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 dichalcogenides(= Mo, W;= 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 MoTemonolayer due to the ferromagnetism induced by the charge injection, which, however, is not observed in other five kinds ofmonolayers. We carefully check band structures of all themonolayers, 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 ofmonolayers.