Coherent scattering in two dimensions: graphene and quantum corrals

Abstract

Two dimensional electronic materials provide a vibrant area for applying basic quantum mechanics and scattering theory. In quantum corrals, multiple scattering leads to resonances closely approximating eigenstates of an equivalently shaped billiard. We extend the analogy using methods from acoustics to demonstrate that the billiard conception of quantum corrals is a useful one even in wavelength regimes close to corral size. Resonance widths can be described by a simple relationship proportional to the perimeter to area ratio of the enclosure and the average reflection of a classical path.