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Recently fabricated InSe monolayers exhibit remarkable characteristics thatindicate the potential of this material to host a number of many-bodyphenomena. Here, we consistently describe collective electronic effects inhole-doped InSe monolayers using advanced many-body techniques. To this end, wederive a realistic electronic-structure model from first principles that takesinto account the most important characteristics of this material, including aflat band with prominent van Hove singularities in the electronic spectrum,strong electron-phonon coupling, and weakly-screened long-ranged Coulombinteractions. We calculate the temperature-dependent phase diagram as afunction of band filling and observe that this system is in a regime withcoexisting charge density wave and ferromagnetic instabilities that are drivenby strong electronic Coulomb correlations. This regime can be achieved atrealistic doping levels and high enough temperatures, and can be verifiedexperimentally. We find that the electron-phonon interaction does not play acrucial role in these effects, effectively suppressing the local Coulombinteraction without changing the qualitative physical picture.

Coexisting charge density wave and ferromagnetic instabilities in monolayer InSe