Correlated electronic structure, orbital-dependent correlations, and Lifshitz transition in tetragonal FeS

Iron-based binary chalcogenide superconductors FeSe and FeS have attracted much recent attention due to their complex orbital-selective correlations and Cooper pairing, offering the minimal model system holding the key properties to understanding the physics of high-${T}_c$ superconductors. Here, using density functional plus dynamical mean-field theory method with full self-consistency over the charge density, we study the effect of electronic correlations on the electronic structure, magnetic properties, orbital-dependent band renormalizations, and Fermi surface of the tetragonal phase of bulk FeS. We perform a direct structural optimization of the ${P}₄/nmm$ crystal structure of paramagnetic FeS, minimizing the total energy of FeS with respect to the lattice constant $a$ and the internal coordinate ${z}_{\mathrm{S}}$ of atom S. Our results show an anomalous sensitivity of the electronic structure and magnetic properties of FeS (intrinsic to all Fe-based chalcogenide and pnictide superconductors) to fine details of its crystal structure, e.g., to a small variation of the chalcogen coordinate ${z}_{\mathrm{S}}$. Upon expansion of the lattice volume (which can be realized, e.g., in ${\mathrm{FeS}}_{1\ensuremath{-}x}{\mathrm{Se}}_x$ and ${\mathrm{FeS}}_{1\ensuremath{-}x}{\mathrm{Te}}_x$), we observe a remarkable change of the electronic structure of FeS which is associated with a complete reconstruction of the Fermi-surface topology (Lifshitz transition). This behavior is ascribed to a correlation-induced shift of the Van Hove singularity associated with the Fe $xy$ and $xz/yz$ orbitals at the $M$ point across the Fermi level. The Lifshitz phase transition is accompanied by a significant growth of local magnetic moments and emergence of strong orbital-selective correlations. It is seen as a pronounced anomaly (``kink'') in the total energies upon expansion of the lattice, associated with a remarkable enhancement of compressibility. This behavior is accompanied by an orbital-dependent formation of local moments, a crossover from itinerant to localized orbital-selective moment behavior of the Fe $3d$ electrons. While exhibiting weak effective mass enhancement of the Fe $3d$ states ${m}^*/m\ensuremath{\sim}1.3--1.4$, correlation effects reveal a strong impact on a position of the Van Hove singularity originating from the Fe $xz/yz$ and $xy$ orbitals at the $M$ point, implying a complex interplay between electronic correlations and band structure effects in FeS. Our results suggest a complex interplay between electronic correlations, magnetism, and lattice degrees of freedom in FeS.