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

Daniel Brinkman, Clemens Heitzinger Heitzinger, Peter A. Markowich

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

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.
Original languageEnglish (US)
Pages (from-to)318-332
Number of pages15
JournalJournal of Computational Physics
Volume257
Issue numberPA
DOIs
StatePublished - Jan 2014

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)
  • Computer Science Applications

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