Large Valley Splitting in van der Waals Heterostructures with Type-III Band Alignment

Abstract

Lifting the valley degeneracy of monolayer transition-metal dichalcogenides (TMDs) can substantially break the balance of carriers in the $K$ and ${K}^{\mathrm{\ensuremath{'}}}$ valleys. This opens a promising way to utilize magnetic materials to break time-reversal symmetry to achieve valley splitting. In the work presented in this paper, we find that the magnitude of the valley splitting in TMD-based van der Waals (vdW) heterostructures is correlated with the strength of the magnetic proximity effect, which is positively related to the interlayer charge transfer and Coulomb interaction. As a result, for the same stacking, large valley splittings can be obtained only when the vdW heterostructure has a type-III, instead of a type-I or type-II, band alignment. We demonstrate this finding in $\mathrm{TMD}/\mathrm{Ni}{Y}_{2}$ ($Y=\mathrm{Cl},\mathrm{Br},\mathrm{I}$) vdW heterostructures in detail based on first-principles calculations, and predict several heterostructures with large valley splittings. This discovery can help to distinguish whether a magnetic material can enable TMDs to produce large valley splittings, and guide experiments for technological applications.