Kubo-Bastin approach for the spin Hall conductivity of decorated graphene

Theoretical predictions and recent experimental results suggest one can engineer spin Hall effect in graphene by enhancing the spin orbit coupling (SOC) 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 SOC with a graphene-only Hamiltonian that takes into account three different local contributions: intrinsic, Rashba and pseudospin inversion asymmetry SOCs (Gmitra et al 2013 Phys. Rev. Lett. 110 246602). We show how the spin Hall and longitudinal conductivities depend on the strength of the contributions 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.