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.

  • Article
  • Published:

Pressure tuning of minibands in MoS2/WSe2 heterostructures revealed by moiré phonons

Nature Nanotechnology volume 18, pages 1147–1153 (2023)Cite this article

Subjects

Abstract

Moiré superlattices of two-dimensional heterostructures arose as a new platform to investigate emergent behaviour in quantum solids with unprecedented tunability. To glean insights into the physics of these systems, it is paramount to discover new probes of the moiré potential and moiré minibands, as well as their dependence on external tuning parameters. Hydrostatic pressure is a powerful control parameter, since it allows to continuously and reversibly enhance the moiré potential. Here we use high pressure to tune the minibands in a rotationally aligned MoS2/WSe2 moiré heterostructure, and show that their evolution can be probed via moiré phonons. The latter are Raman-inactive phonons from the individual layers that are activated by the moiré potential. Moiré phonons manifest themselves as satellite Raman peaks arising exclusively from the heterostructure region, increasing in intensity and frequency under applied pressure. Further theoretical analysis reveals that their scattering rate is directly connected to the moiré potential strength. By comparing the experimental and calculated pressure-induced enhancement, we obtain numerical estimates for the moiré potential amplitude and its pressure dependence. The present work establishes moiré phonons as a sensitive probe of the moiré potential as well as the electronic structures of moiré systems.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: High-pressure Raman experiments on a 0°-MoS2/WSe2 moiré heterostructure.
Fig. 2: Moiré phonons in a 0°-MoS2/WSe2 moiré heterostructure.
Fig. 3: Origin of moiré phonons in a 0°-MoS2/WSe2 heterostructure.
Fig. 4: Miniband evolution with pressure revealed by moiré phonons.

Similar content being viewed by others

Data availability

The datasets generated in the the current study are available via Zenodo at https://zenodo.org/record/7872421 (ref. 63). Source data are provided with this paper.

Code availability

DFT calculations were conducted with the SIESTA code (https://gitlab.com/siesta-project/siesta), which is released under the terms of the GPL open-source license. The proprietary Vienna ab initio simulation package code was used under license no. 5-488 (available at https://www.vasp.at/) for the periodic DFT phonon calculations together with the Phonopy software. Phonopy is an open-source package for phonon calculations at harmonic and quasi-harmonic levels, which is released under the terms of the BSD license and is available at https://phonopy.github.io/phonopy. An implementation of the zone-folding computation is available from the corresponding authors upon reasonable request.

References

  1. Wu, F., Lovorn, T., Tutuc, E. & MacDonald, A. H. Hubbard model physics in transition metal dichalcogenide moiré bands. Phys. Rev. Lett. 121, 026402 (2018).

    Article  CAS  Google Scholar 

  2. Magorrian, S. J. et al. Multifaceted moiré superlattice physics in twisted WSe2 bilayers. Phys. Rev. B 104, 125440 (2021).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  7. Xu, Y. et al. Correlated insulating states at fractional fillings of moiré superlattices. Nature 587, 214–218 (2020).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  9. Gao, Y. et al. Band engineering of large-twist-angle graphene/h-BN moiré superlattices with pressure. Phys. Rev. Lett. 125, 226403 (2020).

    Article  CAS  Google Scholar 

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

    Article  Google Scholar 

  11. Utama, M. et al. Visualization of the flat electronic band in twisted bilayer graphene near the magic angle twist. Nat. Phys. 17, 184–188 (2021).

    Article  CAS  Google Scholar 

  12. Righi, A. et al. Graphene moiré patterns observed by Umklapp double-resonance Raman scattering. Phys. Rev. B 84, 241409 (2011).

