Enhanced spin-orbit coupling in hydrogenated and fluorinated graphenes studied from first principles

The spin-orbit couplings (SOCs) of hydrogenated and fluorinated graphenes are calculated from the first principles method. It is found that the SOC-induced band splittings near their Fermi energies can be significantly enhanced to the order of 10$^{-2}$ eV from the original about 10$^{-6}$ eV of the pure raphene, which is comparable to those found in the diamond and even the archetypal semiconductors. And two different mechanisms are proposed to explain the SOC enhancements in these two systems. The huge SOC enhancements are found to come not only from the sp$^3$ hybridization of carbon atoms, but also from the larger intrinsic SOC of the fluorine atom than the carbon one. We hope many interesting phenomena caused by the SOCs (e.g. the spin Hall effect) can be observed experimentally in these systems.