Valley splitting in the van der Waals heterostructure WSe2/CrI3: The role of atom superposition

A recent experiment shows that the K'K valley degeneracy can be lifted in monolayer WSe2 deposited on a layered ferromagnetic substrate of CrI3. In this work, we take a van der Waals heterostructure WSe2/CrI3 to model the monolayer WSe2 on the CrI3 substrate and investigate the effects underpinning the K'K valley splitting based on first-principles calculations. 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 WSe2/CrI3. Furthermore, we show that the K'K valley splitting can be tuned in the trilayer CrI3/WSe2/CrI3 from nearly zero to more than two times of that in the bilayer WSe2/CrI3 by manipulating the layer alignment.