1-D Dirac Equation, Klein Paradox and Graphene
Solutions of the one dimensional Dirac equation with piece-wise constant potentials are presented using standard methods. These solutions show that the Klein Paradox is non-existent and represents a failure to correctly match solutions across a step potential. Consequences of this exact solution are studied for the step potential and a square barrier. Characteristics of massless Dirac states and the momentum linear band energies for Graphene are shown to have quite different current and momentum properties.
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