Intrinsic spin Hall effect in graphene: Numerical calculations in a   multi-orbital mode
  We study the spin Hall effect (SHE) in graphene using a realistic multi-orbital tight-binding model that includes the atomic spin-orbit interaction. The SHE is found to be induced by the spin-dependent Aharonov-Bohm phase. In the metallic case, the calculated values for the spin Hall conductivity (SHC) are much smaller than the quantized Hall conductivity for realistic parameter values of metallic graphene. In the insulating case, quantization of the SHC is violated due to the multi-orbital effect. The present study suggests that the SHE in a honeycomb lattice is enhanced by chemical doping, such as the substitution of carbon atoms with boron atoms. 
Seiichiro Onari, Yasuhito Ishikawa, Hiroshi Kontani, Jun-ichiro Inoue