The corrections of the electron-phonon interaction to the band strucutre of graphene

The influence of the electron-phonon interaction to the band structure of graphene is studied. The interaction between electron and the longitudinal optical phonons is taken to be a perturbation, then the corrections of the interaction to the band structure are calculated using the perturbation theory. The calculation shows that the band structure down shifts and the electron fermi velocity decreases. These results are in agreement with the experimental data.