    Article  Google Scholar 

  13. Carozo, V. et al. Raman signature of graphene superlattices. Nano Lett. 11, 4527–4534 (2011).

    Article  CAS  Google Scholar 

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

    Article  Google Scholar 

  15. Eliel, G. et al. Intralayer and interlayer electron–phonon interactions in twisted graphene heterostructures. Nat. Commun. 9, 1221 (2018).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  17. Parzefall, P. et al. Moiré phonons in twisted MoSe2–WSe2 heterobilayers and their correlation with interlayer excitons. 2D Mater. 8, 035030 (2021).

    Article  CAS  Google Scholar 

  18. Lin, K.-Q. et al. Large-scale mapping of moiré superlattices by hyperspectral Raman imaging. Adv. Mater. 33, 2008333 (2021).

    Article  CAS  Google Scholar 

  19. Enaldiev, V. V., Ferreira, F., Magorrian, S. J. & Fal’ko, V. I. Piezoelectric networks and ferroelectric domains in twistronic superlattices in WS2/MoS2 and WSe2/MoSe2 bilayers. 2D Mater. 8, 025030 (2021).

    Article  CAS  Google Scholar 

  20. Liu, K. et al. Evolution of interlayer coupling in twisted molybdenum disulfide bilayers. Nat. Commun. 5, 4966 (2014).

    Article  CAS  Google Scholar 

  21. Tateiwa, N. & Haga, Y. Evaluations of pressure-transmitting media for cryogenic experiments with diamond anvil cell. Rev. Sci. Instrum. 80, 123901 (2009).

    Article  Google Scholar 

  22. Feng, Y., Jaramillo, R., Wang, J., Ren, Y. & Rosenbaum, T. Invited article: high-pressure techniques for condensed matter physics at low temperature. Rev. Sci. Instrum. 81, 041301 (2010).

    Article  Google Scholar 

  23. Nayak, A. P. et al. Pressure-dependent optical and vibrational properties of monolayer molybdenum disulfide. Nano Lett. 15, 346–353 (2015).

    Article  CAS  Google Scholar 

  24. Machon, D. et al. Raman scattering studies of graphene under high pressure. J. Raman Spectrosc. 49, 121–129 (2018).

    Article  CAS  Google Scholar 

  25. Alencar, R. S. et al. Atomic-layered MoS2 on SiO2 under high pressure: bimodal adhesion and biaxial strain effects. Phys. Rev. Mater. 1, 024002 (2017).

    Article  Google Scholar 

  26. Chiu, M.-H. et al. Spectroscopic signatures for interlayer coupling in MoS2–WSe2 van der Waals stacking. ACS Nano 8, 9649–9656 (2014).

    Article  CAS  Google Scholar 

  27. Kim, J. et al. Anomalous optical excitations from arrays of whirlpooled lattice distortions in moiré superlattices. Nat. Mater. 21, 890–895 (2022).

    Article  CAS  Google Scholar 

  28. Gong, C. et al. Band alignment of two-dimensional transition metal dichalcogenides: application in tunnel field effect transistors. Appl. Phys. Lett. 103, 053513 (2013).

    Article  Google Scholar 

  29. Kang, J., Tongay, S., Zhou, J., Li, J. & Wu, J. Band offsets and heterostructures of two-dimensional semiconductors. Appl. Phys. Lett. 102, 012111 (2013).

    Article  Google Scholar 

  30. Thygesen, K. S. Calculating excitons, plasmons, and quasiparticles in 2D materials and van der Waals heterostructures. 2D Mater. 4, 022004 (2017).

    Article  Google Scholar 

  31. Alexeev, E. M. et al. Resonantly hybridized excitons in moiré superlattices in van der waals heterostructures. Nature 567, 81–86 (2019).

    Article  CAS  Google Scholar 

  32. Ruiz-Tijerina, D. A. & Fal’ko, V. I. Interlayer hybridization and moiré superlattice minibands for electrons and excitons in heterobilayers of transition-metal dichalcogenides. Phys. Rev. B 99, 125424 (2019).

