Spin-orbit coupling in a graphene bilayer and in graphite

TL;DR

This paper investigates the intrinsic spin-orbit interactions in bilayer graphene and graphite, revealing they are significantly larger than in single-layer graphene and can induce gaps and edge modes.

Contribution

It provides a detailed theoretical analysis of spin-orbit coupling in bilayer graphene and graphite, highlighting their magnitudes and effects on electronic properties.

Findings

Spin-orbit interactions are 10 times larger in bilayer graphene than in single layer.

Spin-orbit coupling opens a gap and creates edge modes in bilayer graphene.

Orthorhombic graphite exhibits the largest spin-orbit couplings, 1-4K.

Abstract

The intrinsic spin-orbit interactions in bilayer graphene and in graphite are studied, using a tight binding model, and an intraatomic 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 pi and sigma bands by interlayer hopping. Their value is in the range 0.1 - 1K. The spin-orbit coupling opens a gap in bilayer graphene, and it 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.