Superconducting properties of a boson-exchange model of doped graphene

We study the superconducting properties of a doped one-layer graphene by using a model in which the interparticle attraction is caused by a boson (phonon-like) excitations. We study the dependence of the superconducting gap Delta and the mean-field critical temperature T-c(MF) on the carrier density, attraction strength, and characteristic (Debye) bosonic frequency. In addition, we study the temperature-carrier density phase diagram of the model by taking into account the thermal fluctuations of the order parameter. We show that the fluctuations result in a significant suppression of T-c(MF), such that the real (Berezinskii-Kosterlitz-Thouless) critical temperature T-c is such lower than T-c(MF). The region T-c \u3c T \u3c (MF)(c) is characterized by a finite density of states at the Fermi level (the pseudogap phase). We show that the width of the temperature interval of the pseudogap phase depends strongly on the model parameters-carrier concentration, attraction amplitude, and boson frequency