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 $α_i$ associated with each hopping term $γ_i$. This analysis also reveals a simple scaling law between the hopping terms $γ_i$ and the electron-phonon coupling $α_i$ which goes beyond the specific DFT technique employed.

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