Suppression of the superconducting transition temperature of doped graphene due to thermal fluctuations of the order parameter

In this Brief Report, we analyze the superconducting properties of doped single- and double-layer graphene systems by taking into account the fluctuations of the superconducting order parameter. Our analysis is rather general, and corresponds to a phenomenological electron-electron (hole-hole) attraction defined by its strength and range, and is independent of the origin of attraction. We show that in this model, similar to the case of two-dimensional doped metal, the thermal fluctuations of the order-parameter result in a significant reduction in the Berezinskii-Kosterlitz-Thouless critical temperature Tc comparing to the mean-field temperature TcMF, and there is a pseudogap phase with a suppressed density of states at temperature range Tc<T<TcMF. At low doping nf, the critical temperature is proportional to nf in the double-layer case, and it is exponentially suppressed in the case of a single layer.