Klein tunneling of massive Dirac fermions in single-layer graphene

Abstract

Abstract For nano-electronics applications of graphene a mass gap in its energy spectrum is needed (like a conventional semiconductor). In this paper, motivated by mass production of graphene, by the use of 2D massive Dirac-like equation we obtain the exact solution for the transmission probability corresponding to the Klein tunneling of massive Dirac fermions through a two-dimensional barrier which can be considered as a n–p–n junction in a graphene nano-transistor, and show that contrary to the case of massless Dirac fermions which results in complete transparency of the barrier for normal incidence, the transmission probability, T, in this case, apart from some resonance conditions that lead to the total transparency of the barrier, is smaller than one and also depends on the band index. We then obtain the transmission through a potential barrier in which the massless electrons acquire a finite mass and find that the transmission, in this case, is independent of the band index and cannot reach unity.