  Theoretical predictions and recent experimental results suggest one can
engineer spin Hall effect in graphene by enhancing the spin-orbit coupling in
the vicinity of an impurity. We use a Chebyshev expansion of the Kubo-Bastin
formula to compute the spin conductivity tensor for a tight-binding model of
graphene with randomly distributed impurities absorbed on top of carbon atoms.
We model the impurity-induced spin-orbit coupling with a graphene-only
Hamiltonian that takes into account three different
contributions~\cite{Gmitra2013} and show how the spin Hall and longitudinal
conductivities depend on the strength of each spin-orbit coupling and the
concentration of impurities. Additionally, we calculate the real-space
projection of the density of states in the vicinity of the Dirac point for
single and multiple impurities and correlate these results with the
conductivity calculations.
