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.

Lightwave valleytronics in a monolayer of tungsten diselenide

Abstract

As conventional electronics approaches its limits1, nanoscience has urgently sought methods of fast control of electrons at the fundamental quantum level2. Lightwave electronics3—the foundation of attosecond science4—uses the oscillating carrier wave of intense light pulses to control the translational motion of the electron’s charge faster than a single cycle of light5,6,7,8,9,10,11,12,13,14,15. Despite being particularly promising information carriers, the internal quantum attributes of spin16 and valley pseudospin17,18,21 have not been switchable on the subcycle scale. Here we demonstrate lightwave-driven changes of the valley pseudospin and introduce distinct signatures in the optical readout. Photogenerated electron–hole pairs in a monolayer of tungsten diselenide are accelerated and collided by a strong lightwave. The emergence of high-odd-order sidebands and anomalous changes in their polarization direction directly attest to the ultrafast pseudospin dynamics. Quantitative computations combining density functional theory with a non-perturbative quantum many-body approach assign the polarization of the sidebands to a lightwave-induced change of the valley pseudospin and confirm that the process is coherent and adiabatic. Our work opens the door to systematic valleytronic logic at optical clock rates.

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

Relevant articles

Open Access articles citing this article.

Access options

Buy article

Get time limited or full article access on ReadCube.

$32.00

All prices are NET prices.

Fig. 1: High-odd-order sideband generation in monolayer WSe2.
Fig. 2: Electronic structure of WSe2 and quantum theory of high-order sideband generation.
Fig. 3: High-order sideband polarization for different crystal orientations.
Fig. 4: Intervalley mixing and lightwave valleytronics.

References

  1. Markov, I. L. Limits on fundamental limits to computation. Nature 512, 147–154 (2014).

    Article  ADS  CAS  Google Scholar 

  2. Ladd, T. D. et al. Quantum computers. Nature 464, 45–53 (2010).

    Article  ADS  CAS  Google Scholar 

  3. Krausz, F. & Stockman, M. I. Attosecond metrology: from electron capture to future signal processing. Nat. Photon. 8, 205–213 (2014).

    Article  ADS  CAS  Google Scholar 

  4. Corkum, P. B. & Krausz, F. Attosecond science. Nat. Phys. 3, 381–387 (2007).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  6. Zaks, B., Liu, R. B. & Sherwin, M. S. Experimental observation of electron–hole recollisions. Nature 483, 580–583 (2012).

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  9. Higuchi, T., Heide, C., Ullman, K., Weber, H. B. & Hommelhoff, P. Light-field-driven currents in graphene. Nature 550, 224–228 (2017).

    Article  ADS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  11. Garg, M. et al. Multi-petahertz electronic metrology. Nature 538, 359–363 (2016).

    Article  ADS  CAS  Google Scholar 

  12. Langer, F. et al. Lightwave-driven quasiparticle collisions on a subcycle timescale. Nature 533, 225–229 (2016).

    Article  ADS  CAS  Google Scholar 

  13. Liu, H. et al. High-harmonic generation from an atomically thin semiconductor. Nat. Phys. 13, 262–265 (2017).

    Article  CAS  Google Scholar 

  14. Yoshikawa, N., Tamaya, T. & Tanaka, K. High-harmonic generation in graphene enhanced by elliptically polarized light excitation. Science 356, 736–738 (2017).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  15. Sivis, M. et al. Tailored semiconductors for high-harmonic optoelectronics. Science 357, 303–306 (2017).

    Article  ADS  CAS  Google Scholar 

  16. Wolf, S. A. et al. Spintronics: a spin-based electronics vision for the future. Science 294, 1488–1495 (2001).

    Article  ADS  CAS  Google Scholar 

  17. Schaibley, J. R. et al. Valleytronics in 2D materials. Nat. Rev. Mater. 1, 16055 (2016).

    Article  ADS  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  19. Xiao, D., Liu, G.-B., Feng, W., Xu, X. & Yao, W. Coupled spin and valley physics in monolayers of MoS2 and other group-VI dichalcogenides. Phys. Rev. Lett. 108, 196802 (2012).

