Electron-phonon interaction and pairing mechanism in superconducting Ca-intercalated bilayer graphene

Using the {\it ab initio} anisotropic Eliashberg theory including Coulomb interactions, we investigate the electron-phonon interaction and the pairing mechanism in the recently-reported superconducting Ca-intercalated bilayer graphene. We find that C$_6$CaC$_6$ can support phonon-mediated superconductivity with a critical temperature $T_{\rm c}=$6.8-8.1~K, in good agreement with experimental data. Our calculations indicate that the low-energy Ca$_{xy}$ vibrations are critical to the pairing, and that it should be possible to resolve two distinct superconducting gaps on the electron and hole Fermi surface pockets.