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In this paper we investigate the electron-phonon coupling in bilayergraphene, as a paradigmatic case for multilayer graphenes where interlayerhoppings are relevant. Using a frozen-phonon approach within the context ofDensity Functional Theory (DFT) and using different optical phonondisplacements we are able to evaluate quantitatively the electron-phononcoupling $\alpha_i$ associated with each hopping term $\gamma_i$. This analysisalso reveals a simple scaling law between the hopping terms $\gamma_i$ and theelectron-phonon coupling $\alpha_i$ which goes beyond the specific DFTtechnique employed.

Hopping-resolved electron-phonon coupling in bilayer graphene