    Article  CAS  Google Scholar 

  33. McDonnell, L. P. et al. Superposition of intra- and inter-layer excitons in twistronic MoSe2/WSe2 bilayers probed by resonant Raman scattering. 2D Mater. 8, 035009 (2021).

    Article  CAS  Google Scholar 

  34. Ferreira, F., Magorrian, S. J., Enaldiev, V. V., Ruiz-Tijerina, D. A. & Fal’ko, V. I. Band energy landscapes in twisted homobilayers of transition metal dichalcogenides. Appl. Phys. Lett. 118, 241602 (2021).

    Article  CAS  Google Scholar 

  35. Selig, M. et al. Excitonic linewidth and coherence lifetime in monolayer transition metal dichalcogenides. Nat. Commun. 7, 13279 (2016).

    Article  CAS  Google Scholar 

  36. Enaldiev, V., Ferreira, F., Magorrian, S. & Fal’ko, V. I. Piezoelectric networks and ferroelectric domains in twistronic superlattices in WS2/MoS2 and WSe2/MoSe2 bilayers. 2D Mater. 8, 025030 (2021).

    Article  CAS  Google Scholar 

  37. Carvalho, B. R. et al. Intervalley scattering by acoustic phonons in two-dimensional MoS2 revealed by double-resonance Raman spectroscopy. Nat. Commun. 8, 14670 (2017).

    Article  Google Scholar 

  38. Pimenta Martins, L. G. et al. Electronic band tuning and multivalley Raman scattering in monolayer transition metal dichalcogenides at high pressures. ACS Nano 16, 8064–8075 (2022).

    Article  CAS  Google Scholar 

  39. Park, J.-H. et al. Synthesis of high-performance monolayer molybdenum disulfide at low temperature. Small Methods 5, 2000720 (2021).

    Article  CAS  Google Scholar 

  40. Arora, A. et al. Excitonic resonances in thin films of WSe2: from monolayer to bulk material. Nanoscale 7, 10421–10429 (2015).

    Article  CAS  Google Scholar 

  41. Vaquero, D. et al. Excitons, trions and Rydberg states in monolayer MoS2 revealed by low-temperature photocurrent spectroscopy. Commun. Phys. 3, 194 (2020).

    Article  CAS  Google Scholar 

  42. Paradisanos, I. et al. Controlling interlayer excitons in MoS2 layers grown by chemical vapor deposition. Nat. Commun. 11, 2391 (2020).

    Article  CAS  Google Scholar 

  43. Wang, J. I.-J. et al. Electronic transport of encapsulated graphene and WSe2 devices fabricated by pick-up of prepatterned hBN. Nano Lett. 15, 1898–1903 (2015).

    Article  CAS  Google Scholar 

  44. Martins, L. G. P. et al. Hard, transparent, sp3-containing 2D phase formed from few-layer graphene under compression. Carbon 173, 744–757 (2021).

    Article  Google Scholar 

  45. Karni, O. et al. Infrared interlayer exciton emission in MoS2/WSe2 heterostructures. Phys. Rev. Lett. 123, 247402 (2019).

    Article  CAS  Google Scholar 

  46. Kozawa, D. et al. Photocarrier relaxation pathway in two-dimensional semiconducting transition metal dichalcogenides. Nat. Commun. 5, 4543 (2014).

    Article  CAS  Google Scholar 

  47. Viner, J. J. S. et al. Excited Rydberg states in MoSe2/WSe2 heterostructures. 2D Mater. 8, 035047 (2021).

    Article  CAS  Google Scholar 

  48. Pisoni, R. et al. Interactions and magnetotransport through spin-valley coupled Landau levels in monolayer MoS2. Phys. Rev. Lett. 121, 247701 (2018).

    Article  CAS  Google Scholar 

  49. Nguyen, P. V. et al. Visualizing electrostatic gating effects in two-dimensional heterostructures. Nature 572, 220–223 (2019).

