| 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. In graphene, we study the unique behavior strain induces on the effective Dirac Hamiltonian by creating an effective pseudomagnetic field. These fields induce an energy splitting of degenerate eigenstates of certain graphene quantum dots which is distinct from that of an applied scalar potential and can in principle be observed in the conductance through the dot. Additionally, for strain bubbles smaller than the effective Dirac wavelength, the scattering is shown to be distinct from other impurity types. This leads to characteristic features in the conductance, as a function of the bubble position, through regions containing a strong strain bubble. |
