  Recent reports of spin-orbit coupling enhancement in chemically modified
graphene have opened doors to studies of the spin Hall effect with massless
chiral fermions. Here, we theoretically investigate the interaction and
impurity density dependence of the extrinsic spin Hall effect in spin-orbit
coupled graphene. We present a nonperturbative quantum diagrammatic calculation
of the spin Hall response function in the strong-coupling regime that
incorporates skew scattering and anomalous impurity density-independent
contributions on equal footing. The spin Hall conductivity dependence on Fermi
energy and electron-impurity interaction strength reveals the existence of
experimentally accessible regions where anomalous quantum processes dominate.
Our findings suggest that spin-orbit-coupled graphene is an ideal model system
for probing the competition between semiclassical and bona fide quantum
scattering mechanisms underlying the spin Hall effect.
