The role of the charge state of surface atoms of a metal substrate in doping of quasi-free-standing graphene

To determine the effect of a metal substrate on the electronic state of quasi-free-standing graphene, a simple model taking into account the presence of the double electric layer on the metal surface is proposed. The arising electrostatic field shifts the Dirac point of graphene, which leads to its doping. An analytical expression for the charge of graphene atoms is obtained. Numerical estimations are made for (111) faces of Cu, Ag, Au, and Pt. The agreement of the obtained estimations with the available results of numerical calculations is discussed.