Superconductivity in the graphene monolayer calculated using the Kubo formulalism

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.