Probing excitonic dark states in single-layer tungsten disulphide

Abstract

Transition metal dichalcogenide (TMDC) monolayers have recently emerged as an important class of two-dimensional semiconductors with potential for electronic and optoelectronic devices1,2. Unlike semi-metallic graphene, layered TMDCs have a sizeable bandgap3. More interestingly, when thinned down to a monolayer, TMDCs transform from indirect-bandgap to direct-bandgap semiconductors4,5, exhibiting a number of intriguing optical phenomena such as valley-selective circular dichroism6,7,8, doping-dependent charged excitons9,10 and strong photocurrent responses11. However, the fundamental mechanism underlying such a strong light–matter interaction is still under intensive investigation. First-principles calculations have predicted a quasiparticle bandgap much larger than the measured optical gap, and an optical response dominated by excitonic effects12,13,14. In particular, a recent study based on a GW plus Bethe–Salpeter equation (GW-BSE) approach, which employed many-body Green’s-function methodology to address electron–electron and electron–hole interactions, theoretically predicted a diversity of strongly bound excitons14. Here we report experimental evidence of a series of excitonic dark states in single-layer WS2 using two-photon excitation spectroscopy. In combination with GW-BSE theory, we prove that the excitons are of Wannier type, meaning that each exciton wavefunction extends over multiple unit cells, but with extraordinarily large binding energy (0.7 electronvolts), leading to a quasiparticle bandgap of 2.7 electronvolts. These strongly bound exciton states are observed to be stable even at room temperature. We reveal an exciton series that deviates substantially from hydrogen models, with a novel energy dependence on the orbital angular momentum. These excitonic energy levels are experimentally found to be robust against environmental perturbations. The discovery of excitonic dark states and exceptionally large binding energy not only sheds light on the importance of many-electron effects in this two-dimensional gapped system, but also holds potential for the device application of TMDC monolayers and their heterostructures15 in computing, communication and bio-sensing.

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Figure 1: Probing the dark exciton states in single-layer WS2 by two-photon luminescence.
Figure 2: Extraordinarily strong excitonic effect in monolayer WS2.
Figure 3: One-photon absorption spectra and real-space exciton wavefunctions in monolayer WS2 from ab initio GW-BSE calculations.
Figure 4: Excitonic energy levels are robust to changes in the dielectric environment and to temperature changes.

References

  1. 1

    Wang, Q. H., Kalantar-Zadeh, K., Kis, A. & Coleman, J. N. Electronics and optoelectronics of two-dimensional transition metal dichalcogenides. Nature Nanotechnol. 7, 699–712 (2012)

    ADS  CAS  Article  Google Scholar 

  2. 2

    Radisavljevic, B., Radenovic, A., Brivio, J., Giacometti, V. & Kis, A. Single-layer MoS2 transistors. Nature Nanotechnol. 6, 147–150 (2011)

    ADS  CAS  Article  Google Scholar 

  3. 3

    Beal, A. R., Knights, J. C. & Liang, W. Y. Transmission spectra of some transition metal dichalcogenides. II. Group VIA: trigonal prismatic coordination. J. Phys. C 5, 3540–3551 (1972)

    ADS  CAS  Article  Google Scholar 

  4. 4

    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)

    ADS  Article  Google Scholar 

  5. 5

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

    ADS  CAS  Article  Google Scholar 

  6. 6

    Zeng, H., Dai, J., Yao, W., Xiao, D. & Cui, X. Valley polarization in MoS2 monolayers by optical pumping. Nature Nanotechnol. 7, 490–493 (2012)

    ADS  CAS  Article  Google Scholar 

  7. 7

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

    ADS  CAS  Article  Google Scholar 

  8. 8

    Cao, T. et al. Valley-selective circular dichroism of monolayer molybdenum disulphide. Nature Commun. 3, 887 (2012)

    ADS  Article  Google Scholar 

  9. 9

    Mak, K. F. et al. Tightly bound trions in monolayer MoS2 . Nature Mater. 12, 207–211 (2012)

    ADS  Article  Google Scholar 

  10. 10

    Ross, J. S. et al. Electrical control of neutral and charged excitons in a monolayer semiconductor. Nature Commun. 4, 1474 (2013)

    ADS  Article  Google Scholar 

  11. 11

    Britnell, L. et al. Strong light-matter interactions in heterostructures of atomically thin films. Science 340, 1311–1314 (2013)

    ADS  CAS  Article  Google Scholar 

  12. 12

    Ramasubramaniam, A. Large excitonic effects in monolayers of molybdenum and tungsten dichalcogenides. Phys. Rev. B 86, 115409 (2012)

    ADS  Article  Google Scholar 

  13. 13

    Cheiwchanchamnangij, T. & Lambrecht, W. R. L. Quasiparticle band structure calculation of monolayer, bilayer, and bulk MoS2 . Phys. Rev. B 85, 205302 (2012)

