Graphene quantum dots: Beyond a Dirac billiard

We present realistic simulations of quantum confinement effects in phase-coherent graphene quantum dots with linear dimensions of 10-40 nm. We determine wave functions and energy-level statistics in the presence of disorder resulting from edge roughness, charge impurities, or short-ranged scatterers. Marked deviations from a simple Dirac billiard for massless fermions are found. We find a remarkably stable dependence of the nearest-neighbor level spacing on edge roughness suggesting that the roughness of fabricated devices can be possibly characterized by the distribution of measured Coulomb blockade peaks.