Atomically thin materials such as graphene and monolayer transition metal dichalcogenides (TMDs) exhibit remarkable physical properties resulting from their reduced dimensionality and crystal symmetry. The family of semiconducting transition metal dichalcogenides is an especially promising platform for fundamental studies of two-dimensional (2D) systems, with potential applications in optoelectronics and valleytronics due to their direct band gap in the monolayer limit and highly efficient light-matter coupling. A crystal lattice with broken inversion symmetry combined with strong spin-orbit interactions leads to a unique combination of the spin and valley degrees of freedom. In addition, the 2D character of the monolayers and weak dielectric screening from the environment yield a significant enhancement of the Coulomb interaction. The resulting formation of bound electron-hole pairs, or excitons, dominates the optical and spin properties of the material. Here we review recent progress in our understanding of the excitonic properties in monolayer TMDs and lay out future challenges. We focus on the consequences of the strong direct and exchange Coulomb interaction, discuss exciton-light interaction and effects of other carriers and excitons on electron-hole pairs in TMDs. Finally, the impact on valley polarization is described and the tuning of the energies and polarization observed in applied electric and magnetic fields is summarized.

The strong light-matter interaction and the valley selective optical selection rules make monolayer (ML) MoS 2 an exciting 2D material for fundamental physics and optoelectronics applications. But, so far, optical transition linewidths even at low temperature are typically as large as a few tens of meV and contain homogeneous and inhomogeneous contributions. This prevented in-depth studies, in contrast to the bettercharacterized ML materials MoSe 2 and WSe 2 . In this work, we show that encapsulation of ML MoS 2 in hexagonal boron nitride can efficiently suppress the inhomogeneous contribution to the exciton linewidth, as we measure in photoluminescence and reflectivity a FWHM down to 2 meV at T ¼ 4 K. Narrow optical transition linewidths are also observed in encapsulated WS 2 , WSe 2 , and MoSe 2 MLs. This indicates that surface protection and substrate flatness are key ingredients for obtaining stable, high-quality samples. Among the new possibilities offered by the well-defined optical transitions, we measure the homogeneous broadening induced by the interaction with phonons in temperature-dependent experiments. We uncover new information on spin and valley physics and present the rotation of valley coherence in applied magnetic fields perpendicular to the ML.