Evolution of Electronic Structure as a Function of Layer Thickness in Group-VIB Transition Metal Dichalcogenides: Emergence of Localization Prototypes

Layered group-VIB transition metal dichalcogenides (with the formula of MX2) are known to show a transition from an indirect band gap in the thick n-monolayer stack (MX2)n to a direct band gap at the n = 1 monolayer limit, thus converting the system into an optically active material suitable for a variety of optoelectronic applications. The origin of this transition has been attributed predominantly to quantum confinement effect at reduced n. Our analysis of the evolution of band-edge energies and wave functions as a function of n using ab initio density functional calculations including the long-range dispersion interaction reveals (i) the indirect-to-direct band gap transformation is triggered not only by (kinetic-energy controlled) quantum confinement but also by (potential-energy controlled) band repulsion and localization. On its own, neither of the two effects can explain by itself the energy evolution of the band-edge states relevant to the transformation; (ii) when n decreased, there emerge distinct regimes with characteristic localization prototypes of band-edge states deciding the optical response of the system. They are distinguished by the real-space direct/indirect in combination with momentum-space direct/indirect nature of electron and hole states and give rise to distinct types of charge distribution of the photoexcited carriers that control excitonic behaviors; (iii) the various regimes associated with different localization prototypes are predicted to change with modification of cations and anions in the complete MX2 (M = Cr, Mo, W and X = S, Se, Te) series. These results offer new insight into understanding the excitonic properties (e.g., binding energy, lifetime etc.) of multiple layered MX2 and their heterostructures.