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:

Creation of moiré bands in a monolayer semiconductor by spatially periodic dielectric screening

Nature Materials volume 20, pages 645–649 (2021)Cite this article

Subjects

Abstract

Moiré superlattices of two-dimensional van der Waals materials have emerged as a powerful platform for designing electronic band structures and discovering emergent physical phenomena. A key concept involves the creation of long-wavelength periodic potential and moiré bands in a crystal through interlayer electronic hybridization or atomic corrugation when two materials are overlaid. Here we demonstrate a new approach based on spatially periodic dielectric screening to create moiré bands in a monolayer semiconductor. This approach relies on reduced dielectric screening of the Coulomb interactions in monolayer semiconductors and their environmental dielectric-dependent electronic band structure. We observe optical transitions between moiré bands in monolayer WSe2 when it is placed close to small-angle-misaligned graphene on hexagonal boron nitride. The moiré bands are a result of long-range Coulomb interactions, which are strongly gate tunable, and can have versatile superlattice symmetries independent of the crystal lattice of the host material. Our result also demonstrates that monolayer semiconductors are sensitive local dielectric sensors.

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: Illustration of creating spatially periodic electronic band structure in monolayer WSe2 by dielectric screening.
Fig. 2: Reflection contrast of devices without and with graphene/hBN alignment.
Fig. 3: Effects of superlattice period and spacer thickness.

Similar content being viewed by others

Data availability

All data supporting the findings of this study are included in the paper. Source data are provided with this paper.

References

  1. Hunt, B. et al. Massive Dirac fermions and Hofstadter butterfly in a van der Waals heterostructure. Science 340, 1427–1430 (2013).

    Article  Google Scholar 

  2. Dean, C. R. et al. Hofstadter’s butterfly and the fractal quantum Hall effect in moiré superlattices. Nature 497, 598–602 (2013).

    Article  CAS  Google Scholar 

  3. Ponomarenko, L. A. et al. Cloning of Dirac fermions in graphene superlattices. Nature 497, 594–597 (2013).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  11. Chen, G. et al. Tunable correlated Chern insulator and ferromagnetism in a moiré superlattice. Nature 579, 56–61 (2020).

    Article  CAS  Google Scholar 

  12. Jin, C. et al. Observation of moiré excitons in WSe2/WS2 heterostructure superlattices. Nature 567, 76–80 (2019).

    Article  CAS  Google Scholar 

  13. 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 

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  16. Qiu, D. Y., Da Jornada, F. H. & Louie, S. G. Optical spectrum of MoS2: many-body effects and diversity of exciton states. Phys. Rev. Lett. 111, 216805 (2013).

    Article  Google Scholar 

  17. He, K. et al. Tightly bound excitons in monolayer WSe2. Phys. Rev. Lett. 113, 026803 (2014).

    Article  CAS  Google Scholar 

  18. Ugeda, M. M. et al. Giant bandgap renormalization and excitonic effects in a monolayer transition metal dichalcogenide semiconductor. Nat. Mater. 13, 1091–1095 (2014).

    Article  CAS  Google Scholar 

  19. Raja, A. et al. Coulomb engineering of the bandgap and excitons in two-dimensional materials. Nat. Commun. 8, 15251 (2017).

    Article  Google Scholar 

  20. Qiu, Z. et al. Giant gate-tunable bandgap renormalization and excitonic effects in a 2D semiconductor. Sci. Adv. 5, eaaw2347 (2019).

    Article  CAS  Google Scholar 

  21. Utama, M. I. B. et al. A dielectric-defined lateral heterojunction in a monolayer semiconductor. Nat. Electron. 2, 60–65 (2019).

    Article  CAS  Google Scholar 

  22. Yankowitz, M. et al. Emergence of superlattice Dirac points in graphene on hexagonal boron nitride. Nat. Phys. 8, 382–386 (2012).

    Article  CAS  Google Scholar 

  23. Liu, Y., Stradins, P. & Wei, S. H. Van der Waals metal–semiconductor junction: weak Fermi level pinning enables effective tuning of Schottky barrier. Sci. Adv. 2, e1600069 (2016).

