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

D. Brinkman, C. Heitzinger, P. A. Markowich

Research output: Contribution to journalArticle

8 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)318-332
Number of pages15
JournalJournal of Computational Physics
Issue numberPA
StatePublished - Jan 15 2014



  • Beam splitter
  • Dirac equation
  • Dirac-Poisson system
  • Finite differences
  • Graphene
  • Veselago lens

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

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