Spin-orbit coupling in a graphene bilayer and in graphite

Abstract

The intrinsic spin-orbit interactions in bilayer graphene and in graphite are studied, using a tight binding model and an intra-atomic LS 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 0.1-1 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, ∼ 1-4 K, in orthorhombic graphite, which does not have a center of inversion. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.