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:

Spin-polarized electrons in monolayer MoS2

Nature Nanotechnology volume 14, pages 432–436 (2019)Cite this article

Subjects

Abstract

Coulomb interactions are crucial in determining the ground state of an ideal two-dimensional electron gas (2DEG) in the limit of low electron densities1. In this regime, Coulomb interactions dominate over single-particle phase-space filling. In silicon and gallium arsenide, electrons are typically localized at these low densities. In contrast, in transition-metal dichalcogenides (TMDs), Coulomb correlations in a 2DEG can be anticipated at experimentally relevant electron densities. Here, we investigate a 2DEG in a gated monolayer of the TMD molybdenum disulfide2. We measure the optical susceptibility, a probe of the 2DEG which is local, minimally invasive and spin selective3. In a magnetic field of 9.0 T and at electron concentrations up to n ≃ 5 × 1012 cm−2, we present evidence that the ground state is spin-polarized. Out of the four available conduction bands4,5, only two are occupied. These two bands have the same spin but different valley quantum numbers. Our results suggest that only two bands are occupied even in the absence of a magnetic field. The spin polarization increases with decreasing 2DEG density, suggesting that Coulomb interactions are a key aspect of the symmetry breaking. We propose that exchange couplings align the spins6. The Bohr radius is so small7 that even electrons located far apart in phase-space interact with each other6.

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

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

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

Fig. 1: Monolayer MoS2.
Fig. 2: Optical susceptibility of a gated monolayer of MoS2.
Fig. 3: Analysis of the optical susceptibility of a gated monolayer of MoS2.
Fig. 4: Electrons and exciton states in monolayer MoS2.

Similar content being viewed by others

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

References

  1. Attaccalite, C., Moroni, S., Gori-Giorgi, P. & Bachelet, G. B. Correlation energy and spin polarisation in the 2D electron gas. Phys. Rev. Lett. 88, 256601 (2002).

    Article  Google Scholar 

  2. 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  Google Scholar 

  3. Xiao, D., Liu, G.-B., Feng, W., Xu, X. & Yao, W. Coupled spin and valley physics in monolayer of MoS2 and other group-VI dichalcogenides. Phys. Rev. Lett. 108, 196902 (2012).

    Google Scholar 

  4. Kormányos, A., Zoloyomi, V., Drummond, N. D. & Burkard, G. Spin–orbit coupling, quantum dots, and qubits in monolayer transition metal dichalcogenides. Phys. Rev. X 4, 011034 (2014).

    Google Scholar 

  5. Liu, G.-B., Shan, W.-Y., Yao, Y., Yao, W. & Xiao, D. Three-band tight-binding model for monolayers of group-VIB transition metal dichalcogenides. Phys. Rev. B 89, 039901 (2014).

    Article  Google Scholar 

  6. Dery, H. Theory of intervalley Coulomb interactions in monolayer transition-metal dichalcogenides. Phys. Rev. B 94, 075421 (2016).

    Article  Google Scholar 

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

    Article  Google Scholar 

  8. Cadiz, F. et al. Excitonic linewidth approaching the homogeneous limit in MoS2-based van der Waals heterostructures. Phys. Rev. X 7, 021026 (2017).

    Google Scholar 

  9. Ajayi, O. A. et al. Approaching the intrinsic photoluminescence linewidth in transition metal dichalcogenide monolayers. 2D Mater. 4, 031011 (2017).

    Article  Google Scholar 

  10. Marinov, K., Avsar, A., Watanabe, K., Taniguchi, T. & Kis, A. Resolving the spin splitting in the conduction band of monolayer MoS2. Nat. Commun. 8, 1938 (2017).

    Article  Google Scholar 

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

    Article  CAS  Google Scholar 

  12. Pisoni, R. et al. Interactions and magnetotransport through spin-valley coupled Landau levels in monolayer MoS2. Phys. Rev. Lett. 121, 247701 (2018).

    Article  CAS  Google Scholar 

  13. Suris, R. A. et al. Excitons and trions modified by interaction with a two-dimensional electron gas. Phys. Status Solidi B 227, 343–352 (2001).

    Article  CAS  Google Scholar 

  14. Ossau, W. J. & Suris, R. Optical Properties of 2D Systems with Interacting Electrons (Kluwer Academic, Dordrecht, 2003).

  15. Efimkin, D. K. & MacDonald, A. H. Many-body theory of trion absorption features in two-dimensional semiconductors. Phys. Rev. B 95, 035417 (2017).

    Article  Google Scholar 

  16. Sidler, M. et al. Fermi polaron-polaritons in charge-tunable atomically thin semiconductors. Nat. Phys. 13, 255–261 (2016).

    Article  Google Scholar 

  17. Plechinger, G. et al. Trion fine structure and coupled spin–valley dynamics in monolayer tungsten disulfide. Nat. Mater. 7, 12715 (2016).

