Spin-orbit coupling in a graphene bilayer and in graphite

The intrinsic spin-orbit interactions in bilayer graphene and in graphite are studied, using a tight binding model and an intra-atomic (L) over right arrow(S) over right arrow coupling. The spin-orbit interactions in bilayer graphene and graphite are larger, by about one order of magnitude, than the interactions in single-layer graphene, due to the mixing of pi and sigma bands by interlayer hopping. Their values are in the range 0.1-1 K. The spin-orbit coupling opens a gap in bilayer graphene, and also gives rise to two edge modes. The spin-orbit couplings are largest, similar to 1-4 K, in orthorhombic graphite, which does not have a center of inversion.