Transport properties of tetragonal iron monosulfide, mackinawite, show a range of complex features. Semiconductive behavior and proximity to metallic states with nodal superconductivity mark this d-band system as unconventional quantum material. Here, we use the density functional dynamical mean-field theory (DFDMFT) scheme to comprehensively explain why tetragonal FeS shows both semiconducting and metallic responses in contrast to tetragonal FeSe which is a pseudogaped metal above the superconducting transition temperature. Within local-density-approximation plus dynamical mean-field theory (LDA+DMFT) we characterize its paramagnetic insulating and metallic phases, showing the proximity of mackinawite to selective Mott localization. We report the coexistence of pseudogaped and anisotropic Dirac-like electronic dispersion at the border of the Mott transition. These findings announce a new understanding of many-particle physics in quantum materials with coexisting Dirac-fermions and pseudogaped electronic states at low energies. Based on our results we propose that in electron-doped FeS substantial changes would be seen when the metallic regime was tuned towards an electronic state that hosts unconventional superconductivity.
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