Light-Matter Interactions in Two-Dimensional Transition Metal Dichalcogenides: Dominant Excitonic Transitions in mono- and few-layer MoX$_2$ and Band Nesting

We report ab initio calculations of the dielectric function of six mono- and bilayer molybdenum dichalcogenides based in a Bethe Salpether equation+G$_0$W$_0$ ansatz, focussing on the excitonic transitions dominating the absorption spectrum up to an excitation energy of 3\,eV. Our calculations suggest that switching chalcogen atoms and the strength of interlayer interactions should affect the detailed composition of the high 'C' peaks in experimental optical spectra of molybdenum dichalcogenides and cause a significant spin-orbit-splitting of the contributing excitonic transitions in monolayer MoSe$_2$ and MoTe$_2$. This can be explained through changes in the electronic dispersion around the Fermi energy along the chalcogen series S$\rightarrow$Se$\rightarrow$Te that move the van-Hove singularities in the density of states of the two-dimensional materials along the \textit{$\Gamma$}-\textit{K} line in the Brillouin zone. Further, we confirm the distinct interlayer character of the '\textsl{C}' peak transition in few-layer MoS$_2$ that was predicted before from experimental data and show that a similar behaviour can be expected for MoSe$_2$ and MoTe$_2$ as well.