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Tuning layer-hybridized moiré excitons by the quantum-confined Stark effect

Nature Nanotechnology volume 16, pages 52–57 (2021)Cite this article

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Abstract

Moiré superlattices offer an unprecedented opportunity for tailoring interactions between quantum particles1,2,3,4,5,6,7,8,9,10,11 and their coupling to electromagnetic fields12,13,14,15,16,17,18. Strong superlattice potentials generate moiré minibands of excitons16,17,18—bound pairs of electrons and holes that reside either in a single layer (intralayer excitons) or in two separate layers (interlayer excitons). Twist-angle-controlled interlayer electronic hybridization can also mix these two types of exciton to combine their strengths13,19,20. Here we report the direct observation of layer-hybridized moiré excitons in angle-aligned WSe2/WS2 and MoSe2/WS2 superlattices by optical reflectance spectroscopy. These excitons manifest a hallmark signature of strong coupling in WSe2/WS2, that is, energy-level anticrossing and oscillator strength redistribution under a vertical electric field. They also exhibit doping-dependent renormalization and hybridization that are sensitive to the electronic correlation effects. Our findings have important implications for emerging many-body states in two-dimensional semiconductors, such as exciton condensates21 and Bose–Hubbard models22, and optoelectronic applications of these materials.

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Fig. 1: Doping-dependent reflectance contrast spectrum of WSe2/WS2 bilayers.
Fig. 2: Electric-field dependence of layer-hybridized excitons in WSe2/WS2 moiré superlattice.
Fig. 3: Electric-field dependence of layer-hybridized excitons in MoSe2/WS2 moiré superlattice.
Fig. 4: Doping dependence of layer-hybridized excitons in WSe2/WS2 moiré superlattice.

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Data availability

The data that support the findings of this study are available within the paper and its Supplementary Information. Additional data are available from the corresponding authors upon request.

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Acknowledgements

Research was primarily supported by the US Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES), under award number DE-SC0019481 (optical spectroscopy and growth of WSe2 crystals). Device fabrication was supported by the Air Force Office of Scientific Research Hybrid Materials MURI under award number FA9550-18-1-0480, and analysis and modelling were supported by the US Army Research Office under award number W911NF-17-1-0605 and the National Science Foundation under award number DMR-2004451. The growth of the hBN crystals was supported by the Elemental Strategy Initiative of MEXT, Japan and CREST (JPMJCR15F3), Japan Science and Technology Agency.

Author information

Authors and Affiliations

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

    Yanhao Tang, Jie Gu, Kin Fai Mak & Jie Shan

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

    Song Liu & James 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

    Kin Fai Mak & Jie Shan

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

    Kin Fai Mak & Jie Shan

Authors
  1. Yanhao Tang
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Contributions

Y.T. and J.G. fabricated the devices and performed the optical measurements. S.L. and J.H. grew the bulk TMD crystals. K.W. and T.T. grew the bulk hBN crystals. Y.T., K.F.M. and J.S. designed the study, performed the analysis and co-wrote the manuscript. All authors discussed the results and commented on the manuscript.

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Correspondence to Kin Fai Mak or Jie Shan.

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Extended data

Extended Data Fig. 1 Doping-dependent reflectance contrast in WSe2/WS2 bilayers.

Results are from WSe2/WS2 bilayers with a twist angle close to 20° (a,b), 60° (c,d), and 0° (e,f). Upper and lower panels show the energy windows corresponding to the fundamental exciton resonances in WS2 and WSe2, respectively. The horizontal dashed lines denote the filling factors of the moiré superlattice (v > 0 for electron filling and v < 0 for hole filling).

Extended Data Fig. 2 Electric-field dependence of layer-hybridized excitons in 60° aligned WSe2/WS2 moiré superlattice.

