This thesis involves the discussion on a detail derivation of AC current in graphene within the frame work of Tight-Binding (TB) model. Within this model, the energy band of graphene is reviewed and the zero band gap is shown to be an exact result without any approximation. Due to the two dimension character of graphene, it is further reviewed that at the specific points of zero band gap a Dirac equation of massless fermion in two dimension (2D) exists. By following the approach of Mishchenko [8], the inadequacy of calculating AC current by perturbation is discussed in detail in this thesis. However in doing so we have found several mistakes in his work. First of all, even following his approach we obtained a different form current j_x (t)=(e^2 E)/2ћ cosωt/(√(1+(evE/ћωΓ)^2 ) (1+√(1+(evE/ћωΓ)^2 )) ). Despite different forms, both works show that the conductivity of graphene is beyond the linear response regime. Furthermore, we have re-analyzed this problem in more systematic way and have found some inconsistencies in Mishchenko’s work. By applying Rotating Wave Approximation (RWA) correctly, we have shown that Mishchenko has ignored a lot of terms which are bigger or at least of the same order as obtained in his results. As a result, it seems his conclusion on AC current is in doubt and the AC current discussion is still opened.

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