Transition to Landau levels in graphene quantum dots

We investigate the electronic eigenstates of graphene quantum dots of realistic size (up to 80 nm diameter) in the presence of a perpendicular magnetic field B. Numerical tight-binding calculations and Coulomb-blockade measurements performed near the Dirac point exhibit the transition from the linear density of states at B=0 to the Landau-level regime at high fields. Details of this transition sensitively depend on the underlying graphene lattice structure, bulk defects, and localization effects at the edges. Key to the understanding of the parametric evolution of the levels is the strength of the valley-symmetry-breaking K-K' scattering. We show that the parametric variation in the level variance provides a quantitative measure for this scattering mechanism. We perform measurements of the parametric motion of Coulomb-blockade peaks as a function of magnetic field and find good agreement. We demonstrate that the magnetic-field dependence of graphene energy levels may serve as a sensitive indicator for the properties of graphene quantum dots and, in further consequence, for the validity of the Dirac picture.