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Many of the exotic properties proposed to occur in graphene rely on thepossibility of increasing the spin orbit coupling (SOC). By combininganalytical and numerical tight binding calculations, in this work we study theSOC induced by heavy adatoms with active electrons living in $p$ orbitals.Depending on the position of the adatoms on graphene different kinds of SOCappear. Adatoms located in hollow position induce spin conserving intrinsiclike SOC whereas a random distribution of adatoms induces a spin flippingRashba like SOC. The induced SOC is linearly proportional to the adatomsconcentration, indicating the inexistent interference effects between differentadatoms. By computing the Hall conductivity we have proved the stability of thetopological quantum Hall phases created by the adatoms against inhomogeneousspin orbit coupling . For the case of Pb adatoms, we find that a concentrationof 0.1 adatom per carbon atom generates SOC's of the order of $\sim$40$meV$.

Spin Orbit Coupling in Graphene Induced by Heavy Adatoms with Electrons in the Outer-Shell $p$ Orbitals