Substrate effects on the energy and damping of the G and 2D modes in graphene

Using a microscopic model and Greenʹs function technique we have shown that the phonon G and 2D modes in graphene shift to higher energies (blue shift) for compressive substrates (SiC, Ir) and to lower energies (red shift) for tensile substrates (sapphire, fcc Ni, Ru) in qualitative agreement with the experimental data. The damping is always enhanced due to the substrate effects. The shifts can be understood by the lattice mismatch between the graphene and the underlying substrate, caused by the strain effect and resulting in lattice constant and hopping integral changes on the surface in graphene. We have shown that the influence of the anharmonic electron–phonon interaction is much stronger compared to that of the hopping integral. Taking it into account we can explain the differences observed in graphene grown on Cu(111) and Cu(100) substrates.