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We study the superconducting phase transition, both in a graphene bilayer andin graphite. For that purpose we derive the mean-field effective potential fora stack of graphene layers presenting hopping between adjacent sheets. Fordescribing superconductivity, we assume there is an on-site attractiveinteraction between electrons and determine the superconducting criticaltemperature as a function of the chemical potential. This displays adome-shaped curve, in agreement with previous results for two-dimensional Diracfermions. We show that the hopping between adjacent layers increases thecritical temperature for small values of the chemical potential. Finally, weconsider a minimal model for graphite and show that the transition temperatureis higher than that for the graphene bilayer for small values of chemicalpotential. This might explain why intrinsic superconductivity is observed ingraphite.

Superconductivity in graphene stacks: from the bilayer to graphite