Electric control of nearly free electron states and ferromagnetism in the transition-metal dichalcogenides monolayers

Using the first-principles calculations, we explore the nearly free electron (NFE) states in the transition-metal dichalcogenidesMX₂(M= Mo, W;X= S, Se, Te) monolayers. It is found that both the external electric field and electron (not hole) injection can flexibly tune the energy levels of the NFE states, which can shift down to the Fermi level and result in novel transport properties. In addition, we find that the valley polarization can be induced by both electron and hole doping in MoTe₂monolayer due to the ferromagnetism induced by the charge injection, which, however, is not observed in other five kinds ofMX₂monolayers. We carefully check band structures of all theMX₂monolayers, and find that the exchange splitting in the top of the valence band and the bottom of conduction band plays the key role in the ferromagnetism. Our researches enrich the electronic, spintronic, and valleytronic properties ofMX₂monolayers.