Probing excitonic dark states in single-layer tungsten disulphide


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.


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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.

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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).

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