Electron-phonon interaction and valley splittings in graphene

Based upon first-principles calculations, a two-valley effective mass theory has been developed for graphene in a strong magnetic field and the electron-phonon couplings calculated using density-functional perturbation theory. We showed that the electron interaction with phonons about the Brilouin zone corners can lead to valley-splittings which increases linearly with the magnetic field, in agreement with a recent experimental observation.