Superconductivity in the graphene monolayer calculated using the Kubo formulalism

Highlights: • We employ the Dirac fermions and we get the linear dispersion relation for the graphene. • From the spin current operator written in terms of the Dirac fermions, we use the Kubo formula to calculate the transport coefficients. • We make the diagrammatic expansion for the Green's function with objective to include the scattering electron-electron on the results. • As we obtain the AC conductivity that tends to zero at ω → 0 and a finite Drude's weight for all T values, we will have a superconductor behavior for the spin transport and hence for the electron transport in this system. - Abstract: We have employed the massless Dirac's fermions formalism together with the Kubo's linear response theory to study the transport by electrons in the graphene monolayer. We have calculated the electric conductivity and verified the behavior of the AC and DC electric conductivities of the system that is known to be a relativistic electron plasma. Our results show a superconductor behavior to the electron transport and consequently the spin transport for all values of T > 0 and a behavior of the AC conductivity tending to infinity in the limit ω → 0. In $T=0$ our results show an insulator behavior with a transition from a superconductor state at T > 0 to an insulator state at $T=0$.