Crystal-field effects in graphene with interface-induced spin-orbit coupling

TL;DR

This paper theoretically investigates how crystalline fields and substrate interactions induce anisotropic spin-orbit coupling in graphene, potentially leading to quantum spin Hall states with robust edge modes.

Contribution

It introduces a perturbative approach combined with the Slater-Koster method to derive effective Hamiltonians for graphene on layered substrates with strong SOC and crystal fields.

Findings

Anisotropic proximity spin-orbit interactions are generated by substrate crystal fields.

In certain conditions, the system behaves as a quantum spin Hall insulator.

Substrate choice is crucial for inducing and controlling anisotropic SOC in graphene.

Abstract

We consider theoretically the influence of crystalline fields on the electronic structure of graphene placed on a layered material with reduced symmetry and large spin-orbit coupling (SOC). We use a perturbative procedure combined with the Slater-Koster method to derive the low-energy effective Hamiltonian around the $K$ points and estimate the magnitude of the effective couplings. Two simple models for the envisaged graphene-substrate hybrid bilayer are considered, in which the relevant atomic orbitals hybridize with either top or hollow sites of the graphene honeycomb lattice. In both cases, the interlayer coupling to a crystal-field-split substrate is found to generate highly anisotropic proximity spin-orbit interactions, including in-plane 'spin-valley' coupling. Interestingly, when an anisotropic intrinsic-type SOC becomes sizeable, the bilayer system is effectively a quantum spin Hall insulator characterized by in-plane helical edge states robust against Bychkov-Rashba effect. Finally, we discuss the type of substrate required to achieve anisotropic proximity-induced SOC and suggest possible candidates to further explore crystal field effects in graphene-based heterostructures.