Spin-orbit gap of graphene: First-principles calculations

Even though graphene is a low-energy system consisting of a two-dimensional honeycomb lattice of carbon atoms, its quasiparticle excitations are fully described by the (2+1) -dimensional relativistic Dirac equation. In this paper we show that, while the spin-orbit interaction in graphene is of the order of 40. 3em{0ex}meV, it opens up a gap of the order of 10^-30. 3em{0ex}meV at the Dirac points. We present a first-principles calculation of the spin-orbit gap, and explain the behavior in terms of a simple tight-binding model. Our result also shows that the recently predicted quantum spin Hall effect in graphene can occur only at unrealistically low temperature.