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

Abstract

Using first-principles calculations within density functional theory, we investigate the intrinsic spin Hall effect in monolayers of group-VI transition-metal dichalcogenides $M{X}_{2}$ ($M=\mathrm{Mo},\phantom{\rule{0.16em}{0ex}}\phantom{\rule{0.16em}{0ex}}\mathrm{W}$ and $X=\mathrm{S},\phantom{\rule{0.16em}{0ex}}\phantom{\rule{0.16em}{0ex}}\mathrm{Se}$). $M{X}_{2}$ 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.