Standard Model for Superconductivity in Graphite Intercalation Compounds: Prediction of Optimum $T_c$

Based on the model that was successfully applied to the explanation of superconductivity with the transition temperature $T_c$ of about 0.1K or less in the alkali- intercalated graphite compounds such as KC$_8$, RbC$_8$, and CsC$_8$ in 1982 [Y. Takada, {\it J. Phys. Soc. Jpn.} {\bf 51}, 63 (1982) ], we have calculated $T_c$ for the alkaline-earth- intercalated graphite compounds including CaC$_6$, YbC$_6$, and SrC$_6$ with $T_c$ of about 10K or less to find that the same model reproduces the observed $T_c$ in those compounds as well, indicating that it is a standard model for superconductivity in the graphite intercalation compounds with $T_c$ ranging over three orders of magnitude. The difference in $T_c$ by two orders between KC$_8$ and CaC$_6$ can be accounted for by (i) doubling $Z$ the valency of the metal ions, which enhances $T_c$ by one order, and (ii) tripling $m^*$ the effective mass of the superconducting three-dimensional electrons in the interlayer band, which also enhances $T_c$ by one order. Enhancement of $T_c$ well beyond 10 K is also predicted in this model, if intercalant metals are judiciously chosen so that both $Z$ and $m^*$ are increased further.