spin/valley Hall effect from the mirror symmetry breaking in monolayer MoS₂

For a 1H phase monolayer MoS_2, we calculate the Berry curvature, which generates the intrinsic spin/valley Hall effect in the material. By using the kp perturbation theory, we investigate the effect of the mirror symmetry breaking on the monolayer MoS₂ where the degree of the symmetry breaking can be controlled by a gate voltage. We show that the Berry curvature depends significantly on the gate voltage and this dependence arises from the spin-momentum coupling in the symmetry broken environment. We calculate the spin/valley Hall conductivity which can explain recent experimental results. We also extend this analysis to a bilayer MoS₂.