    CAS  Google Scholar 

  18. Courtade, E. et al. Charged excitons in monolayer WSe2: experiment and theory. Phys. Rev. B 96, 085302 (2017).

    Article  Google Scholar 

  19. Yu, H., Cui, X., Xu, X. & Yao, W. Valley excitons in two-dimensional semiconductors. Natl Sci. Rev. 2, 57–70 (2015).

    Article  CAS  Google Scholar 

  20. Back, P. et al. Giant paramagnetism-induced valley polarization of electrons in charge-tunable monolayer MoSe2. Phys. Rev. Lett. 118, 237404 (2017).

    Article  Google Scholar 

  21. Hawrylak, P. Optical properties of a two-dimensional electron gas: evolution of spectra from excitons to Fermi-edge singularities. Phys. Rev. B 44, 3821 (1991).

    Article  CAS  Google Scholar 

  22. Huard, V., Cox, R. T., Saminadayar, K., Arnoult, A. & Tatarenko, S. Bound states in optical absorption of semiconductor quantum wells containing a two-dimensional electron gas. Phys. Rev. Lett. 84, 187 (2000).

    Article  CAS  Google Scholar 

  23. Wang, Z., Mak, K. F. & Shan, J. Strongly interaction-enhanced valley magnetic response in monolayer WSe2. Phys. Rev. Lett. 120, 066402 (2018).

    Article  CAS  Google Scholar 

  24. Wang, Z., Shan, J. & Mak, K. F. Valley- and spin-polarized Landau levels in monolayer WSe2. Nat. Nanotechnol. 12, 144–149 (2016).

    Article  Google Scholar 

  25. Stier, A. V., McCreary, K. M., Jonker, B. T., Kono, J. & Crooker, S. A. Exciton diamagnetic shifts and valley Zeeman effects in monolayer WS2 and MoS2 to 65 Tesla. Nat. Commun. 7, 10643 (2016).

    Article  CAS  Google Scholar 

  26. Scrace, T. et al. Magnetoluminescence and valley polarized state of a two-dimensional electron gas in WS2 monolayers. Nat. Nanotechnol. 10, 603 (2015).

    Article  CAS  Google Scholar 

  27. Mermin, N. D. & Wagner, H. Absence of ferromagnetism or antiferromagnetism in one- or two-dimensional isotropic Heisenberg models. Phys. Rev. Lett. 17, 1133 (1966).

    Article  CAS  Google Scholar 

  28. Żak, R. A., Maslov, D. & Loss, D. Spin susceptibility of interacting two-dimensional electrons in the presence of spin–orbit coupling. Phys. Rev. B 82, 115415 (2010).

    Article  Google Scholar 

  29. Zhao, C. et al. Enhanced valley splitting in monolayer WSe2 due to magnetic exchange field. Nat. Nanotechnol. 12, 757 (2017).

    Article  CAS  Google Scholar 

  30. Yu, L. et al. Graphene/MoS2 hybrid technology for large-scale two-dimensional electronics. Nano Lett. 14, 3055–3063 (2014).

    Article  CAS  Google Scholar 

Download references

Acknowledgements

We thank J. Klinovaja, D. Loss and D. Miserev, and also G. Burkard, A. Pearce and A. Kormányos, for discussions. The work in Basel was financially supported by SNF (Project No. 200020_156637), NCCR QSIT and QCQT. P.M. acknowledges support from grants OTKA PD-121052, OTKA FK123894 and the Bolyai Fellowship. K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by the MEXT, Japan, JSPS KAKENHI grant numbers JP18K19136 and the CREST (JPMJCR15F3), JST.

Author information

Authors and Affiliations

  1. Department of Physics, University of Basel, Basel, Switzerland

    Jonas Gaël Roch, Guillaume Froehlicher, Nadine Leisgang, Peter Makk & Richard John Warburton

  2. Department of Physics, Budapest University of Technology and Economics and Nanoelectronics ‘Momentum’ Research Group of the Hungarian Academy of Sciences, Budapest, Hungary

    Peter Makk

  3. National Institute for Material Science, Tsukuba, Japan

    Kenji Watanabe & Takashi Taniguchi

Authors
  1. Jonas Gaël Roch
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Guillaume Froehlicher
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Nadine Leisgang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Peter Makk
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Kenji Watanabe
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Takashi Taniguchi
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Richard John Warburton
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

G.F. and J.G.R. carried out the experiments. G.F., J.G.R., N.L. and P.M. fabricated the device. G.F. and J.G.R. carried out the data analysis. K.W. and T.T. grew the hexagonal boron nitride crystals. J.G.R. and R.J.W. wrote the manuscript with input from all authors.

Corresponding author

Correspondence to Jonas Gaël Roch.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Journal peer review information: Nature Nanotechnology thanks Ahmet Avsar and Benedikt Scharf 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.

Supplementary information

Supplementary Information

Supplementary Figures 1–14, Supplementary Table 1

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Roch, J.G., Froehlicher, G., Leisgang, N. et al. Spin-polarized electrons in monolayer MoS2. Nat. Nanotechnol. 14, 432–436 (2019). https://doi.org/10.1038/s41565-019-0397-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41565-019-0397-y

This article is cited by

Search

Advanced 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