Intrinsic and substrate induced spin-orbit interaction in chirally stacked trilayer graphene

TL;DR

This paper combines group theory and tight-binding methods to analyze intrinsic and substrate-induced spin-orbit interactions in ABC stacked trilayer graphene, revealing how multilayer stacking modifies SOC effects.

Contribution

It introduces a detailed tight-binding model including d orbitals for trilayer graphene and derives effective Hamiltonians for low-energy SOC physics, considering substrate effects.

Findings

Larger set of d orbitals needed for accurate SOC modeling.

Substrate or adatom-induced SOC can be layer-specific.

Rashba SOC effects are suppressed at the K point in multilayers.

Abstract

We present a combined group-theoretical and tight-binding approach to calculate the intrinsic spin-orbit coupling (SOC) in ABC stacked trilayer graphene. We find that compared to monolayer graphene, a larger set of d orbitals (in particular the d_{z^2} orbital) needs to be taken into account. We also consider the intrinsic SOC in bilayer graphene, because the comparison between our tight-binding bilayer results and the density functional computations of Ref.[40] allows us to estimate the values of the trilayer SOC parameters as well. We also discuss the situation when a substrate or adatoms induce strong SOC in only one of the layers of bilayer or ABC trilayer graphene. Both for the case of intrinsic and externally induced SOC we derive effective Hamiltonians which describe the low-energy spin-orbit physics. We find that at the K point of the Brillouin zone the effect of Bychkov-Rashba type SOC is suppressed in bilayer and ABC trilayer graphene compared to monolayer graphene.