  First-principles calculations of the electronic structure and vibrational
modes, in a system of graphene bilayers and trilayers intercalated with
alkaline earth atoms, are resented. It is found that, in similarity to the case
of superconducting graphite intercalation compounds, the Fermi level is crossed
by an s-band derived from the intercalant states, as well as graphitic
pi-bands. The electron-phonon coupling parameter is found to be 0.60 and 0.80,
respectively, in calcium intercalated graphene bilayers and trilayers. In
superconducting CaC6 graphite intercalation compound, the calculated value for
the electron-phonon coupling parameter is 0.83. It is concluded that
two-dimensional superconductivity is possible in a system of a few graphene
layers intercalated with calcium.
