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 ∝ Eβ. 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 → e(1 + (Ωτ)2) making electronic conductivity non-linear. The effect of magnetic filed is also considered. I