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


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.

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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.

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


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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



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.

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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.

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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).

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