    Article  Google Scholar 

  24. Wang, G. et al. Colloquium: excitons in atomically thin transition metal dichalcogenides. Rev. Mod. Phys. 90, 021001 (2018).

    Article  CAS  Google Scholar 

  25. Mak, K. F. & Shan, J. Photonics and optoelectronics of 2D semiconductor transition metal dichalcogenides. Nat. Photonics 10, 216–226 (2016).

    Article  CAS  Google Scholar 

  26. Schmitt-Rink, S., Chemla, D. S. & Miller, D. A. B. Linear and nonlinear optical properties of semiconductor quantum wells. Adv. Phys. 38, 89–188 (1988).

    Article  Google Scholar 

  27. Chernikov, A. et al. Exciton binding energy and nonhydrogenic Rydberg series in monolayer WS2. Phys. Rev. Lett. 113, 076802 (2014).

    Article  CAS  Google Scholar 

  28. Ye, Z. et al. Probing excitonic dark states in single-layer tungsten disulphide. Nature 513, 214–218 (2014).

    Article  CAS  Google Scholar 

  29. Stier, A. V. et al. Magnetooptics of exciton Rydberg states in a monolayer semiconductor. Phys. Rev. Lett. 120, 057405 (2018).

    Article  CAS  Google Scholar 

  30. Gao, S., Liang, Y., Spataru, C. D. & Yang, L. Dynamical excitonic effects in doped two-dimensional semiconductors. Nano Lett. 16, 5568–5573 (2016).

    Article  CAS  Google Scholar 

  31. Hwang, E. H. & Das Sarma, S. Dielectric function, screening, and plasmons in two-dimensional graphene. Phys. Rev. B 75, 205418 (2007).

    Article  Google Scholar 

  32. Yankowitz, M., Ma, Q., Jarillo-Herrero, P. & LeRoy, B. J. Van der Waals heterostructures combining graphene and hexagonal boron nitride. Nat. Rev. Phys. 1, 112–125 (2019).

    Article  CAS  Google Scholar 

  33. Berkelbach, T. C., Hybertsen, M. S. & Reichman, D. R. Theory of neutral and charged excitons in monolayer transition metal dichalcogenides. Phys. Rev. B 88, 045318 (2013).

    Article  Google Scholar 

  34. Kormányos, A. et al. Monolayer MoS2: trigonal warping, the Γ valley, and spin–orbit coupling effects. Phys. Rev. B 88, 045416 (2013).

    Article  Google Scholar 

  35. Wu, F., Lovorn, T. & Macdonald, A. H. Topological exciton bands in moiré heterojunctions. Phys. Rev. Lett. 118, 147401 (2017).

    Article  Google Scholar 

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

    Article  Google Scholar 

  37. Forsythe, C. et al. Band structure engineering of 2D materials using patterned dielectric superlattices. Nat. Nanotechnol. 13, 566–571 (2018).

    Article  CAS  Google Scholar 

  38. Shi, L. K., Ma, J. & Song, J. C. W. Gate-tunable flat bands in van der Waals patterned dielectric superlattices. 2D Mater. 7, 015028 (2020).

    Article  CAS  Google Scholar 

  39. Britnell, L. et al. Electron tunneling through ultrathin boron nitride crystalline barriers. Nano Lett. 12, 1707–1710 (2012).

    Article  CAS  Google Scholar 

  40. Wang, L. et al. One-dimensional electrical contact to a two-dimensional material. Science 342, 614–617 (2013).

    Article  CAS  Google Scholar 

  41. Movva, H. C. P. et al. Density-dependent quantum Hall states and Zeeman splitting in monolayer and bilayer WSe2. Phys. Rev. Lett. 118, 247701 (2017).

    Article  Google Scholar 

  42. Goryca, M. et al. Revealing exciton masses and dielectric properties of monolayer semiconductors with high magnetic fields. Nat. Commun. 10, 4172 (2019).