    Article  ADS  Google Scholar 

  20. Aivazian, G. et al. Magnetic control of valley pseudospin in monolayer WSe2. Nat. Phys. 11, 148–152 (2015).

    Article  CAS  Google Scholar 

  21. Ye, Z., Sun, D. & Heinz, T. F. Optical manipulation of valley pseudospin. Nat. Phys. 13, 26–29 (2017).

    Article  CAS  Google Scholar 

  22. Bloch, F. Über die Quantenmechanik der Elektronen in Kristallgittern. Z. Phys. 52, 555–600 (1929).

    Article  ADS  Google Scholar 

  23. Kira, M. & Koch, S. W. Semiconductor Quantum Optics (Cambridge Univ. Press, Cambridge, 2012).

  24. Yan, J.-Y. Theory of excitonic high-order sideband generation in semiconductors under a strong terahertz field. Phys. Rev. B 78, 075204 (2008).

    Article  ADS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  26. Banks, H. B. et al. Dynamical birefringence: electron–hole recollisions as probes of Berry curvature. Phys. Rev. X 7, 041042 (2017).

    Google Scholar 

  27. Mak, K. F., He, K., Shan, J. & Heinz, T. F. Control of valley polarization in monolayer MoS2 by optical helicity. Nat. Nanotechnol. 7, 494–498 (2012).

    Article  ADS  CAS  Google Scholar 

  28. Jones, A. M. et al. Optical generation of excitonic valley coherence in monolayer WSe2. Nat. Nanotechnol. 8, 634–638 (2013).

    Article  ADS  CAS  Google Scholar 

  29. Wang, G. et al. Control of exciton valley coherence in transition metal dichalcogenide monolayers. Phys. Rev. Lett. 117, 187401 (2016).

    Article  ADS  CAS  Google Scholar 

  30. Rycerz, A., Tworzydło, J. & Beenakker, C. W. J. Valley filter and valley valve in graphene. Nat. Phys. 3, 172–175 (2007).

    Article  CAS  Google Scholar 

  31. Gallot, G. & Grischkowsky, D. Electro-optic detection of terahertz radiation. J. Opt. Soc. Am. B 16, 1204–1212 (1999).

    Article  ADS  CAS  Google Scholar 

  32. Poellmann, C. et al. Resonant internal quantum transitions and femtosecond radiative decay of excitons in monolayer WSe2. Nat. Mater. 14, 889–893 (2015).

    Article  ADS  CAS  Google Scholar 

  33. Blaha, P., Schwarz, K., Madsen, G. K. H., Kvasnicka, D. & Luitz, J. Wien2k, An Augmented Plane Wave+Local Orbitals Program for Calculating Crystal Properties http://susi.theochem.tuwien.ac.at/ (Vienna Univ. Technology, Vienna, 2013).

  34. Kormányos, A. et al. k·p theory for two-dimensional transition metal dichalcogenide semiconductors. 2D Mater. 2, 022001 (2015).

    Article  Google Scholar 

  35. Singh, D. J. & Nordström, L. Planewaves, Pseudopotentials, and the LAPW Method (Springer, New York, 2006).

  36. Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865 (1996).

    Article  ADS  CAS  Google Scholar 

  37. Steinhoff, A., Rösner, M., Jahnke, F., Wehling, T. O. & Gies, C. Influence of excited carriers on the optical and electronic properties of MoS2. Nano Lett. 14, 3743–3748 (2014).

    Article  ADS  CAS  Google Scholar 

  38. Mootz, M., Kira, M. & Koch, S. W. Sequential build-up of quantum-optical correlations. J. Opt. Soc. Am. B 29, A17–A24 (2012).

    Article  ADS  CAS  Google Scholar 

  39. Kira, M. Hyperbolic Bloch equations: atom-cluster kinetics of an interacting Bose gas. Ann. Phys. 356, 185–243 (2015).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  40. Mootz, M., Kira, M. & Koch, S. W. Pair-excitation energetics of highly correlated many-body states. New J. Phys. 15, 093040 (2013).

