We theoretically study the proximity spin-orbit coupling (SOC) in graphene on a transition-metal dichalcogenides (TMDC) monolayer stacked with arbitrary twist angles. We find that the relative rotation greatly enhances the spin splitting of graphene, typically by a few to ten times compared to the nonrotated geometry, and the maximum splitting is achieved around ${20}^{\circ }$. The induced SOC can be changed from the Zeeman type to the Rashba type by rotation. The spin splitting is also quite sensitive to the gate-induced potential, and it sharply rises when the graphene's Dirac point is shifted toward the TMDC band. The theoretical method does not need the exact lattice matching and it is applicable to any incommensurate bilayer systems. It is useful for the twist-angle engineering of a variety of van der Waals proximity effects.

• Received 23 January 2019
• Revised 13 February 2019

DOI:https://doi.org/10.1103/PhysRevB.99.075438