Fig. 3: Thermodynamic charge transition levels and electronic structure of Co_S.

a Formation energy of Co_S as a function of Fermi level for the neutral and the two charged states. The charge transition levels, i.e., (+/0) and (0/−), are referenced to the band-edge positions of pristine WS₂ as obtained with PBE0 incorporating 22% of Fock exchange PBE0(0.22). b Orbital diagram of the localized defect states for neutral Co_S. Resonant states within the valence band and conduction band manifolds are not depicted. The characters of the localized states are indicated by the specific d orbitals of the Co atom [e.g., Co(\({d}_{{z}^{2}}\)) as the highest occupied state in the minority channel] and, if any, the d orbitals of the W atoms in the nearest neighbor (W^NN). The occupied (unoccupied) states are shown by the filled (empty) rectangles, the height of which indicates the degree of dispersion. The localized electrons in the majority (minority) channel are indicated by the arrows pointing up (down). The band-edge positions (in horizontal dashed lines) refer to those of the pristine WS₂ obtained with PBE0 (0.22). Energies are referenced to the vacuum level. SOC is not taken into account for the localized defect states. c Top view of the charge density (in blue) for the three \({\rm{Co}}_{{{{{{{{\rm{S}}}}}}}}}^{0}\) defect states as indicated in (b). The W and S atoms are represented by the gray and yellow spheres, respectively. The isovalue is 0.001 e/ų.