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 Δ and the mean-field critical temperature TcMF 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 TcMF, such that the real (Berezinskii-Kosterlitz-Thouless) critical temperature Tc is much lower than TcMF. The region Tc