Tunable valley splitting and an anomalous valley Hall effect in hole-doped WS by proximity coupling with a ferromagnetic MnO monolayer.

Two-dimensional (2D) valleytronic systems can provide information storage and processing advantages that complement or surpass those of conventional charge and spin-based semiconductor technologies. For efficient use of the valley degree of freedom, the major challenge currently is to lift the valley degeneracy to achieve valley splitting for further valleytronic operations. In this work, we demonstrate that valley splitting and efficient hole-doping in monolayer WS can be achieved by the proximity coupling effect of 2D ferromagnetic MnO using density functional theory and Berry curvature calculations. A valley splitting of 43 meV is induced in the valence band of WS. The efficient hole-doping moves the Fermi level just located between the valence band maxima of the K and K' valleys, which is suitable for the valley-polarized transport. The magnitude of valley splitting relies on the strength of interfacial orbital hybridization and can be tuned continually by applying interfacial compression or an electric field. Owing to the sizable Berry curvature and time-reversal symmetry breaking of WS, a spin- and valley-polarized anomalous Hall current can be generated. Then, we proposed a valleytronic device that can be used as a filter for both the spin and valley based on this WS/MnO van der Waals heterostructure.