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The negligible intrinsic spin-orbit coupling (SOC) in graphene can beenhanced by proximity effects in stacked heterostructures of graphene andtransition metal dichalcogenides (TMDCs). The composition of the TMDC layerplays a key role in determining the nature and strength of the resultant SOCinduced in the graphene layer. Here, we study the evolution of theproximity-induced SOC as the TMDC layer is deliberately defected. Alloyed ${\rmG/W_{\chi}Mo_{1-\chi}Se_2}$ heterostructures with diverse compositions ($\chi$)and defect distributions are simulated using density functional theory.Comparison with continuum and tight-binding models allows both local and globalsignatures 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 behaviour follow a simple effective mediummodel which depends only on the composition ratio of the metallic species inthe TMDC layer. Furthermore, we demonstrate that the topological state of suchalloyed systems can be feasibly tuned by controlling this ratio.

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