  In this work, we investigate spin and valley transport properties of a
WSe$_2$ monolayer placed on top of a ferromagnetic insulator. We are interested
in controlling the transport properties by applying external potentials to the
system. To obtain spin an valley polarizations, we have considered a single and
a double barrier structure with gate potentials. We have analyzed how the
efficiency of these polarized transport properties depend on the gate-potential
intensities and geometrical configurations. Additionally, we investigate how
the spin and valley transport properties are modified when an ac-potential is
applied to the system. We have obtained a controllable modulation of the spin
and valley polarizations as a function of the intensity and frequency of the
ac-potential, mainly in the terahertz range. These results validate the
proposal of double quantum well structures of WSe$_2$ as candidates to provide
spin and valley dependent transport within an optimal geometrical parameter
regime.
