Transmission through biased graphene strip

Abstract

We solve the 2D Dirac equation describing graphene in the presence of a linear vector potential. The discretization of the transverse momentum due to the infinite mass boundary condition reduced our 2D Dirac equation to an effective massive 1D Dirac equation with an effective mass equal to the quantized transverse momentum. We use both a numerical Poincaré Map approach, based on space discretization of the original Dirac equation, and direct analytical method. These two approaches have been used to study tunneling phenomena through a biased graphene strip. The numerical results generated by the Poincaré Map are in complete agreement with the analytical results.

Transmission in graphene through time-oscillating linear barrier

“…To give comparison and show the relevance of our finding, we plots two cases according to choice of the barrier heights (V 0 , V 1 ). Indeed, Figure 3(b) illustrates a particular case of a linear barrier (V 0 = 20, V 1 = 0) studied in our previous work [18] where transmission corresponding to the Klein zone is omitted and transmission oscillates around a minimum, then it behaves in the same way as shown in 3(a). Figure 3(c) presents the case of a simple square barrier V 0 → V 1 = 30 where the Klein zone is conserved and transmission corresponding to energies V 1 − 2k y ≤ E ≤ V 0 + 2k y is replaced by another in range V 1 − k y ≤ E ≤ V 1 + k y without oscillations [24].…”

“…which can be written in terms of the parabolic cylinder function [18] such that the first component is given by…”

Effect of magnetic field on Goos-Hänchen shifts in gaped graphene triangular barrier

“…where we have set k η = s 3 (ǫ − v 2 ), s 3 = sign(ǫ − v 2 ) correspond to positive and negative energy solutions. The second spinor component can be derived from (16) to obtain…”

Goos-Hänchen shifts in graphene-based linear barrier

“…In our previous work [10], we have solved the 2D Dirac equation describing graphene in the presence of a linear vector potential. The discretization of the transverse momentum due to the infinite mass boundary condition reduced our 2D Dirac equation to an effective massive 1D Dirac equation with an effective mass equal to the quantized transverse momentum.…”

“…Motivated by our previous work [10,11], we consider Dirac fermions in graphene subjected to a linear barrier potential and study the GH shifts. From the solution of the energy spectrum we show how to derive the GH shifts as function of different physical parameters based on the phase shifts in transmission and reflection.…”