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

TL;DR

This paper employs a Chebyshev expansion of the Kubo-Bastin formula to analyze how impurity-induced spin-orbit coupling affects the spin Hall conductivity in decorated graphene, providing detailed numerical insights.

Contribution

It introduces a computational approach to evaluate spin Hall conductivity in graphene with impurities, considering multiple spin-orbit coupling mechanisms and impurity concentrations.

Findings

Spin Hall conductivity varies with impurity concentration and spin-orbit coupling strength.

Real-space density of states correlates with conductivity behavior near the Dirac point.

Impurity-induced spin-orbit effects can be engineered to enhance spin Hall effects in graphene.

Abstract

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.