  Inspired by the profound physical connotations and potential application
prospects of the valleytronics, we design a two-dimensional (2D) WS2/h-VN
magnetic van der Waals (vdW) heterostructure and study the control of valley
degree of freedom through the first-principles calculations. A considerable
spin splitting of 627 meV is obtained at the K valley, accompanied with a
strong suppression of that at the K' valley. An intrinsic large valley
splitting of 376 meV is generated in the valence band, which corresponds to an
effective Zeeman magnetic field of 2703 T. Besides of the valence band, the
conduction band of WS2 possesses a remarkable spin splitting also, and valley
labelled dark exciton states are present at the K' valley. The strengths of
spin and valley splitting relied on the interfacial orbital hybridization are
further tuned continually by the in-plane strain and interlayer spacing.
Maximum spin and valley splitting of 654 and 412 meV are finally achieved,
respectively, and the effective Zeeman magnetic field can be enhanced to 2989T
with a -3 % strain. Time-reversal symmetry breaking and the sizable Berry
curvature in the heterostructure lead to a prominent anomalous Hall
conductivity at the K and K' valleys. Based on these finding, a prototype
filter device for both the valley and spin is proposed.
