We report on a theoretical study of the spin Hall Effect (SHE) and weak antilocal-ization (WAL) in graphene/transition metal dichalcogenide (TMDC) heterostructures, computed through efficient real-space quantum transport methods, and using realistic tight-binding models parametrized from ab initio calculations. The graphene/WS 2 system is found to maximize spin proximity effects compared to graphene on MoS 2 , WSe 2 , or MoSe 2 , with a crucial role played by disorder, given the disappearance of SHE signals in the presence of strong intervalley scattering. Notably, we found that stronger WAL effects are concomitant with weaker charge-to-spin conversion efficiency. For further experimental studies of graphene/TMDC heterostructures, our findings provide guidelines for reaching the upper limit of spin current formation and for fully harvesting the potential of two-dimensional materials for spintronic applications.

This document is the unedited Author's version of a Submitted Work that was subsequently accepted for publication in Nano Letters, copyright\c{opyright}American Chemical Society after peer review. To access the final edited and published work see http://pubs.acs.org/articlesonrequest/AOR-c2pZ8WnmG7pcF4MIivjz