    Article  ADS  Google Scholar 

  41. Kira, M. & Koch, S. W. Many-body correlations and excitonic effects in semiconductor spectroscopy. Prog. Quantum Electron. 30, 155–296 (2006).

    Article  ADS  Google Scholar 

  42. Kira, M. Coherent quantum depletion of an interacting atom condensate. Nat. Commun. 6, 6624 (2015).

    Article  ADS  CAS  Google Scholar 

  43. Smith, R. P. et al. Extraction of many-body configurations from nonlinear absorption in semiconductor quantum wells. Phys. Rev. Lett. 104, 247401 (2010).

    Article  ADS  CAS  Google Scholar 

  44. Loss, D. & DiVincenzo, D. P. Quantum computation with quantum dots. Phys. Rev. A 57, 120–126 (1998).

    Article  ADS  CAS  Google Scholar 

Download references

Acknowledgements

The work in Regensburg was supported by the European Research Council through grant number 305003 (QUANTUMsubCYCLE) as well as by the Deutsche Forschungsgemeinschaft (through grant number HU 1598/2-1, SFB 1277, projects A05, B05 and B06, and GRK 1570) and the work in Marburg and Michigan by the Deutsche Forschungsgemeinschaft (through SFB 1083 and grant numbers KI 917/3-1 and KI 917/2-2).

Reviewer information

Nature thanks J. Wang and the other anonymous reviewer(s) for their contribution to the peer review of this work.

Author information

Authors and Affiliations

Authors

Contributions

F.L., P.G.H., C.P.S., S.S., S.W.K., M.K. and R.H. conceived the study. F.L., C.P.S., S.S. and R.H. carried out the experiment and analysed the data. P.N., C.S. and T.K. provided, processed and characterized the samples. M.G. and J.F. performed the DFT calculations and P.G.H., J.T.S., U.H., S.W.K. and M.K. developed the quantum-mechanical model, carried out the computations and analysed the data. All authors discussed the results and contributed to the writing of the manuscript.

Corresponding author

Correspondence to M. Kira.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

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 Sample orientation.

a, Azimuthal scan of the second-harmonic intensity polarized parallel to the excitation pulse, ISHG,|| (blue curve), revealing the armchair direction at a crystal angle of φ = 30°. The dashed line marks the expected scaling proportional to sin2(3φ). Around the polar diagram, the hexagonal Brillouin zone of WSe2 is depicted with the high-symmetry points. b, Optical microscope image of the exfoliated monolayer on the visco-elastic gel film used for exfoliation. Areas appearing in lighter grey are few-layer tungsten diselenide. c, Monolayer sample after transfer to a diamond substrate. The contrast of this image has been enhanced to improve the visibility of the atomically thin WSe2 film. The red arrows mark the same edge in b and c, which has been identified as the zigzag direction using the SHG scan.

Extended Data Fig. 2 Polarization of subcycle sideband emission.

Circularly polarized 10-fs near-infrared (NIR) pulses (polarization-resolved intensity depicted as black spheres) excite valley-polarized electron–hole pairs in a monolayer of tungsten diselenide. Simultaneously, an atomically strong terahertz wave is applied in the zigzag direction and may transfer electrons and holes to the non-excited K′ valley. The high-order sideband emission resulting from coherent electron–hole collisions driven by the most intense half-cycle is measured to have an elliptical polarization (blue spheres), and contains contributions from the opposite valley. Our quantum theory reproduces this polarization state (red curve) and reveals a transfer yield of 66% to the initially unexcited K′ valley.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Langer, F., Schmid, C.P., Schlauderer, S. et al. Lightwave valleytronics in a monolayer of tungsten diselenide. Nature 557, 76–80 (2018). https://doi.org/10.1038/s41586-018-0013-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41586-018-0013-6

This article is cited by

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

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