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 Delta(SO) at K. Prior approximate calculations give results from 1.2 K (approximate to 0.1 meV) down to 10 mK (approximate to 0.00086 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 Delta(SO)approximate to 0.6 K or 0.05 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.