    ADS  Article  Google Scholar 

  14. 14

    Qiu, D. Y., Felipe, H. & Louie, S. G. Optical spectrum of MoS2: many-body effects and diversity of exciton states. Phys. Rev. Lett. 111, 216805 (2013)

    ADS  Article  Google Scholar 

  15. 15

    Geim, A. K. & Grigorieva, I. V. Van der Waals heterostructures. Nature 499, 419–425 (2013)

    CAS  Article  Google Scholar 

  16. 16

    Knox, R. S. Theory of Excitons (Academic, 1963)

    Google Scholar 

  17. 17

    Scholes, G. D. & Rumbles, G. Excitons in nanoscale systems. Nature Mater. 5, 683–696 (2006)

    ADS  CAS  Article  Google Scholar 

  18. 18

    Hybertsen, M. S. & Louie, S. G. Electron correlation in semiconductors and insulators: band gaps and quasiparticle energies. Phys. Rev. B 34, 5390–5413 (1986)

    ADS  CAS  Article  Google Scholar 

  19. 19

    Rohlfing, M. & Louie, S. G. Electron-hole excitations and optical spectra from first principles. Phys. Rev. B 62, 4927–4944 (2000)

    ADS  CAS  Article  Google Scholar 

  20. 20

    Wang, F., Dukovic, G., Brus, L. E. & Heinz, T. F. The optical resonances in carbon nanotubes arise from excitons. Science 308, 838–841 (2005)

    ADS  CAS  Article  Google Scholar 

  21. 21

    Ye, Y. et al. Exciton-dominant electroluminescence from a diode of monolayer MoS2 . Appl. Phys. Lett. 104, 193508 (2014)

    ADS  Article  Google Scholar 

  22. 22

    Kumar, N. et al. Exciton-exciton annihilation in MoSe2 monolayers. Phys. Rev. B 89, 125427 (2014)

    ADS  Article  Google Scholar 

  23. 23

    Deslippe, J. et al. BerkeleyGW: A massively parallel computer package for the calculation of the quasiparticle and optical properties of materials and nanostructures. Comput. Phys. Commun. 183, 1269–1289 (2012)

    ADS  CAS  Article  Google Scholar 

  24. 24

    Deslippe, J. et al. Electron-hole interaction in carbon nanotubes: novel screening and exciton excitation spectra. Nano Lett. 9, 1330–1334 (2009)

    ADS  CAS  Article  Google Scholar 

  25. 25

    Keldysh, L. V. Coulomb interaction in thin semiconductor and semimetal films. J. Exp. Theor. Phys. Lett. 29, 658–660 (1979)

    Google Scholar 

  26. 26

    Spataru, C. D., Ismail-Beigi, S., Benedict, L. X. & Louie, S. G. Excitonic effects and optical spectra of single-walled carbon nanotubes. Phys. Rev. Lett. 92, 077402 (2004)

    ADS  Article  Google Scholar 

  27. 27

    Ishihara, T., Takahashi, J. & Goto, T. Optical properties due to electronic transitions in two-dimensional semiconductors (CnH2n+1NH3)2PbI4 . Phys. Rev. B 42, 11099–11107 (1990)

    ADS  CAS  Article  Google Scholar 

  28. 28

    Maultzsch, J. et al. Exciton binding energies in carbon nanotubes from two-photon photoluminescence. Phys. Rev. B 72, 241402 (2005)

    ADS  Article  Google Scholar 

  29. 29

    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)

    ADS  Article  Google Scholar 

Download references

Acknowledgements

This research was supported by the Lawrence Berkeley National Laboratory through the Office of Basic Energy Sciences, US Department of Energy under contract no. DE-AC02-05CH11231: the experimental work was supported by Sub-wavelength Metamaterial Design, Physics and Applications Program, and the theory part was supported by the Theory Program (GW-BSE calculations and simulations) and by the SciDAC Program on Excited State Phenomena (computer codes and algorithm developments), with computer time provided by the DOE National Energy Research Scientific Computing Center (NERSC). Z.Y. acknowledges discussions with T. Ishihara and F. Wang.

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Z.Y. and X.Z. initiated this research topic; Z.Y., K.O., X.Y. and Y.W. conducted the optical experiments; Z.Y. and H.Z. prepared samples; T.C. and S.G.L. performed the first-principles calculations; Z.Y., T.C., S.G.L. and X.Z. analysed the results and prepared the manuscript. All authors contributed to discussions and manuscript revision.

Corresponding authors

Correspondence to Steven G. Louie or Xiang Zhang.

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The authors declare no competing financial interests.

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Ye, Z., Cao, T., O’Brien, K. et al. Probing excitonic dark states in single-layer tungsten disulphide. Nature 513, 214–218 (2014). https://doi.org/10.1038/nature13734

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