Energy derivative of the reflectance contrast spectrum at selected electric fields is shown for gate voltage at 3.5 V (a) and 6 V (b) (corresponding to filling factor close to 1 and 2). The spectra are vertically displaced for clarity. The dotted lines are guides to the eye for the resonance energy of the exciton features.

Extended Data Fig. 3 Electric-field dependence of excitons in 0° aligned WSe2/WS2.

Contour plot of the reflectance contrast spectrum as a function of applied electric field at fixed filling factor near 1. Interlayer excitons are not observed. The intralayer exciton resonances do not depend on the electric field.

Extended Data Fig. 4 Electric-field dependence of hybridized exciton amplitudes.

a, b, c, Decomposition of the amplitude squared of the hybridized iX (a), X1 (b) and X2 (c) states into the uncoupled states at varying electric fields. Black, red and blue lines denote the amplitude squared of the uncoupled interlayer exciton iX0, intralayer exciton X10 and intralayer exciton X20 states, respectively. The results are obtained by solving the eigenvalue equation for the three-level system described in the main text. All of the states in the three-level Hamiltonian are normalized. d, e, f, Electric-field dependence of the sum of the uncoupled X10 and X20 amplitude squared (solid line) for the hybridized iX (d), X1 (e) and X2 (f) states. The calculated results are compared to the peak amplitude (proportional to oscillator strength) of the corresponding excitons (symbols connected by blue lines). Since only the uncoupled intralayer excitons X10 and X20 couple to light strongly, the oscillator strength of the hybridized excitons is well approximated by the sum of these two contributions. The experimental results agree reasonably well with the three-level model.

Extended Data Fig. 5

Electric-field dependence of layer-hybridized excitons in MoSe2/WS2 moiré superlattice (second device).

Extended Data Fig. 6

Doping dependence of layer-hybridized excitons in 60° aligned WSe2/WS2 moiré superlattice under fixed electric fields (a–h). The dashed lines denote from bottom to top filling factor 0, 1, and 2.

Extended Data Fig. 7 Electric-field dependence of layer-hybridized excitons in WSe2/WS2 moiré superlattice at filling factor of 0.57 (VG=2.5 V).

Same measurement as in Fig. 2 away from integer filling factors. Two spectral features are discernable for hybridized X1. Coupled three-level analysis is performed for each feature. The extracted parameters from the model are shown in Fig. 4 with the size of the symbols representing the oscillator strength of the two features.

Extended Data Fig. 8 Polarization-resolved SHG intensity.

a, b, Second-harmonic intensity as a function of the polarization angle of the excitation light from WSe2/WS2 bilayers with a twist angle close to 0° (a) and 60° (b). Black, red and blue lines represent measurements on the isolated WSe2 monolayer, isolated WS2 monolayer, and bilayer, respectively. Samples are excited by linearly polarized light under normal incidence. The cross-polarized component of the second harmonic is detected. The second-harmonic radiation from each monolayer is added constructively in the 0° bilayer sample (a) and destructively in the 60° bilayer sample (b).

Extended Data Fig. 9 Band alignment in WSe2/WS2.

Type II band alignment of 60° aligned WSe2/WS2 bilayer (a) and PL spectrum of the fundamental interlayer exciton (b).

Extended Data Fig. 10 Band alignment in MoSe2/WS2.

a,b, Doping-dependent reflectance contrast spectrum of a 20° aligned MoSe2/WS2 bilayer focusing on the fundamental intralyer exciton in MoSe2 (a) and WS2 (b). The horizontal dashed lines mark the onset of electron and hole doping. The intralyer exciton in MoSe2 loses oscillator strength and evolves into the red-shifted feature (charged excitons) upon both electron and hole doping, suggesting a type I band alignment.

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Tang, Y., Gu, J., Liu, S. et al. Tuning layer-hybridized moiré excitons by the quantum-confined Stark effect. Nat. Nanotechnol. 16, 52–57 (2021). https://doi.org/10.1038/s41565-020-00783-2

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