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Van der Waals heterostructure polaritons with moiré-induced nonlinearity

Abstract

Controlling matter–light interactions with cavities is of fundamental importance in modern science and technology1. This is exemplified in the strong-coupling regime, where matter–light hybrid modes form, with properties that are controllable by optical-wavelength photons2,3. By contrast, matter excitations on the nanometre scale are harder to access. In two-dimensional van der Waals heterostructures, a tunable moiré lattice potential for electronic excitations may form4, enabling the generation of correlated electron gases in the lattice potentials5,6,7,8,9. Excitons confined in moiré lattices have also been reported10,11, but no cooperative effects have been observed and interactions with light have remained perturbative12,13,14,15. Here, by integrating MoSe2–WS2 heterobilayers in a microcavity, we establish cooperative coupling between moiré-lattice excitons and microcavity photons up to the temperature of liquid nitrogen, thereby integrating versatile control of both matter and light into one platform. The density dependence of the moiré polaritons reveals strong nonlinearity due to exciton blockade, suppressed exciton energy shift and suppressed excitation-induced dephasing, all of which are consistent with the quantum confined nature of the moiré excitons. Such a moiré polariton system combines strong nonlinearity and microscopic-scale tuning of matter excitations using cavity engineering and long-range light coherence, providing a platform with which to study collective phenomena from tunable arrays of quantum emitters.

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Fig. 1: Moiré polariton system and the constituent moiré excitons and microcavity.
Fig. 2: Strong coupling and dispersions of moiré and ML polaritons.
Fig. 3: Nonlinearity of moiré hBL and ML polaritons.
Fig. 4: Enhanced nonlinearity by moiré lattice confinement.

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Data availability

The data that support the findings of this study are available from the corresponding author upon request.

References

  1. Walther, H., Varcoe, B. T. H., Englert, B.-G. & Becker, T. Cavity quantum electrodynamics. Rep. Prog. Phys. 69, 1325–1382 (2006).

    Article  ADS  Google Scholar 

  2. Deng, H., Haug, H. & Yamamoto, Y. Exciton-polariton Bose–Einstein condensation. Rev. Mod. Phys. 82, 1489–1537 (2010).

    Article  ADS  CAS  Google Scholar 

  3. Schneider, C. et al. Exciton-polariton trapping and potential landscape engineering. Rep. Prog. Phys. 80, 016503 (2017).

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  Google Scholar 

  11. Yu, H., Liu, G.-B., Tang, J., Xu, X. & Yao, W. Moiré excitons: from programmable quantum emitter arrays to spin-orbit coupled artificial lattices. Sci. Adv. 3, e1701696 (2017).

    Article  ADS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  16. Ritsch, H., Domokos, P., Brennecke, F. & Esslinger, T. Cold atoms in cavity-generated dynamical optical potentials. Rev. Mod. Phys. 85, 553–601 (2013).

    Article  ADS  CAS  Google Scholar 

  17. González-Tudela, A., Hung, C.-L., Chang, D. E., Cirac, J. I. & Kimble, H. J. Subwavelength vacuum lattices and atomatom interactions in two-dimensional photonic crystals. Nat. Photonics 9, 320–325 (2015).

    Article  ADS  Google Scholar 

  18. Léonard, J., Morales, A., Zupancic, P., Esslinger, T. & Donner, T. Supersolid formation in a quantum gas breaking a continuous translational symmetry. Nature 543, 87–90 (2017).

    Article  ADS  Google Scholar 

  19. Zhang, L. et al. Twist-angle dependence of moiré excitons in WS2 /MoSe2 heterobilayers. Nat. Commun. 11, 5888 (2020).

    Article  ADS  CAS  Google Scholar 

  20. Tang, Y. et al. Tuning layer-hybridized moiré excitons by the quantum-confined Stark effect. Nat. Nanotechnol. 16, 52–57 (2021).

    Article  ADS  CAS  Google Scholar 

  21. Chernikov, A., Ruppert, C., Hill, H. M., Rigosi, A. F. & Heinz, T. F. Population inversion and giant bandgap renormalization in atomically thin WS2 layers. Nat. Photonics 9, 466–470 (2015).

    Article  ADS  CAS  Google Scholar 

  22. Scuri, G. et al. Large excitonic reflectivity of monolayer MoSe2 encapsulated in hexagonal boron nitride. Phys. Rev. Lett. 120, 037402 (2018).

    Article  ADS  CAS  Google Scholar 

  23. Emmanuele, R. P. A. et al. Highly nonlinear trion-polaritons in a monolayer semiconductor. Nat. Commun. 11, 3589 (2020).

    Article  ADS  CAS  Google Scholar 

  24. Gu, J. et al. Enhanced nonlinear interaction of polaritons via excitonic Rydberg states in monolayer WSe2. Preprint at https://arxiv.org/abs/1912.12544 (2019).

