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We study the spin Hall effect (SHE) in graphene using a realisticmulti-orbital tight-binding model that includes the atomic spin-orbitinteraction. The SHE is found to be induced by the spin-dependent Aharonov-Bohmphase. In the metallic case, the calculated values for the spin Hallconductivity (SHC) are much smaller than the quantized Hall conductivity forrealistic parameter values of metallic graphene. In the insulating case,quantization of the SHC is violated due to the multi-orbital effect. Thepresent study suggests that the SHE in a honeycomb lattice is enhanced bychemical doping, such as the substitution of carbon atoms with boron atoms.

Intrinsic spin Hall effect in graphene: Numerical calculations in a multi-orbital mode