Why is KC$_8$ superconductor and LiC$_6$ is not?

We have performed angle-resolved photoemission spectroscopy studies of the electronic structure in LiC$_6$ and KC$_8$, a non-superconducting and a superconducting graphite intercalation compound, respectively. We have found that the charge transfer from the intercalant layers to graphene layers is larger in KC$_8$ than in LiC$_6$, opposite of what might be expected from their chemical composition. We have also measured the strength of the electron-phonon interaction on the graphene-derived Fermi surface to carbon derived phonons in both materials and found that it follows a universal trend where the coupling strength and superconductivity monotonically increase with transfer of electrons into the graphene-derived $\pi^{\ast}$ states. This correlation between the filling of graphene $\pi^{\ast}$ states, the strength of the electron-phonon coupling and superconductivity suggests that both graphene-derived electrons and graphene-derived phonons are crucial for superconductivity in GICs.