Vacancy localization effects on MX2 transition metal dichalcogenides: a systematic ab-initio study

Two-dimensional transition metal dichalcogenides (MX$_2$) vacancy formation energetics is extensively investigated. Within an ab-initio approach we study the MX$_2$ systems, with M=Mo, W, Ni, Pd and Pt, and X=S, Se, and Te. Here we classify that chalcogen vacancies are always energetic favorable over the transition metal ones. However, for late transition metals Pd $4d$, and Pt $5d$ the metal vacancy are experimentally achievable, bringing up localized magnetic moments within the semiconducting matrix. By quantifying the localization of the chalcogen vacancy states we evidentiate that it rules the intra- and inter-vacancy interactions that establish both the number of vacancy states neatly lying within the semiconducting gap, as well as its electronic dispersion and SOC splitting. Combining different vacancies and phase variability 1T and 1H of the explored systems allow us to construct a guiding picture for the vacancy states localization.