The electronic band structure of graphene in the presence of spin-orbit coupling and transverse electric field is investigated from first principles using the linearized augmented plane-wave method. The spin-orbit coupling opens a gap at the K(K′)-point of the magnitude of 24 μeV (0.28 K). This intrinsic splitting comes 96% from the usually neglected d and higher orbitals. The electric field induces an additional (extrinsic) Bychkov-Rashba-type splitting of 10 μeV (0.11 K) per V/nm, coming from the σ-π mixing. A 'mini-ripple' configuration with every other atom is shifted out of the sheet by less than 1% differs little from the intrinsic case.
@article{arxiv.0904.3315,
title = {Band-structure topologies of graphene: spin-orbit coupling effects from first principles},
author = {M. Gmitra and S. Konschuh and C. Ertler and C. Ambrosch-Draxl and J. Fabian},
journal= {arXiv preprint arXiv:0904.3315},
year = {2013}
}