Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Letter
  • Published:

High-harmonic generation from an atomically thin semiconductor

Abstract

High-harmonic generation (HHG) in bulk solids permits the exploration of materials in a new regime of strong fields and attosecond timescales1,2,3,4,5,6. The generation process has been discussed in the context of strongly driven electron dynamics in single-particle bands7,8,9,10,11,12,13,14. Two-dimensional materials exhibit distinctive electronic properties compared to the bulk that could significantly modify the HHG process15,16, including different symmetries17,18,19, access to individual valleys20,21 and enhanced many-body interactions22,23,24,25. Here we demonstrate non-perturbative HHG from a monolayer MoS2 crystal, with even and odd harmonics extending to the 13th order. The even orders are predominantly polarized perpendicular to the pump and are compatible with the anomalous transverse intraband current arising from the material’s Berry curvature, while the weak parallel component suggests the importance of interband transitions. The odd harmonics exhibit a significant enhancement in efficiency per layer compared to the bulk, which is attributed to correlation effects. The combination of strong many-body Coulomb interactions and widely tunable electronic properties in two-dimensional materials offers a new platform for attosecond physics.

This is a preview of subscription content, access via your institution

Access options

Buy this article

Prices may be subject to local taxes which are calculated during checkout

Figure 1: HHG spectrum from monolayer MoS2.
Figure 2: Dependence of HHG on pump intensity for monolayer MoS2.
Figure 3: Dependence of HHG on crystallographic orientation of monolayer MoS2.
Figure 4: Comparison of the HHG efficiency of an isolated monolayer of MoS2 (red bars) with a monolayer of the bulk crystal (blue bars).

Similar content being viewed by others

References

  1. Ghimire, S. et al. Observation of high-order harmonic generation in a bulk crystal. Nat. Phys. 7, 138–141 (2011).

    Article  Google Scholar 

  2. Schubert, O. et al. Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations. Nat. Photon. 8, 119–123 (2014).

    Article  ADS  Google Scholar 

  3. Luu, T. T. et al. Extreme ultraviolet high-harmonic spectroscopy of solids. Nature 521, 498–502 (2015).

    Article  ADS  Google Scholar 

  4. Vampa, G. et al. Linking high harmonics from gases and solids. Nature 522, 462–464 (2015).

    Article  ADS  Google Scholar 

  5. Hohenleutner, M. et al. Real-time observation of interfering crystal electrons in high-harmonic generation. Nature 523, 572–575 (2015).

    Article  ADS  Google Scholar 

  6. Ndabashimiye, G. et al. Solid-state harmonics beyond the atomic limit. Nature 534, 520–523 (2016).

    Article  ADS  Google Scholar 

  7. Ghimire, S. et al. Generation and propagation of high-order harmonics in crystals. Phys. Rev. A 85, 043836 (2012).

    Article  ADS  Google Scholar 

  8. Golde, D., Meier, T. & Koch, S. W. High harmonics generated in semiconductor nanostructures by the coupled dynamics of optical inter- and intraband excitations. Phys. Rev. B 77, 075330 (2008).

    Article  ADS  Google Scholar 

  9. Hawkins, P. G., Ivanov, M. Y. & Yakovlev, V. S. Effect of multiple conduction bands on high-harmonic emission from dielectrics. Phys. Rev. A 91, 013405 (2015).

    Article  ADS  Google Scholar 

  10. Higuchi, T., Stockman, M. I. & Hommelhoff, P. Strong-field perspective on high-harmonic radiation from bulk solids. Phys. Rev. Lett. 113, 213901 (2014).

    Article  ADS  Google Scholar 

  11. Vampa, G., McDonald, C. R., Orlando, G., Corkum, P. B. & Brabec, T. Semiclassical analysis of high harmonic generation in bulk crystals. Phys. Rev. B 91, 064302 (2015).

    Article  ADS  Google Scholar 

  12. Vampa, G. et al. Theoretical analysis of high-harmonic generation in solids. Phys. Rev. Lett. 113, 073901 (2014).

    Article  ADS  Google Scholar 

  13. Wu, M., Ghimire, S., Reis, D. A., Schafer, K. J. & Gaarde, M. B. High-harmonic generation from Bloch electrons in solids. Phys. Rev. A 91, 043839 (2015).

    Article  ADS  Google Scholar 

  14. Kemper, A. F., Moritz, B., Freericks, J. K. & Devereaux, T. P. Theoretical description of high-order harmonic generation in solids. New J. Phys. 15, 023003 (2013).

    Article  ADS  MathSciNet  Google Scholar 

  15. Al-Naib, I., Sipe, J. E. & Dignam, M. M. High harmonic generation in undoped graphene: interplay of inter- and intraband dynamics. Phys. Rev. B 90, 245423 (2014).

