Abstract
The spin-orbit coupling in graphene induces spectral gaps at the high-symmetry points. The relevant gap at the point is similar to the splitting of the orbitals in the carbon atom, being roughly 8.5 meV. The splitting at the point is orders of magnitude smaller. Earlier tight-binding theories indicated the value of this intrinsic gap of , based on the coupling. All-electron first-principles calculations give much higher values, between 25 and , due to the presence of the orbitals of the symmetry in the Bloch states at . A realistic multiband tight-binding model is presented to explain the effects the orbitals play in the spin-orbit coupling at . The coupling is found irrelevant to the value of the intrinsic spin-orbit-induced gap. On the other hand, the extrinsic spin-orbit coupling (of the Bychkov-Rashba type), appearing in the presence of a transverse electric field, is dominated by the hybridization, in agreement with previous theories. Tight-binding parameters are obtained by fitting to first-principles calculations, which also provide qualitative support for the model when considering the trends in the spin-orbit-induced gap in graphene under strain. Finally, an effective single-orbital next-nearest-neighbor hopping model accounting for the spin-orbit effects is derived.
2 More- Received 19 July 2010
DOI:https://doi.org/10.1103/PhysRevB.82.245412
©2010 American Physical Society