 49.

    Jung, J., Raoux, A., Qiao, Z. & MacDonald, A. H. Ab initio theory of moiré superlattice bands in layered two-dimensional materials. Phys. Rev. B 89, 205414 (2014).

    Google Scholar 

  50. 50.

    Bistritzer, R. & MacDonald, A. H. Moiré bands in twisted double-layer graphene. Proc. Natl Acad. Sci. USA 108, 12233–12237 (2011).

    CAS  Google Scholar 

  51. 51.

    Kresse, G. & Hafner, J. Ab initio molecular dynamics for liquid metals. Phys. Rev. B 47, 558–561 (1993).

    CAS  Google Scholar 

  52. 52.

    Kresse, G. & Hafner, J. Ab initio molecular-dynamics simulation of the liquid-metal–amorphous-semiconductor transition in germanium. Phys. Rev. B 49, 251–271 (1994).

    Google Scholar 

Download references

Acknowledgements

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

Affiliations

Authors

Contributions

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.

Corresponding authors

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

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature Materials thanks the anonymous reviewers for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

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

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Quan, J., Linhart, L., Lin, ML. et al. Phonon renormalization in reconstructed MoS2 moiré superlattices. Nat. Mater. (2021). https://doi.org/10.1038/s41563-021-00960-1

Download citation

Further reading

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing