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 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 $10\mu \mathrm{eV}$. We find that the origin of this giant local enhancement is the $s{p}^3$ corrugation and the breaking of local pseudospin inversion symmetry, as in the case of hydrogen adatoms. Similarly to hydrogen, also 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.

• Received 10 July 2015
• Revised 24 November 2015

DOI:https://doi.org/10.1103/PhysRevB.93.045423