Transmission through Biased Graphene Strip
  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 Poincare 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 Poincare Map are in complete agreement with the analytical results. 
Hocine Bahlouli, El Bouazzaoui Choubabi, Abderrahim El Mouhafid, Ahmed   Jellal
cond-mat.mes-hall hep-th math-ph math.MP quant-ph