Simulation of hopping in disordered fractal arrays of graphene quantum dots

Diffusion regimes of charge carriers in artificial quasi-fractal graphene quantum dot (GQD) superlattices forming hexagonal and triangular carpet are investigated. Using the generalized Miller-Abrahams relations for hopping rates we perform Monte Carlo simulation of charge carrier hopping in artificial 2d disordered arrays of armchair GQDs. The variations of the anomalous advection-diffusion parameters as functions of localization radius, electric field intensity, levels of energetic and structural disorder are studied. (paper)