First-principles study of valley splitting of transition-metal dichalcogenides in MX/CrI (M = W, Mo; X = S, Se, Te) van der Waals heterostructures.

The rapid development of valleytronics makes the application of two-dimensional (2D) transition-metal dichalcogenides (TMDs) in valley electronics important. As a new degree of freedom, valley splitting of TMDs has been achieved and tuned by many methods. Among them, using the magnetic proximity effect (MPE) generated from the interface of 2D van der Waals (vdW) heterostructures stacked with TMDs and one magnetic substrate, valley splitting can be achieved through band edge lifting at the adjacent K/K' valley. However, the comprehensive mechanism and strategy of valley splitting in 2D TMD heterostructures need to be explored ulteriorly. Here, we systematically investigated valley splitting of MX in MX/CrI (M = W, Mo; X = S, Se, Te) vdW heterostructures using first-principles approaches. We demonstrated that twisting is an effective method to enhance valley splitting in MX/CrI vdW heterostructures. Furthermore, we also showed a ∼10 times enhancement in valley splitting by changing the stacking patterns between WTe and CrI layers. We attribute this to the interlayer magnetic and electronic coupling between the two layers of the vdW heterostructure. The present results provide a theoretical basis and effective methods for tuning valley splitting 2D TMD heterostructures.