    Article  ADS  Google Scholar 

  16. Kelardeh, H. K., Apalkov, V. & Stockman, M. I. Graphene in ultrafast and superstrong laser fields. Phys. Rev. B 91, 045439 (2015).

    Article  ADS  Google Scholar 

  17. Kumar, N. et al. Second harmonic microscopy of monolayer MoS2 . Phys. Rev. B 87, 161403 (2013).

    Article  ADS  Google Scholar 

  18. Li, Y. et al. Probing symmetry properties of few-layer MoS2 and h-BN by optical second-harmonic generation. Nano Lett. 13, 3329–3333 (2013).

    Article  ADS  Google Scholar 

  19. Malard, L. M., Alencar, T. V., Barboza, A. P. M., Mak, K. F. & de Paula, A. M. Observation of intense second harmonic generation from MoS2 atomic crystals. Phys. Rev. B 87, 201401 (2013).

    Article  ADS  Google Scholar 

  20. Xu, X., Yao, W., Xiao, D. & Heinz, T. F. Spin and pseudospins in layered transition metal dichalcogenides. Nat. Phys. 10, 343–350 (2014).

    Article  Google Scholar 

  21. Mak, K. F., McGill, K. L., Park, J. & McEuen, P. L. The valley Hall effect in MoS2 transistors. Science 344, 1489–1492 (2014).

    Article  ADS  Google Scholar 

  22. Chernikov, A. et al. Exciton binding energy and nonhydrogenic Rydberg series in monolayer WS2 . Phys. Rev. Lett. 113, 076802 (2014).

    Article  ADS  Google Scholar 

  23. He, K. et al. Tightly bound excitons in monolayer WSe2 . Phys. Rev. Lett. 113, 026803 (2014).

    Article  ADS  Google Scholar 

  24. Ye, Z. et al. Probing excitonic dark states in single-layer tungsten disulphide. Nature 513, 214–218 (2014).

    Article  ADS  Google Scholar 

  25. Mak, K. F. et al. Tightly bound trions in monolayer MoS2 . Nat. Mater. 12, 207–211 (2013).

    Article  ADS  Google Scholar 

  26. Xiao, D., Chang, M.-C. & Niu, Q. Berry phase effects on electronic properties. Rev. Mod. Phys. 82, 1959–2007 (2010).

    Article  ADS  MathSciNet  Google Scholar 

  27. Mak, K. F., Lee, C., Hone, J., Shan, J. & Heinz, T. F. Atomically thin MoS2: a new direct-gap semiconductor. Phys. Rev. Lett. 105, 136805 (2010).

    Article  ADS  Google Scholar 

  28. Splendiani, A. et al. Emerging photoluminescence in monolayer MoS2 . Nano Lett. 10, 1271–1275 (2010).

    Article  ADS  Google Scholar 

  29. Ellis, J. K., Lucero, M. J. & Scuseria, G. E. The indirect to direct band gap transition in multilayered MoS2 as predicted by screened hybrid density functional theory. Appl. Phys. Lett. 99, 261908 (2011).

    Article  ADS  Google Scholar 

  30. Vampa, G. et al. All-optical reconstruction of crystal band structure. Phys. Rev. Lett. 115, 193603 (2015).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

This project was supported primarily by the Air Force Office of Scientific Research under Grant Nos. FA9550-14-1-0108 and FA9550-14-1-0268. Additional support for Y.L. and T.F.H. was provided by the AMOS program, Chemical Sciences, Geosciences, and Biosciences Division, Basic Energy Sciences, U.S. Department of Energy under Contract No. DE-AC02-76-SFO0515 and by the Gordon and Betty Moore Foundation’s EPiQS Initiative through Grant No. GBMF4545. S.G. and Y.S.Y. acknowledge the support from the Office of Science Early Career Research Program. We thank P. H. Bucksbaum for useful discussions.

Author information

Authors and Affiliations

Authors

Contributions

H.L. and Y.L. contributed equally to this work, built the experimental set-up, carried out the measurements and analysed the data. D.A.R. and T.F.H. conceived the experiment. H.L., Y.L., Y.S.Y., S.G., T.F.H. and D.A.R. contribute to the interpretation of the data. All authors contributed to the discussions and the preparation of the manuscript.

Corresponding author

Correspondence to David A. Reis.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary information

Supplementary information (PDF 1563 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, H., Li, Y., You, Y. et al. High-harmonic generation from an atomically thin semiconductor. Nature Phys 13, 262–265 (2017). https://doi.org/10.1038/nphys3946

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue date:

  • DOI: https://doi.org/10.1038/nphys3946

This article is cited by

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing