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 $\tau \propto {\mathcal{E}}^{\beta }$. We find that close to the Dirac point, the characteristic exponent $\beta =+2$ corresponds to acoustic phonon scattering. $\beta =+1$ long-range Coulomb scattering mechanism. $\beta =-1$ is short-range delta potential scattering in which the conductivity is constant of temperature. The $\beta =0$ 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 $e\to e(1+(\mathrm{\Omega }\tau {)}^2)$ making electronic conductivity non-linear. The effect of magnetic filed is also considered.