Recent results on the optical properties of monolayer and few layers of semiconducting transition metal dichalcogenides are reviewed. Experimental observations are presented and discussed in the frame of existing models, highlighting the limits of our understanding in this emerging field of research. We first introduce the representative band structure of these systems and their interband optical transitions. The effect of an external magnetic field is then considered to discuss Zeeman spectroscopy and optical pumping experiments, both revealing phenomena related to the valley degree of freedom. Finally, we discuss the observation of single photon emitters in different types of layered materials, including wide band gap hexagonal boron nitride. While going through these topics, we try to focus on open questions and on experimental observations, which do not yet have a clear explanation.

We present a comprehensive optical study of thin flakes of tungsten disulfide (WS₂) with thickness ranging from mono- to octalayer and in the bulk limit.

We perform a theoretical study of radiative decay of dark intravalley excitons in transition metal dichalcogenide monolayers. This decay necessarily involves an electronic spin flip. The intrinsic decay mechanism due to interband spin–flip dipole moment perpendicular to the monolayer plane, gives a rate about 100–1000 times smaller than that of bright excitons. However, we find that this mechanism also introduces an energy splitting due to a local field effect, and the whole oscillator strength is contained in the higher-energy component, while the lowest-energy state remains dark and needs an extrinsic spin–flip mechanism for the decay. Rashba effect due to a perpendicular electric field or a dielectric substrate, gives a negligible radiative decay rate (about 10 ⁷ times slower than that of bright excitons). Spin flip due to Zeeman effect in a sufficiently strong in-plane magnetic field can give a decay rate comparable to that due to the intrinsic interband spin–flip dipole.

We demonstrate that, in monolayers (MLs) of semiconducting transition metal dichalcogenides, the $s$-type Rydberg series of excitonic states follows a simple energy ladder: ${\epsilon }_n=-{\mathrm{Ry}}^{*}/(n+\delta {)}^2$, $n=1,2,\dots$, in which ${\mathrm{Ry}}^{*}$ is very close to the Rydberg energy scaled by the dielectric constant of the medium surrounding the ML and by the reduced effective electron-hole mass, whereas the ML polarizability is accounted for only by $\delta$. This is justified by the analysis of experimental data on excitonic resonances, as extracted from magneto-optical measurements of a high-quality ${\mathrm{WSe}}_2$ ML encapsulated in hexagonal boron nitride (hBN), and well reproduced with an analytically solvable Schrödinger equation when approximating the electron-hole potential in the form of a modified Kratzer potential. Applying our convention to other ${\mathrm{MoSe}}_2$, ${\mathrm{WS}}_2$, ${\mathrm{MoS}}_2$ MLs encapsulated in hBN, we estimate an apparent magnitude of $\delta$ for each of the studied structures. Intriguingly, $\delta$ is found to be close to zero for ${\mathrm{WSe}}_2$ as well as for ${\mathrm{MoS}}_2$ monolayers, what implies that the energy ladder of excitonic states in these two-dimensional structures resembles that of Rydberg states of a three-dimensional hydrogen atom.

Monolayers of semiconducting transition metal dichalcogenides are two-dimensional direct-gap systems which host tightly bound excitons with an internal degree of freedom corresponding to the valley of the constituting carriers. Strong spin-orbit interaction and the resulting ordering of the spin-split subbands in the valence and conduction bands makes the lowest-lying excitons in $W{X}_2$ ($X$ being S or Se) spin forbidden and optically dark. With polarization-resolved photoluminescence experiments performed on a ${\mathrm{WSe}}_2$ monolayer encapsulated in a hexagonal boron nitride, we show how the intrinsic exchange interaction in combination with the applied in-plane and/or out-of-plane magnetic fields enables one to probe and manipulate the valley degree of freedom of the dark excitons.