Intrinsic Spin-Orbit Interaction in Graphene

In graphene, we report the first theoretical demonstration of how the intrinsic spin orbit interaction can be deduced from the theory and how it can be controlled by tuning a uniform magnetic field, and/or by changing the strength of a long range Coulomb like impurity (adatom), as well as gap parameter. In the impurity context, we find that intrinsic spin-orbit interaction energy may be enhanced by increasing the strength of magnetic field and/or by decreasing the band gap mass term. Additionally, it may be strongly enhanced by increasing the impurity strength. Furthermore, from the proposal of Kane and Mele [Phys. Rev. Lett. 95, 226801 (2005)], it was discussed that the pristine graphene has a quantized spin Hall effect regime where the Rashba type spin orbit interaction term is smaller than that of intrinsic one. Our analysis suggest the nonexistence of such a regime in the ground state of flat graphene.