We report a systematic study on strong enhancement of spin-orbit interaction (SOI) in graphene driven by transition-metal dichalcogenides (TMDs). Low temperature magnetotoransport measurements of graphene proximitized to different TMDs (monolayer and bulk WSe$_2$, WS$_2$ and monolayer MoS$_2$) all exhibit weak antilocalization peaks, a signature of strong SOI induced in graphene. The amplitudes of the induced SOI are different for different materials and thickness, and we find that monolayer WSe$_2$ and WS$_2$ can induce much stronger SOI than bulk ones and also monolayer MoS$_2$. The estimated spin-orbit (SO) scattering strength for the former reaches $sim$ 10 meV whereas for the latter it is around 1 meV or less. We also discuss the symmetry and type of the induced SOI in detail, especially focusing on the identification of intrinsic and valley-Zeeman (VZ) SOI via the dominant spin relaxation mechanism. Our findings offer insight on the possible realization of the quantum spin Hall (QSH) state in graphene.
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