Excitonic superconductivity in monolayer-bilayer graphene

We study the excitonic mechanism of superconductivity in monolayer-bilayer graphene system by using Eliashberg theory. The electrons of the monolayer interact with virtual excitons and plasmons from the bilayer, producing an attractive interaction at low frequency among the electrons, leading to the possibility of excitonic superconductivity. These virtual excitons and plasmons are contained in the polarization function. We derive the Eliashberg spectral function via the polarization functions of two layers in the random phase approximation. Migdal's adiabaticity condition for the validity of Eliashberg theory can be satisfied since the Fermi velocity of the two layers can be dramatically distinct. Finally, we show that the excitonic mechanism should produce superconductivity at a reasonable Tc through this purely electronic mechanism.