First-principles calculation of the spin-orbit splitting in graphene

Recent success in making macroscopic graphene samples has stimulated interest in possible unusual electron physics near the Brillouin zone (BZ) vertex K, notably the prediction of a spin quantum Hall effect. Observability depends critically on the size of the spin-orbit gap ₒ₎ at K. Prior approximate calculations give results from 1. 20. 3em{0ex}K (0. 10. 3em{0ex}meV) down to 100. 3em{0ex}mK (0. 000860. 3em{0ex}meV). We report fully first-principles all-electron calculations of this splitting using large Gaussian basis sets and the Douglas-Kroll-Hess methodology in the density functional theory fitting function code GTOFF. Our result ₒ₎0. 60. 3em{0ex}K or 0. 050. 3em{0ex}meV is robust against the choice of the approximate exchange-correlation functional and against variations of the lattice constant, density of the BZ scan, basis set enrichment, and key numerical convergence parameters.