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 $T_c^{\text{MF}}$, and there is a pseudogap phase with a suppressed density of states at temperature range $T_c<T<T_c^{\text{MF}}$. 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.

Figure 1

The doping dependence of the mean-field and the BKT critical temperatures in the case of one-layer (top) and two-layer (bottom) graphene. All values of the parameters are given in eV.

Figure 2

An approximate curve of the DOS at $n_f=0.2$, when $T_c^{\text{MF}}\simeq 1.86T_c$, and different values of temperature in the case of one-layer graphene. The model parameters are the same as in Fig. 1 (for details of calculations, see Ref. 16).