Effect of electron–phonon interaction on the conductivity and work function of epitaxial graphene

In the context of the cluster model of epitaxial graphene, the condition for a stepwise change in the charge of carbon atoms under the action of graphene–substrate electron–phonon interaction and an external electric field is derived. Such charge transfer brings about corresponding steps of the static conductivity and work function of epitaxial graphene. Numerical estimates for the case of weak coupling of quasi-free graphene with metal and semiconductor substrates are given.