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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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## Data availability

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

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## 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.

## Author information

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.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

## Additional information

Peer review information Nature thanks Qihua Xiong 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 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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