Scattering resonances in two-dimensional crystals with application to graphene

We address the band structure of two-dimensional crystals above the vacuum level in the context of discrete states immersed in the three-dimensional continuum. Scattering resonances are discovered that originate from the coupling of the in-plane and perpendicular motions, as elucidated by the analysis of an exactly solvable model. Some of the resonances turn into true bound states at high-symmetry k vectors. Ab initio scattering theory verifies the existence of the resonances in realistic graphene and shows that they lead to a total reflection of the incident electron below and total transmission above the resonance energy.