Intrinsic spin Hall effect in monolayers of group-VI dichalcogenides: A first-principles study

Using first-principles calculations within density functional theory, we investigate the intrinsic spin Hall effect in monolayers of group-VI transition-metal dichalcogenides MX ₂ (M=Mo,W and X=S,Se). MX ₂ monolayers are direct band-gap semiconductors with two degenerate valleys located at the corners of the hexagonal Brillouin zone. Because of the inversion symmetry breaking and the strong spin-orbit coupling, charge carriers in opposite valleys carry opposite Berry curvature and spin moment, giving rise to both a valley-Hall and a spin-Hall effect. We also show that the intrinsic spin Hall conductivity in inversion-symmetric bulk dichalcogenides is an order of magnitude smaller compared to monolayers. Our result demonstrates monolayer dichalcogenides as an ideal platform for the integration of valleytronics and spintronics.