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 E LE S 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 π and σ bands by interlayer hopping. Their values are in the range 0.1–1K. The spin–orbit coupling opens a gap in bilayer graphene, and also gives rise to two edge modes. The spin–orbit couplings are largest,∼1–4K, in orthorhombic graphite, which does not have a center of inversion.