Nonlinear Electrical Transport in Dirac and Semi-Dirac Systems

In this thesis, we investigate some properties of nonlinear electrical transport in Dirac and Semi-Dirac systems. In the first part, we used incident fields to derive the non-linear conductivity for a general material. More specifically, we examined the conductivity for one incident field and two incident fields with both different intensity and frequency. More recently, graphene has attracted the attention of many researchers around the world because of its superior properties. In more detail, we used a recursive method (the expansion of the Fermi-Dirac distribution up to higher orders) to find both the linear and nonlinear conductivity results for one incident field. Our result suggest that both the single frequency and frequency tripled nonlinear conductivity become different to the linear conductivity under a moderate electric field strength of 104 V/cm in both their real and imaginary components. Next, we used the same method of one incident field for two incident fields in the calculation of conductivity, then we examined the transmission properties in the thin film. The results showed that the transmission of graphene is significantly altered depending on elements of electric fields and frequencies.