  In this work, we predict the emergence of the valley Edelstein Effect (VEE),
which is an electric-field-induced spin polarization effect, in gated monolayer
transition metal dichalcogenides (MTMDs). We found an unconventional
valley-dependent response in which the spin-polarization is parallel to the
applied electric field with opposite spin-polarization generated by opposite
valleys. This is in sharp contrast to the conventional Edelstein effect in
which the induced spin-polarization is perpendicular to the applied electric
field. We identify the origin of VEE as combined effects of conventional
Edelstein effect and valley-dependent Berry curvatures induced by coexisting
Rashba and Ising SOCs in gated MTMDs. Experimental schemes to detect the VEE
are also considered.
