Relaxation of the monolayer of epitaxial graphene caused by the electron-phonon interaction with a substrate

Normal (relative to the substrate) vibrations of single-layer graphene as a whole have been considered in the terms of simple models of epitaxial graphene and electron-phonon interaction. The consideration has been performed for both metal and semiconductor substrates. The presented evaluations show that the possibility of appearance of two competitive electronic states of graphene adatoms is realized only for large constants of the electron-phonon coupling. It has also been shown that the graphene sheet can relax both “inward” and “outward”.