Phase diagram of electron-doped dichalcogenides

Using first-principle calculations, we examine the sequence of phases in electron-doped dichalcogenides, such as recently realized in field-gated MoS₂. Upon increasing the electron-doping level, we observe a succession of semiconducting, metallic, superconducting, and charge density wave regimes, i.e., in different order compared to the phase diagram of metallic dichalcogenides, such as TiSe₂. Both instabilities trace back to a softening of phonons, which couple the electron populated conduction band minima. The superconducting dome, calculated using Eliashberg theory, is found to fit the experimentally observed phase diagram, obtained from resistivity measurements. The charge density wave phase at higher electron doping concentrations as predicted from instabilities in the phonon modes is further corroborated by detecting the accompanying lattice deformation in density-functional-based supercell relaxations. Upon charge density wave formation, doped MoS₂ remains metallic but undergoes a Lifschitz transition, where the number of Fermi pockets is reduced.