Proximity spin-orbit coupling in graphene on alloyed transition metal dichalcogenides

The negligible intrinsic spin-orbit coupling (SOC) in graphene can be enhanced by proximity effects in stacked heterostructures of graphene and transition metal dichalcogenides (TMDCs). The composition of the TMDC layer plays a key role in determining the nature and strength of the resultant SOC induced in the graphene layer. Here, we study the evolution of the proximity--induced SOC as the TMDC layer is deliberately defected. Alloyed $\mathrm{G}/{\mathrm{W}}_{\ensuremath{\chi}}{\mathrm{Mo}}_{1\ensuremath{-}\ensuremath{\chi}}{\mathrm{Se}}_{2}$ heterostructures with diverse compositions ($\ensuremath{\chi}$) and defect distributions are simulated using density functional theory. Comparison with continuum and tight-binding models allows both local and global signatures of the metal-atom alloying to be clarified. Our findings show that, despite some dramatic perturbation of local parameters for individual defects, the low-energy spin and electronic behavior follow a simple effective medium model which depends only on the composition ratio of the metallic species in the TMDC layer. Furthermore, we demonstrate that the topological state of such alloyed systems can be feasibly tuned by controlling this ratio.