A series of long-lived excitons in a monolayer of tungsten disulphide are found to have strong binding energy and an energy dependence on orbital momentum that significantly deviates from conventional, three-dimensional, behaviour. The emergence of graphene optoelectronics has stimulated the development of near-transparent two-dimensional semiconductor materials. Much attention is focusing on the potentially extremely versatile transition metal dichalcogenides, such as molybdenum disulphide and tungsten disulphide, as components for ultrathin electronic devices. The physical origins of the unusually strong light–matter interactions in these materials remain unclear. An active topic in this area is how excitons (electron-hole pairs generated by light) behave in these low-dimensional systems. Here Xiang Zhang and colleagues report the discovery of a series of two-dimensional excitonic dark states in monolayer tungsten disulphide that have strong binding energy and an energy dependence on orbital momentum that significantly deviates from conventional (3D) behaviour. The findings open new avenues for fundamental research and opportunities to design devices such as photodetectors and photovoltaic cells. 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.

Probing excitonic dark states in single-layer tungsten disulphide