Abstract
We show that inversion symmetry breaking together with spin-orbit coupling leads to coupled spin and valley physics in monolayer MoS2 and group-VI dichalcogenides, making possible controls of spin and valley in these 2D materials. The spin-valley coupling at the valence band edges suppresses spin and valley relaxation, as flip of each index alone is forbidden by the ∼ 0.1 eV valley contrasting spin splitting. Valley Hall and spin Hall effects coexist in both electron-doped and hole-doped systems. Optical interband transitions have frequency-dependent polarization selection rules which allow selective photoexcitation of carriers with various combination of valley and spin indices. Photo-induced spin Hall and valley Hall effects can generate long lived spin and valley accumulations on sample boundaries. The physics discussed here provides a route towards the integration of valleytronics and spintronics in multi-valley materials with strong spin-orbit coupling and inversion symmetry breaking.