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General Scattering Mechanism and Transport in Graphene

Using quasi-time dependent semi-classical transport theory in RTA, we obtained coupled current equations in the presence of time varying field and based on general scattering mechanism $τ\propto \mathcal{E}^β$. We find that close to the Dirac point, the characteristic exponent $β= +2$ corresponds to acoustic phonon scattering. $β= +1$ long-range Coulomb scattering mechanism. $β= -1$ is short-range delta potential scattering in which the conductivity is constant of temperature. The $β= 0$ case is ballistic limit. In the low energy dynamics of Dirac electrons in graphene, the effect of the time-dependent electric field is to alter just the electron charge by $e \to e(1 + (Ωτ)^2)$ making electronic conductivity non-linear. The effect of magnetic filed is also considered.