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 2×2 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, 7×7, 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 μeV. We find that the origin of this giant local enhancement is
the sp3 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.Comment: 9 pages, 10 figure