Valley splitting in the van derWaals heterostructure WSe 2 /CrI 3 : The role of atom superposition
A recent experiment shows that the K'K valley degeneracy can be lifted in monolayer WSe 2 deposited on a layered ferromagnetic substrate of CrI 3 . In this work, we take a van der Waals heterostructure WSe 2 /CrI 3 to model the monolayer WSe 2 on the CrI 3 substrate and investigate the effects underpinning the K'K valley splitting based on first-principles calculations. Here, we demonstrate that the interfacial atom superposition plays an important role and a W-Cr superposition is essential for a relatively large valley splitting. The results indicate inevitable sample-to-sample variations in the K'K valley splitting in the WSe 2 /CrI 3 . Furthermore, we show that the K'K valley splitting can be tuned in the trilayer CrI 3 /WSe 2 /CrI 3 from nearly zero to more than two times of that in the bilayer WSe2/CrI3 by manipulating the layer alignment.