Hopping-resolved electron-phonon coupling in bilayer graphene

In this paper we investigate the electron-phonon coupling in bilayer graphene, as a paradigmatic case for multilayer graphenes where interlayer hoppings are relevant. Using a frozen-phonon approach within the context of density functional theory (DFT) and using different optical phonon displacements, we are able to evaluate quantitatively the electron-phonon coupling alpha(i) associated with each hopping term gamma(i). This analysis also reveals a simple scaling law between the hopping terms gamma(i) and the electron-phonon coupling alpha(i) which goes beyond the specific DFT technique employed.