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Prediction of switchable half semiconductor in d$^{1}$ transition metal dichalcogenide monolayers

We propose that a half semiconducting state can exist in trigonal-prismatic transition metal dichalcogenide (TMDC) monolayers of d$^{1}$ configuration. In that state both electrons and holes are spin polarized and share the same spin channel. On the basis of hybrid density functional theory, we predict in particular that VS$_2$ monolayers are half semiconductors with a direct band gap. Moreover, we find that the conduction electron spin orientation of VS$_2$ switches under moderate strain. Our predictions thus open up intriguing possibilities for applications of VS$_2$ in spintronics and optoelectronics. Our analysis of trigonal-prismatic group-V MX$_2$ (M=V, Nb, Ta; X=S, Se, Te) monolayers reveals a broad diversity of electronic states that can be understood qualitatively in terms of localization of $d$ electrons.