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# Evidence for moiré excitons in van der Waals heterostructures

## Abstract

Recent advances in the isolation and stacking of monolayers of van der Waals materials have provided approaches for the preparation of quantum materials in the ultimate two-dimensional limit1,2. In van der Waals heterostructures formed by stacking two monolayer semiconductors, lattice mismatch or rotational misalignment introduces an in-plane moiré superlattice3. It is widely recognized that the moiré superlattice can modulate the electronic band structure of the material and lead to transport properties such as unconventional superconductivity4 and insulating behaviour driven by correlations5,6,7; however, the influence of the moiré superlattice on optical properties has not been investigated experimentally. Here we report the observation of multiple interlayer exciton resonances with either positive or negative circularly polarized emission in a molybdenum diselenide/tungsten diselenide (MoSe2/WSe2) heterobilayer with a small twist angle. We attribute these resonances to excitonic ground and excited states confined within the moiré potential. This interpretation is supported by recombination dynamics and by the dependence of these interlayer exciton resonances on twist angle and temperature. These results suggest the feasibility of engineering artificial excitonic crystals using van der Waals heterostructures for nanophotonics and quantum information applications.

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## Data availability

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

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## Acknowledgements

The work performed by K.T., J.C., A.H.M. and X. Li was primarily supported by the National Science Foundation (NSF) through the Center for Dynamics and Control of Materials, an NSF MRSEC, under Cooperative Agreement DMR-1720595. X. Li also acknowledges partial support from NSF EFMA-1542747 and the Welch Foundation via grant F-1662. The theoretical work by F.W. was supported by the US Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division. J.Q acknowledges support from the China Scholarship Council (grant 201706050068). A.H.M., K.K. and E.T. were supported in part by Army Research Office (ARO) grant W911NF-17-1-0312 (MURI). X. Lu and L.Y. are supported by the Air Force Office of Scientific Research (AFOSR) FA9550-17-1-0304 and NSF DMR-1455346. S.K. was financially supported by National Research Foundation of Korea (NRF) grant funded by the South Korean government (2017R1D1B04036381). K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by the MEXT, Japan and JSPS KAKENHI grant JP15K21722. A.R. and S.K.B. acknowledge support from the NASCENT Engineering Research Centre (ERC) funded by NSF grant EEC-1160494. D.A.S acknowledges support from the NSF Graduate Research Fellowship Program. N.L. acknowledges support from NSF CMMI-1351875. The Texas Nanofabrication Facility, where some of the work was carried out, is a member of the National Nanotechnology Coordinated Infrastructure, which is supported by the NSF (grant ECCS-1542159). This work is an official contribution of NIST, which is not subject to copyright in the United States.

## Author information

Authors

### Contributions

K.T. and G.M. performed the steady-state and time-resolved optical measurements. F.W. and X. Lu performed the calculations. K.T., J.C., J.E., A.Z., M.C., T.T. and K.W. prepared the samples. A.S., K.K., A.R., T.A., J.Q. and D.A.S. assisted with the experiments. K.T., G.M., F.W. and X. Li wrote the manuscript. E.T., S.K.B., N.L., K.L.S., S.K., L.Y., A.H.M. and X. Li supervised the project. All authors discussed the results and commented on the manuscript at all stages.

### Corresponding authors

Correspondence to Fengcheng Wu or Xiaoqin Li.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

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## Extended data figures and tables

### Extended Data Fig. 1 Band structure DFT calculation for different stacking types.

a, The three stacking types ($${{\rm{R}}}_{{\rm{h}}}^{{\rm{h}}}$$$${{\rm{R}}}_{{\rm{h}}}^{{\rm{X}}}$$ and $${{\rm{R}}}_{{\rm{h}}}^{{\rm{M}}}$$) of the bilayer MoSe2/WSe2 heterostructure and corresponding DFT-calculated band structures. b, Interlayer distance and bandgap of the three stacking types. c, First-principles GW-BSE calculation results for the quasiparticle bandgap and exciton-binding energy of different stacking types.

### Extended Data Fig. 2 Second-harmonic generation.

a, Polarization-resolved SHG signal as the sample is rotated in a plane normal to the incident laser. The peaks of the SHG signal correspond to the armchair axes of the crystal. b, Schematics of the phase-resolved SHG setup. c, SHG phase-resolved spectra between the monolayers and the beta barium borate crystal with signals in phase for a twist angle of approximately 0° between the monolayers. d, As in c but with out-of-phase signals for a twist angle of approximately 60°.

### Extended Data Fig. 3 Moiré exciton theory model.

a, Moiré reciprocal lattice vectors in the first shell. b, Real-space map of the centre-of-mass wavefunctions for peak 4. c, d, The spatial variation of the σ+ (c) and σ (d) components of the optical matrix elements.

### Extended Data Fig. 4 Thermal decay and recombination dynamics of a heterobilayer with a twist angle of 1°.

a, Temperature dependence of the photoluminescence between 25 K and 70 K. b, Time-resolved photoluminescence dynamics (points) at energies close to the four interlayer exciton transitions labelled in the inset. The solid lines are biexponential fits to the data. The inset shows the emission energy dependence of the fast and slow decay times.

### Extended Data Fig. 5 Comparison of photoluminescence between two heterobilayers with slightly different twist angles.

a, Steady-state photoluminescence spectra from the 1° sample (sample 1) and the 2° sample (sample 2). b, Time-resolved photoluminescence dynamics for interlayer exciton emission at 1,320 meV, as indicated by the shaded area in a.

### Extended Data Fig. 6 Spectra from different heterobilayer stacking configurations.

Comparison between interlayer exciton resonances from an H-type sample (upper panel) and an R-type sample (lower panel).

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Tran, K., Moody, G., Wu, F. et al. Evidence for moiré excitons in van der Waals heterostructures. Nature 567, 71–75 (2019). https://doi.org/10.1038/s41586-019-0975-z

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