  25. Kravtsov, V. et al. Nonlinear polaritons in a monolayer semiconductor coupled to optical bound states in the continuum. Light Sci. Appl. 9, 56 (2020).

    Article  ADS  CAS  Google Scholar 

  26. Moody, G. et al. Intrinsic homogeneous linewidth and broadening mechanisms of excitons in monolayer transition metal dichalcogenides. Nat. Commun. 6, 8315 (2015).

    Article  ADS  CAS  Google Scholar 

  27. Huang, D., Chyi, J.-I. & Morkoc¸, H. Carrier effects on the excitonic absorption in GaAs quantum-well structures: phase-space filling. Phys. Rev. B 42, 5147–5153 (1990).

    Article  ADS  CAS  Google Scholar 

  28. Tan, L. B. et al. Interacting polaron-polaritons. Phys. Rev. X 10, 021011 (2020).

    CAS  Google Scholar 

  29. Ballarini, D. et al. All-optical polariton transistor. Nat. Commun. 4, 1778 (2013).

    Article  ADS  CAS  Google Scholar 

  30. Walker, P. M. et al. Ultra-low-power hybrid light matter solitons. Nat. Commun. 6, 8317 (2015).

    Article  ADS  CAS  Google Scholar 

  31. Berloff, N. G. et al. Realizing the classical XY Hamiltonian in polariton simulators. Nat. Mater. 16, 1120–1126 (2017).

    Article  ADS  CAS  Google Scholar 

  32. Delteil, A. et al. Towards polariton blockade of confined exciton polaritons. Nat. Mater. 18, 219–222 (2019).

    Article  CAS  Google Scholar 

  33. Muñoz-Matutano, G. et al. Emergence of quantum correlations from interacting fibre-cavity polaritons. Nat. Mater. 18, 213–218 (2019).

    Article  Google Scholar 

  34. Kim, S. et al. Emergence of microfrequency comb via limit cycles in dissipatively coupled condensates. Phys. Rev. B 101, 085302 (2020).

    Article  ADS  CAS  Google Scholar 

  35. Daskalakis, K. S., Maier, S. A., Murray, R. & Kna-Cohen, S. Nonlinear interactions in an organic polariton condensate. Nat. Mater. 13, 271–278 (2014).

    Article  ADS  CAS  Google Scholar 

  36. Barachati, F. et al. Interacting polariton fluids in a monolayer of tungsten disulfide. Nat. Nanotechnol. 13, 906–909 (2018).

    Article  ADS  CAS  Google Scholar 

  37. Yu, H. & Yao, W. Electrically tunable topological transport of moiré polaritons. Sci. Bull. 65, 1555–1562 (2020).

    Article  CAS  Google Scholar 

Download references

Acknowledgements

We are grateful to D. Steel and M. Kira for discussions. L.Z., S.H., S.R.F. and H.D. acknowledge support by the Army Research Office under award W911NF-17-1-0312. L.Z. and H.D. also acknowledge support by the Air Force Office of Scientific Research under award FA2386-18-1-4086 and by the National Science Foundation under award DMR 1838412. S.R.F. also acknowledges support from the US Department of Energy, Office of Science, Office of Basic Energy Sciences, under award DE-SC0017971. F.W. is supported by the Laboratory for Physical Sciences. Y.-H.C. acknowledges support by the Young Scholar Fellowship Program of the Ministry of Science and Technology (MOST) in Taiwan, under grant MOST 108-2636-M-006-010. K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by MEXT, Japan, grant number JPMXP0112101001, JSPS KAKENHI grant number JP20H00354 and CREST (JPMJCR15F3), JST.

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Authors and Affiliations

Authors

Contributions

H.D. and L.Z. conceived the experiment. L.Z. performed the measurements. F.W. provided theoretical models. L.Z. and Z.Z. fabricated the device. L.Z. and H.D. performed data analysis. S.H. deposited the silver mirror. Y.-H.C. grew the bottom DBR mirror. K.W. and T.T. grew hBN single crystals. H.D. and S.R.F. supervised the projects. L.Z. and H.D. wrote the paper with inputs from other authors. All authors discussed the results, data analysis and the paper.

Corresponding author

Correspondence to Hui Deng.

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The authors declare no competing interests.

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Peer review information Nature thanks Qihua Xiong and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data figures and tables

Extended Data Fig. 1 hBL twist angle.

Twist angle of the hBL described in the main text, measured by second-harmonic generation (SHG) spectroscopy. a, Polarization-dependent (SHG) signal measured on the ML WS2 (green open circles) and MoSe2 (blue filled squares) regions of the hBL, and the corresponding fits with sinusoidal functions (green and blue solid lines). b, The SHG signal from the ML WS2, ML MoSe2 and hBL regions, measured with the same experimental configurations. The suppressed SHG signal from the hBL, resulting from destructive interference, indicates that the stacking order is H-stacking. The twist angle is determined to be 56.5° ± 0.8°.