    Article  CAS  Google Scholar 

  43. Keldysh, L. V. Coulomb interaction in thin semiconductor and semimetal films. JETP Lett. 29, 658–660 (1979).

    Google Scholar 

Download references

Acknowledgements

We thank C. Jin for fruitful discussions. This work was supported by the US Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES), under award number DE-SC0019481 (growth of WSe2 crystals), the Air Force Office of Scientific Research Hybrid Materials MURI under award number FA9550-18-1-0480 (device characterization) and the US Army Research Office under grant number W911NF-17-1-0605 (optical spectroscopy and analysis). We also acknowledge support from the National Science Foundation (Platform for the Accelerated Realization, Analysis, and Discovery of Interface Materials (PARADIM)) under cooperative agreement number DMR-1539918 (device fabrication). Growth of the hBN crystals was supported by the Elemental Strategy Initiative of MEXT, Japan and CREST (JPMJCR15F3), JST. K.F.M. acknowledges support from a David and Lucille Packard Fellowship.

Author information

Authors and Affiliations

  1. School of Applied and Engineering Physics, Cornell University, Ithaca, NY, USA

    Yang Xu, Connor Horn, Jiacheng Zhu, Yanhao Tang, Liguo Ma, Lizhong Li, Jie Shan & Kin Fai Mak

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

    Song Liu & James C. Hone

  3. National Institute for Materials Science, Tsukuba, Japan

    Kenji Watanabe & Takashi Taniguchi

  4. Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, NY, USA

    Jie Shan & Kin Fai Mak

  5. Kavli Institute at Cornell for Nanoscale Science, Ithaca, NY, USA

    Jie Shan & Kin Fai Mak

Authors
  1. Yang Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Connor Horn
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jiacheng Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yanhao Tang
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Liguo Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Lizhong Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Song Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Kenji Watanabe
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. Takashi Taniguchi
    View author publications

    You can also search for this author in PubMed Google Scholar

  10. James C. Hone
    View author publications

    You can also search for this author in PubMed Google Scholar

  11. Jie Shan
    View author publications

    You can also search for this author in PubMed Google Scholar

  12. Kin Fai Mak
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Y.X. performed the measurements with assistance from Y.T., L.M. and L.L. Y.X., C.H. and J.Z. fabricated the devices and analysed the data. S.L. and J.C.H. grew the bulk WSe2 crystals, and K.W. and T.T. grew the bulk hBN crystals. Y.X., J.S. and K.F.M. designed the scientific objectives, oversaw the project and co-wrote the manuscript. All authors discussed the results and commented on the manuscript.

Corresponding authors

Correspondence to Jie Shan or Kin Fai Mak.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature Materials thanks G. Eda, B. LeRoy and the other, anonymous, reviewer(s) 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.

Extended data

Extended Data Fig. 1 Optical image of device D1.

The black, blue, and yellow dashed curves outline the few-layer graphite gate electrode, the graphene layer, and the WSe2 monolayer, respectively. The scale bar is 15 μm. The device structure of D1 is shown in Fig. 1c.

Extended Data Fig. 2 Optical images from device D3.

a-d, f, Components of device D3 on Si substrates before transfer. They include, from the bottom up according to Fig. 1c, the bottom hBN layer (a), the WSe2 monolayer (b), the monolayer hBN spacer (c), the graphene layer (d), and the top hBN layer (f). e, An optical image of the sample before picking up the top hBN layer. The WSe2 monolayer, the one-layer hBN spacer, and the graphene layer are outlined with yellow, red, and blue dashed curves, respectively. The sharp edge (120° angle) of the graphene layer (d) and the top hBN layer (f) are aligned before transfer. The final device shows optical transition replicas in areas both with (Fig. 3c) and without the hBN spacer (Fig. 3a).

Extended Data Fig. 3 AFM of device D3 (part of the sample).

a, AFM topography image. b, Height measurement along the red line in (a). The step size (~ 0.36 nm) corresponds to the thickness of an hBN monolayer.

Source data

Extended Data Fig. 4 Magneto-optical spectroscopy of device D1 at Vg ≈ 0 V.

a, Reflection contrast spectrum (ΔR/R0) as a function of out-of-plane magnetic field at the graphene Dirac point. The white light probe is left circularly polarized (σ+). b, The magnetic-field dependence of the 1s, 2s, 3s, …6s exciton energy is extracted from (a). The filled and empty symbols denote the values measured with σ+ and σ- light, respectively. The latter is equivalent to σ+ probe under a negative magnetic field. The red dashed lines are best fits of the Keldysh potential model as described in the text.

