Spin-orbit coupling in methyl functionalized graphene

TL;DR

This study uses first-principles calculations to analyze how methyl functionalization significantly enhances spin-orbit coupling in graphene, revealing the effects of local structural changes and impurity scattering.

Contribution

It provides the first detailed quantification of spin-orbit effects induced by methyl groups on graphene, including effective Hamiltonian parameters and local electronic structure insights.

Findings

Spin-orbit splittings up to 0.6 meV in dense limits.

Giant spin-orbit coupling (~1 meV) induced by methyl groups.

Methyl acts as a resonant scatterer near charge neutrality.

Abstract

We present first-principles calculations of the electronic band structure and spin-orbit effects in graphene functionalized with methyl molecules in dense and dilute limits. The dense limit is represented by a 2$\times$2 graphene supercell functionalized with one methyl admolecule. The calculated spin-orbit splittings are up to $0.6$ meV. The dilute limit is deduced by investigating a large, 7$\times$7, supercell with one methyl admolecule. The electronic band structure of this supercell is fitted to a symmetry-derived effective Hamiltonian, allowing us to extract specific hopping parameters including intrinsic, Rashba, and PIA (pseudospin inversion asymmetry) spin-orbit terms. These proximity-induced spin-orbit parameters have magnitudes of about 1 meV, giant compared to pristine graphene whose intrinsic spin-orbit coupling is about 10 $\mu$eV. We find that the origin of this giant local enhancement is the $sp^3$ corrugation and the breaking of local pseudospin inversion symmetry, as in the case of hydrogen adatoms. Also similar to hydrogen, methyl acts as a resonant scatterer, with a narrow resonance peak near the charge neutrality point. We also calculate STM-like images showing the local charge densities at different energies around methyl on graphene.