Tetragonal transition metal dichalcogenides with diverse electronic properties

Hexagonal transition metal dichalcogenides (TMDCs) represent a famous material family with rich structural phases and elemental compositions, whose diverse electronic properties, like magnetism, topological property, and superconductivity (SC), spark promising applications in the interdisciplinary field of ``XX-tronics''. Here we found tetragonal TMDCs with distorted Lieb ($d\mathrm{Lieb}$) lattice present similar electronic properties as hexagonal TMDCs, by demonstrating the stability of transition metal diselenides ($d\mathrm{Lieb}\ensuremath{-}M{\mathrm{Se}}_{2}$) and ditellurides ($d\mathrm{Lieb}\ensuremath{-}M{\mathrm{Te}}_{2}$) with semiconductivity, half-metallicity, magnetic metallicity, topological electronic states, or phonon-mediated SC. Specifically, $d\mathrm{Lieb}\ensuremath{-}\mathrm{TiS}{\mathrm{e}}_{2}$ and $d\mathrm{Lieb}\ensuremath{-}\mathrm{TiT}{\mathrm{e}}_{2}$ are semiconductors, whereas partial occupation of localized ${d}_{{z}^{2}}$ states induces Stoner magnetism in $d\mathrm{Lieb}\ensuremath{-}M{\mathrm{Se}}_{2}$ ($M=\mathrm{Nb}$, V, Cr) with half-metallicity and in $d\mathrm{Lieb}\ensuremath{-}\mathrm{MnS}{\mathrm{e}}_{2}$ with metallicity. Notably, as the only TMDC monolayer with the magnetism stemming from Nb atom, $d\mathrm{Lieb}\ensuremath{-}\mathrm{NbS}{\mathrm{e}}_{2}$ monolayer was found exhibiting exotic chiral topological edge states. The Stoner magnetism will be suppressed in $d\mathrm{Lieb}\ensuremath{-}\mathrm{FeS}{\mathrm{e}}_{2}$ monolayer with fully occupied ${d}_{{z}^{2}}$ states, which could enable phonon-mediated SC with a transition temperature ${T}_{\mathrm{C}}\ensuremath{\sim}4$ Kelvin. Together with our previously proposed disulfides $d\mathrm{Lieb}\ensuremath{-}M{\mathrm{S}}_{2}$, this work provides an overview table for tetragonal TMDCs with diverse electronic properties, which appear as promising alternatives for hexagonal TMDCs in the application of ``XX-tronics''.