Non-adiabatic phonons within the doped graphene layers of XC${}_6$ compounds

We report the first Raman scattering measurements of BaC${}_6$, SrC${}_6$, and YbC${}_6$, which along with new data on CaC${}_6$, permits a systematic study of the phonons and the electron-phonon interaction within the doped graphene layers of these compounds. The out-of-plane carbon phonon softens as the spacing of the graphene layers is reduced in the series BaC${}_6$, SrC${}_6$, YbC${}_6$, and CaC${}_6$. This is due to increasing charge in the ${\pi }^{\ast }$ electronic band. Electron-phonon interaction effects between the in-plane carbon modes at $\approx 1500$\invcm and the ${\pi }^{\ast }$ electrons cause a strong non-adiabatic renormalization. As charge is transferred into the ${\pi }^{\ast }$ band these non-adiabatic effects are found to increase concurrent with a reduction in the phonon lifetime.