Dirac reflection for a single-layer graphene quantum well

We address the problem of Dirac fermions graphene quantum well and we focus on the low energy approximation for the Hamiltonian of the system where the former can be described by a Dirac-like Hamiltonian. Interesting relations are obtained and used to discuss the influence of the spin-orbit coupling, which induces an effective mass-like term, on the transport properties of Single-layer graphene quantum well. It's found that the reflection probability of incident electrons is sensitive to the effective mass-like term. This can be explained by the dependence of R on the incident electrons direction and their energies. Notably, we found that the reflection probability for massive fermions with a very small angle, i.e. the wave-vector along the transport direction is zero in the GQW, can be greatly suppressed.