    Article  CAS  Google Scholar 

  50. Gustafsson, M. V. et al. Ambipolar Landau levels and strong band-selective carrier interactions in monolayer WSe2. Nat. Mater. 17, 411–415 (2018).

    Article  Google Scholar 

  51. Hohenberg, P. & Kohn, W. Inhomogeneous electron gas. Phys. Rev. 136, B864 (1964).

    Article  Google Scholar 

  52. Kohn, W. & Sham, L. J. Self-consistent equations including exchange and correlation effects. Phys. Rev. 140, A1133–A1138 (1965).

    Article  Google Scholar 

  53. Soler, J. M. et al. The SIESTA method for ab initio order-N materials simulation. J. Phys.: Condens. Matter 14, 2745 (2002).

    CAS  Google Scholar 

  54. Troullier, N. & Martins, J. L. Efficient pseudopotentials for plane-wave calculations. Phys. Rev. B 43, 1993–2006 (1991).

    Article  CAS  Google Scholar 

  55. Kleinman, L. & Bylander, D. Efficacious form for model pseudopotentials. Phys. Rev. Lett. 48, 1425 (1982).

    Article  CAS  Google Scholar 

  56. Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865 (1996).

    Article  CAS  Google Scholar 

  57. Moreno, J. & Soler, J. M. Optimal meshes for integrals in real- and reciprocal-space unit cells. Phys. Rev. B 45, 13891–13898 (1992).

    Article  CAS  Google Scholar 

  58. Blöchl, P. E. Projector augmented-wave method. Phys. Rev. B 50, 17953–17979 (1994).

    Article  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  61. Kresse, G. & Furthmüller, J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput. Mater. Sci. 6, 15–50 (1996).

    Article  CAS  Google Scholar 

  62. Togo, A. & Tanaka, I. First principles phonon calculations in materials science. Scr. Mater. 108, 1–5 (2015).

    Article  CAS  Google Scholar 

  63. Pimenta Martins, L. G. et al. Dataset for pressure-tuning of minibands in MoS2/WSe2 heterostructures revealed by moiré phonons. Zenodo https://doi.org/10.5281/zenodo.7872421 (2023).

Download references

Acknowledgements

L.G.P.M., J.-H.P. and J.K. acknowledge support from the MURI project by the US Army Research Office (ARO) under grant no. W911NF-18-1-0431. D.A.R.-T. acknowledges funding from PAPIIT-DGAPA-UNAM grant IA106523, and CONACyT grant 1564464. R.C. acknowledges support from the National Science Foundation under grant no. 1751739 and the STC Center for Integrated Quantum Materials, NSF, grant no. DMR-1231319. L.G.P.M. and J.K. acknowledge support from CNPq under the program Ciência sem Fronteiras (206251/2014-9). L.G.C. acknowledges support from CNPq through grant 309537/2019-3. M.S.C.M. and M.J.S.M. acknowledge financial support from CNPq, FAPEMIG and INCT-Nanocarbono. M.J.S.M. acknowledges support from the Universidade Federal de Ouro Preto (UFOP). We also acknowledge computational support from CESUP-UFRGS. This work was performed in part at the Center for Nanoscale Systems (CNS), a member of the National Nanotechnology Coordinated Infrastructure Network (NNCI), which is supported by the National Science Foundation under NSF award no. 1541959.

Author information

Author notes

  1. These authors contributed equally: Luiz G. Pimenta Martins, David A. Ruiz-Tijerina.

Authors and Affiliations

  1. Physics Department, Massachusetts Institute of Technology, Cambridge, MA, USA

    Luiz G. Pimenta Martins, Connor A. Occhialini, Qian Song & Riccardo Comin

  2. Departamento de Física Química, Instituto de Física, Universidad Nacional Autónoma de México, Ciudad de México, Mexico

