Quasi-bound states induced by one-dimensional potentials in graphene

Abstract

We suggest a simple approach for studying the quasi-bound fermion states induced by one-dimensional potentials in graphene. Detailed calculations have been performed for symmetric double barrier structures and $n\text{\ensuremath{-}}p\text{\ensuremath{-}}n$ junctions. Besides the crucial role of the transverse motion of carriers, we systematically examine the influence of different structure parameters such as the barrier width in double barrier structures or the potential slope in $n\text{\ensuremath{-}}p\text{\ensuremath{-}}n$ junctions on the energy spectrum and, especially, on the resonant-level width and, therefore, the localization of quasi-bound states.