Superconductivity in Alkali-Earth intercalated graphite.

It has long been known that Graphite intercalated compounds (GICs) can display a superconducting behavior at low temperature. However, until the discovery of YbC$_6$ and CaC$_6$, the critical temperatures achieved were typically inferior to 5 Kelvin. Using density functional theory we study superconductivity in AC$_6$ with A=Mg,Ca,Sr,Ba. We find that at zero pressure Ca, Ba and Sr intercalated graphite are superconducting with critical temperatures (T$_c$) 11.5, 0.2 K and 3.0 K, respectively. We study the pressure dependence of T$_c$. We find that the SrC$_6$ and BaC$_6$ critical temperatures should be substantially enhanced by pressure. On the contrary, for CaC$_6$ we find that in the 0 to 5 GPa region, T$_c$ weakly increases with pressure. The increase is much smaller than what shown in several recent experiments. Thus we suggest that in CaC$_6$ stacking faults or a continous phase transformation,such as an increase in staging could occur at finite pressure. Finally we argue that, although MgC$_6$ is unstable, the synthesis of intercalated systems of the kind Mg$_x$Ca$_{1-x}$C$_y$ could lead to higher critical temperatures. \newline \newline [1] M. Calandra and F. Mauri, Phys. Rev. Lett. {\bf 95}, 237002 (2005) \newline [2] M. Calandra and F. Mauri Phys. Rev. B 74, 094507 (2006)