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F. Libisch, J. Burgdörfer, S. Rotter:
"Eigenstates of graphene quantum dots: beyond the Dirac equation";
Vortrag: Seminarvortrag, RWTH Aachen, Deutschland (eingeladen); 03.12.2009.

Graphene has raised considerable attention in the past few years as possible candidate for nanoelectronic devices. One reason for this interest is the special linear dispersion relation of graphene, which allows a treatment based on the Dirac equation. Effects like Klein tunneling and the Veselago lens, which are known from ultrarelativistic physics, are applied to graphene nanodevices. However, for finitesized graphene quantum dots, edges and lattice defects are difficult to describe based on a continuum equation. We therefore numerically study eigenstates of graphene-based quantum dots of realistic diameter D ~ 60 nm using a third-nearest neighbor tight-binding approach. In particular, we investigate the focusing effect at p-n transitions (Veselago lens) and the magnetic-field dependence of bound states. Our approach allows detailed calculation of the electron densities as a function of disorder or magnetic field strength. We find that the above defects locally break the correspondence to the Dirac equation, and that great care has to be taken to recover predictions based on the Dirac formalism for realistic devices.

graphene, quantum dots, Dirac billiards