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Possibility of superconductivity due to electron-phonon interaction in graphene

We discuss the possibility of superconductivity in graphene taking into account both electron-phonon and electron-electron Coulomb interactions. The analysis is carried out assuming that the Fermi energy is far away from the Dirac points, such that the density of the particles (electrons or holes) is high. We derive proper Eliashberg equations that allow us to estimate the critical superconducting temperature. The most favorable is pairing of electrons belonging to different valleys in the spectrum. Using values of electron-phonon coupling estimated in other publications we obtain the critical temperature T_c as a function of the electron (hole) density. This temperature can reach the order of 10 K at the Fermi energy of order 1-2 eV. We show that the dependence of the intervalley pairing on the impurity concentration should be weak.