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 T-c comparing to the mean-field temperature T-c(MF), and there is a pseudogap phase with a suppressed density of states at temperature range T-c < T < T-c(MF). At low doping n(f), the critical temperature is proportional to n(f) in the double-layer case, and it is exponentially suppressed in the case of a single layer.