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 a 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.
