A convergent 2D finite-difference scheme for the Dirac-Poisson system and the simulation of graphene

Abstract
We present a convergent finite-difference scheme of second order in both space and time for the 2D electromagnetic Dirac equation. We apply this method in the self-consistent Dirac-Poisson system to the simulation of graphene. The model is justified for low energies, where the particles have wave vectors sufficiently close to the Dirac points. In particular, we demonstrate that our method can be used to calculate solutions of the Dirac-Poisson system where potentials act as beam splitters or Veselago lenses. © 2013 Elsevier Inc.

Citation
Brinkman, D., Heitzinger, C., & Markowich, P. A. (2014). A convergent 2D finite-difference scheme for the Dirac–Poisson system and the simulation of graphene. Journal of Computational Physics, 257, 318–332. doi:10.1016/j.jcp.2013.09.052

Acknowledgements
The authors acknowledge support from King Abdullah University of Science and Technology (KAUST) Award Number KUK-I1-007-43 and from the WWTF (Vienna Science and Technology Fund) Project Number MA09-028.

Publisher
Elsevier BV

Journal
Journal of Computational Physics

DOI
10.1016/j.jcp.2013.09.052

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