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# Momentum-space indirect interlayer excitons in transition-metal dichalcogenide van der Waals heterostructures

## Abstract

Monolayers of transition-metal dichalcogenides feature exceptional optical properties that are dominated by tightly bound electron–hole pairs, called excitons. Creating van der Waals heterostructures by deterministically stacking individual monolayers can tune various properties via the choice of materials1 and the relative orientation of the layers2,3. In these structures, a new type of exciton emerges where the electron and hole are spatially separated into different layers. These interlayer excitons4,5,6 allow exploration of many-body quantum phenomena7,8 and are ideally suited for valleytronic applications9. A basic model of a fully spatially separated electron and hole stemming from the K valleys of the monolayer Brillouin zones is usually applied to describe such excitons. Here, we combine photoluminescence spectroscopy and first-principles calculations to expand the concept of interlayer excitons. We identify a partially charge-separated electron–hole pair in MoS2/WSe2 heterostructures where the hole resides at the Γ point and the electron is located in a K valley. We control the emission energy of this new type of momentum-space indirect, yet strongly bound exciton by variation of the relative orientation of the layers. These findings represent a crucial step towards the understanding and control of excitonic effects in van der Waals heterostructures and devices.

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## Acknowledgements

The work is financially supported by the German Research Foundation (DFG) under grant numbers SE 651/45-1, GRK 1570, KO 3612/1-1 and KO 3612/3-1. G.S. gratefully acknowledges financial support by the Ministry of Education and Science of the Russian Federation (grant no. K3-2017-064). Computational resources for this project were provided by ZIH Dresden.

## Author information

Authors

### Contributions

F.M., P.N., C. Schüller and T.K. conceived the experiments. F.M. fabricated the samples and performed the optical spectroscopy and data analysis together with P.N., G.P. and T.K. N.P. and C. Strunk annealed samples and performed AFM measurements. J.K. performed the DFT calculations together with F.S. and G.S., interpreted the results and supervised the theoretical analysis. A.C. carried out the exciton modelling under the supervision of D.R.R. using parameters provided by J.K. J.K. D.R.R. and T.K. wrote the paper together with F.M. and P.N. All authors discussed the results.

### Corresponding authors

Correspondence to Jens Kunstmann or Tobias Korn.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

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## Supplementary information

### Supplementary Information

Supplementary Figures 1–13, Supplementary Tables 1 and 2, Supplementary References

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Kunstmann, J., Mooshammer, F., Nagler, P. et al. Momentum-space indirect interlayer excitons in transition-metal dichalcogenide van der Waals heterostructures. Nature Phys 14, 801–805 (2018). https://doi.org/10.1038/s41567-018-0123-y

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