Extended Data Fig. 2 Temperature dependence of moiré exciton.

Temperature dependence of the moiré excitons X1 and X2 measured from a separate hBL prepared on a sapphire substrate. The black dashed lines are guides for the eyes. The two exciton states can be well resolved up to 200 K, which could exclude charged excitons or excitons trapped by defects.

Extended Data Fig. 3 Schematic of the device.

a, Schematic of the device showing the different layers of a heterostructure embedded inside a microcavity that consists of a bottom DBR and a top silver mirror. b, Microscope image of the hBL on top of the DBR mirror, taken before depositing the PMMA layer and the silver mirror. c, Thickness of each layer of the device.

Extended Data Fig. 4 Photoluminescence from the moiré polariton.

Left, angle-resolved photoluminescence spectrum of an hBL in a cavity, excited by a continuous-wave laser with energy of 2.3 eV and power of 50 μW. To enhance the visibility of states at higher energy, the emission intensity above 1.607 eV is magnified five times. Right, simulated angle-resolved absorption, which agrees well with the measurement.

Extended Data Fig. 5 Transition from strong coupling to weak coupling driven by thermal broadening.

a, b, Transition from strong coupling to weak coupling, measured from the temperature dependence of Ω1 (red open circles) and (γc + γX1)/2 (purple triangles) (a) and Ω2 (red open circles) and (γc + γX2)/2 (purple triangles) (b). γc = 2.7 meV is constant with temperature. Ω1 and Ω2 drop below the average linewidth at about 100 K, showing the transition to the weak-coupling regime. Ω1 and Ω2 are extracted by fitting the angle-resolved white-light reflection spectra with equation (1) and the error bars correspond to the 95% confidence interval. γX1 and γX2 are measured independently from the bare hBL, and the error bars correspond to the 95% confidence interval of the Lorentzian fit.

Extended Data Fig. 6 Time-resolved photoluminescence of ML exciton, ML trion, hBL excitons and hBL trion.

a, b, Time-resolved photoluminescence spectra measured by a streak camera for ML MoSe2 (a) and hBL WS2–MoSe2 (b). (The hBL data are collected from a sample different from that discussed in the main text, which is not integrated with the microcavity.) The different resonances are labelled with white arrows, including the ML exciton (ML-X), ML trion (ML-T), moiré exciton at higher energy (hBL-X2), moiré exciton at lower energy (hBL-X1) and moiré trion (hBL-T). c, d, Time-resolved decay of ML-X (c) and hBL-X1 (d), obtained by integrating the spectrum in the range labelled by the red rectangles in a, b. The red solid lines in c, d are fits with a single exponential decay function. The photoluminescence decay time for ML-X and hBL-X1 is 6.7 ps and 8.0 ps, respectively.

Extended Data Fig. 7 Strong nonlinearity measured in another device.

a, Angle-resolved white-light reflection spectra taken at 5 K on the second sample. White solid lines are fits using the coupled-oscillator model. Dashed white lines are fitted energies of the uncoupled cavity photon and excitons. b, Power-dependent reflection spectra for the lower polariton (left) and middle polariton (right). c, Shift of polariton energies versus carrier density (logarithmic scale) obtained from b. d, Extracted nonlinear coefficients for lower polariton (red circles) and the calculations using fitted polariton energies (solid line). The error bars on the energy data correspond to the 95% confidence interval of the Lorentzian fit. The error bars of g correspond to the 95% confidence interval of the fit using g(n) = |dE(n)/dn|.

Extended Data Fig. 8 Profile of the laser used for nonlinearity characterization.

Profile of the pulsed laser (red dot) used for the nonlinearity measurement of moiré polaritons, compared with the moiré excitons X1 and X2 (blue dots) and moiré polaritons (black dots). The laser has a negligibly small tail on X2 and UP.

Extended Data Fig. 9 Dipole–dipole interaction strength as a function of twist angle θ.

\({U}_{{\rm{dd}}}^{(0)}\) and \({U}_{{\rm{dd}}}^{(1)}\) are the onsite and nearest-neighbour interaction strength, respectively.

Extended Data Fig. 10 Effect of moiré exciton X2 on the nonlinearity of polaritons.

Calculated shifts of hBL LPs and hBL MPs as a function of Ω2. When Ω2 changes by 10%, hBL LPs and hBL MPs shift by only 0.16 meV on average, which is negligible compared to the shift induced by exciton X1 (up to 2 meV; Fig. 3c).

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Zhang, L., Wu, F., Hou, S. et al. Van der Waals heterostructure polaritons with moiré-induced nonlinearity. Nature 591, 61–65 (2021). https://doi.org/10.1038/s41586-021-03228-5

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