Scattering resonances in graphene

TL;DR

This paper investigates scattering resonances in graphene's band structure, revealing how in-plane and perpendicular motions couple to produce resonances that affect electron transmission and reflection.

Contribution

It introduces an exactly solvable model and ab initio calculations to identify and analyze scattering resonances in graphene's continuum states.

Findings

Resonances originate from coupling of in-plane and perpendicular motions.

Some resonances become true bound states at high-symmetry points.

Resonances cause total reflection below and total transmission above their energies.

Abstract

We address the two-dimensional band-structure of graphene 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 $\kv$ vectors. {\it 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.