Nonequivalence of the step-like potentials between the tight-binding model and the Dirac equation description used in graphene study

In previous calculations about the electronic transport properties through a gated region in graphene, a step-like potential is frequently adopted to mimic the gated barrier in two different theoretical models, i.e. the tight-binding model and the Dirac equation description. Our theoretical investigation indicates that the same step-like potential but used in the two distinct models are not equivalent. In the Dirac equation, a step-like potential can not reflect the normally incident electron due to Klein paradox. However, in tight-binding model, such a potential includes the scattering terms which can destroy the pseudo-spin conservation to cause a finite reflection. Thus, the electron transmission is not perfect.