    David A. Ruiz-Tijerina

  3. Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA, USA

    Ji-Hoon Park, Ang-Yu Lu & Jing Kong

  4. Instituto de Física, Universidade Federal Fluminense, Niterói, Brazil

    Pedro Venezuela

  5. Departamento de Física, Universidade Federal de Minas Gerais, Belo Horizonte, Brazil

    Luiz G. Cançado & Mário S. C. Mazzoni

  6. Departamento de Física, Universidade Federal de Ouro Preto, Ouro Preto, Brazil

    Matheus J. S. Matos

Authors
  1. Luiz G. Pimenta Martins
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. David A. Ruiz-Tijerina
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Connor A. Occhialini
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ji-Hoon Park
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Qian Song
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Ang-Yu Lu
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Pedro Venezuela
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Luiz G. Cançado
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. Mário S. C. Mazzoni
    View author publications

    You can also search for this author in PubMed Google Scholar

  10. Matheus J. S. Matos
    View author publications

    You can also search for this author in PubMed Google Scholar

  11. Jing Kong
    View author publications

    You can also search for this author in PubMed Google Scholar

  12. Riccardo Comin
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

L.G.P.M., J.K. and R.C. conceived the project. J.K. and R.C. supervised the project. D.A.R.-T. proposed the effective model for the pressure-dependent moiré potential, and carried out the zone-folding analysis and Raman rate computations. L.G.P.M., J.-H.P., Q.S. and A.-Y.L. prepared the TMD samples on a silicon substrate. L.G.P.M. and C.A.O. carried out the high-pressure Raman and PL experiments, and they analysed the experimental data. D.A.R.-T., L.G.P.M. and L.G.C. developed the proposed scattering mechanisms for moiré phonons. M.J.S.M., M.S.C.M. and P.V. carried out the DFT calculations. L.G.P.M., D.A.R.-T., J.K. and R.C. wrote the manuscript. All authors contributed to the scientific discussions and data interpretation.

Corresponding authors

Correspondence to Luiz G. Pimenta Martins, Jing Kong or Riccardo Comin.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Nanotechnology thanks Christian Schüller, and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Additional information

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

Extended data

Extended Data Fig. 1 Raman frequencies as a function of pressure, measured both in the heterostructure and in the individual layers.

a A’1 of MoS2. b E’ of MoS2. c nearly-degenerate E’ and A’1 modes of WSe2.

Extended Data Fig. 2 Raman spectra of WSe2, MoS2, and MoS2/WSe2 at increasing pressures, zoomed-in the M3 peak spectral region.

The MoS2 M3 moiré phonon Raman peak is downshifted with respect to the MoS2 E’ peak. Its intensity increases with increasing pressure. The pressure is indicated at the top right corner of each panel.

Extended Data Fig. 3 Optical image of loaded sample inside of the DAC.

Regions 1, 2 and 3, corresponding to WSe2 monolayer, MoS2 monolayer and a rotationally-aligned MoS2/WSe2 heterostructure, respectively. During the loading process, the other two MoS2/WSe2 heterostructures, indicated by the red arrows, got partially damaged. Image taken with a 650 nm edge filter to enhance the optical contrast.

Supplementary information

Supplementary Information

Supplementary Sections 1–5, Figs. 1–5 and discussion.

Reporting Summary

Source data

Source Data Fig. 1

Unprocessed Raman data shown in Fig. 1d,e.

Source Data Fig. 2

Experimental and fitting data points for Fig. 2a–d, and unprocessed polarized Raman data shown in Fig. 2e.

Source Data Fig. 4

Experimental and fitting data points for Fig. 4a,b.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pimenta Martins, L.G., Ruiz-Tijerina, D.A., Occhialini, C.A. et al. Pressure tuning of minibands in MoS2/WSe2 heterostructures revealed by moiré phonons. Nat. Nanotechnol. 18, 1147–1153 (2023). https://doi.org/10.1038/s41565-023-01413-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41565-023-01413-3

This article is cited by

Search

Advanced 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