Large Valley Splitting in Monolayer Transition Metal Dichalcogenides by Proximity Coupling to Magnetic Substrate

Lifting the valley degeneracy in monolayer transition metal dichalcogenides is indispensable for valley operations. In this work, we show that valley polarization can be achieved by proximity coupling monolayer transition metal dichalcogenides to magnetic insulator substrate, and the magnitude of valley splitting can be continually tuned by external pressure and strain. Due to the sizeable Berry curvature and time-reversal symmetry breaking in transition metal dichalcogenides when placed on magnetic substrate, a spin and valley polarized anomalous Hall current can be obtained in the presence of in-plane electrical field, which provides a mean to detect the valleys by electric measurements and forms the basis for valleytronic device. These findings are also applicable to other valley materials coupling to magnetic insulators.