Estimation of the electron–phonon coupling constants for graphene and metallic and nonmetallic substrates

Two modes of graphene–substrate interaction have been considered: a weak van der Waals bond and a strong covalent bond. The Lennard–Jones potential and Harrison bond-orbital method are used in the former and latter cases, respectively. Analytical expressions for the electron–phonon interaction constants, which contain only two parameters (binding energy $E_B$ for graphene and a substrate and distance $d$ between them) have been obtained. The constants have been calculated for metallic, semiconductor, and dielectric substrates.