Tailoring the valley Zeeman splitting of WS₂ on multilayer graphene systems

Van der Waals layered materials are highly sensitive to interactions with adjacent layers. In semiconductor van der Waals heterostructures, the signatures of interlayer coupling are effectively observed in the excitonic valley Zeeman splitting. Specifically for WS₂/graphene systems, the valley Zeeman splitting is a multi-step, energetically resonant process, with different bands mediating the interlayer coupling [Faria Junior et al., 2D Materials 10, 034002 (2023)]. Here, we further investigate this multi-step proximity effect in van der Waals heterostructures composed of WS₂ and multilayer graphene. Our first-principles calculations reveal that in these asymmetric structures, valley Zeeman physics can be efficiently tailored by external electric fields, strongly depending on the atomic registry and the number of graphene layers in the system. Our results offer fundamental microscopic insights on how spin and orbital angular momenta of electrons can be effectively transferred and externally manipulated across van der Waals interfaces.