Source data

Extended Data Fig. 5 Magneto-optical spectroscopy of device D1 at Vg = 5 V.

a, b, Same as Fig. S4 for doped graphene. The dashed lines in (a) show the fan-like interband Landau level transitions for B > 0 T, which converge to the band gap energy at zero field. Unlike the case at the graphene Dirac point, the Keldysh potential model cannot describe all the exciton states. The fitting parameters are chosen to best match the exciton excited states. The predicted 1 s energy from the model is about 60 meV higher than the experimental result. c, Energy of the Ns state as a function of N for N = 2 – 11 at B = -9 T. Solid red line is a linear fit. d, Reflection contrast spectrum (left, black line) and its first derivative with respect to energy (right, red line) at zero magnetic field. The vertical red dashed line indicates the band edge transition (~ 1.8 eV).

Source data

Extended Data Fig. 6 Gate-dependent quasiparticle band gap energy of device D1 at zero magnetic field.

The contour plot is the first derivative of the reflection contrast spectrum with respect to energy. The black curve is the gate-dependent band edge transition determined using the methods described in the text.

Source data

Extended Data Fig. 7 Gate-dependent optical replica energy at different hBN spacer thickness.

a, b, The hBN spacer thickness is ~0.36 and ~2 nm for device D3 and D5, respectively.

Source data

Extended Data Fig. 8 Decoupling of electronic hybridization.

Gate voltage dependent reflection contrast spectrum for angle-aligned WSe2/WS2 heterobilayer without (a) and with (b) a monolayer hBN spacer. The dashed lines in a mark the enhanced contrast at the electron and hole Mott states with moiré filling factor ν = +1 and ν = −1, respectively. The dashed line in b marks the onset of hole doping in the WSe2 layer.

Source data

Extended Data Fig. 9 Periodic screening versus periodic electric potential.

a, b, The spatial dependence of the WSe2 band gap Eg (separation between the conduction band minimum CBM and the valence band maximum VBM), the 1s binding energy energy Eb(1s), and the 1s exciton energy E(1s) in (a) a periodic screening and (b) a periodic electric potential environment. The ε is the dielectric constant and V is the scalar electric potential.

Extended Data Fig. 10

Gate-dependent reflection contrast spectrum for a WSe2 monolayer (a) and WSe2/graphene heterobilayer (b) encapsulated by hBN and gated with few-layer graphite. White dashed lines in (a) mark the onset of electron and hole doping in WSe2. b, shows the same data as Fig. 2a in a larger energy range and different color scale, indicating the absence of charged excitons.

Source data

Source data

Source Data Fig. 2

Raw data for generating the reflection contrast colour contour plots and linecuts, extracted band edge, first and second replica energies.

Source Data Fig. 3

Raw data for generating the reflection contrast colour contour plots, and extracted Δ1 and Δ2.

Source Data Extended Data Fig. 3

Raw data for the AFM measurement linecut.

Source Data Extended Data Fig. 4

Raw data for generating the reflection contrast contour plot and extracted exciton energies, as well the exciton energies simulated from the Keldysh potential model.

Source Data Extended Data Fig. 5

Raw data for generating the reflection contrast contour plot, linecut and extracted exciton energies, as well the exciton energies simulated from the Keldysh potential model.

Source Data Extended Data Fig. 6

Smoothed reflection contrast derivative data, and the extracted band edge energies.

Source Data Extended Data Fig. 7

Extracted first and second replica energies for two additional samples.

Source Data Extended Data Fig. 8

Raw data for generating the reflection contrast contour plots.

Source Data Extended Data Fig. 10

Raw data for generating the reflection contrast contour plots (a); the data for (b) are contained in Source Data Fig. 2.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Xu, Y., Horn, C., Zhu, J. et al. Creation of moiré bands in a monolayer semiconductor by spatially periodic dielectric screening. Nat. Mater. 20, 645–649 (2021). https://doi.org/10.1038/s41563-020-00888-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41563-020-00888-y

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