Spin–orbit coupling in a graphene bilayer and in graphite

F Guinea

doi:10.1088/1367-2630/12/8/083063

F Guinea

Open Access

https://doi.org/10.1088/1367-2630/12/8/083063

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Abstract

The intrinsic spin–orbit interactions in bilayer graphene and in graphite are studied, using a tight binding model and an intra-atomic 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.

Highlights

The isolation and control of the number of carriers in single and few layer graphene flakes[1, 2] has lead to a large research activity exploring all aspects of these materials[3]
The application of graphene to spintronic devices[4,5,6,7,8,9,10] and to spin qubits[11,12,13] is being intensively studied. The understanding of these devices requires a knowledge of the electronic spin-orbit interaction. This interaction turns single layer graphene into a topological insulator[14], which shows a bulk gap and edge states at all boundaries
We describe the electronic bands of a graphene bilayer using a tight binding model, with four orbitals, the 2s and the three 2p orbitals, per carbon atom

Summary

INTRODUCTION

The isolation and control of the number of carriers in single and few layer graphene flakes[1, 2] has lead to a large research activity exploring all aspects of these materials[3]. We do not consider hoppings and spin orbit interactions which include d levels, they can contribute to the total magnitude of the spin-orbit couplings[18, 28]. The main contribution to the effective spin-orbit at the Fermi level due to the interlayer coupling is due to the hoppings between p orbitals in nearest neighbor atoms in different layers. This interaction gives rise to the parameters γ3 and γ4 in the parametrization of the bands in graphite. The first term describes the intrinsic spin-orbit coupling in single layer graphene. The term proportional to λ3 can be viewed as a Rashba coupling with opposite signs in the two layers

RESULTS

Π kya 3

CONCLUSIONS