Evolution of microscopic localization in graphene in a magnetic field from scattering resonances to quantum dots

Graphene exhibits rich new physics and great promise for applications in electronics. The half-integer quantum Hall effect and high carrier mobility are critically dependent on interactions with impurities/substrates and localization of Dirac fermions in realistic devices. We microscopically study these interactions using scanning tunnelling spectroscopy (STS) of exfoliated graphene on a SiO2 substrate in an applied magnetic field. The magnetic field strongly affects the electronic behaviour of the graphene; the states condense into well-defined Landau levels with a dramatic change in the character of localization. In zero magnetic field, weakly localized states are created by the substrate induced disorder potential. In strong magnetic fields, the two-dimensional electron gas breaks into a network of interacting quantum dots formed at the potential hills and valleys of the disorder potential. Our results demonstrate how graphene properties are perturbed by the disorder potential; a finding essential for the physics and applications of graphene.