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

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

doi:10.1016/j.jcp.2013.09.052

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

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

CLAS-NS: Mathematics and Statistical Sciences, School of (SMSS)

Research output: Contribution to journal › Article › peer-review

9 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.

Original language	English (US)
Pages (from-to)	318-332
Number of pages	15
Journal	Journal of Computational Physics
Volume	257
Issue number	PA
DOIs	https://doi.org/10.1016/j.jcp.2013.09.052
State	Published - Jan 15 2014

Keywords

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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AB - 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.

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KW - Finite differences

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KW - Veselago lens

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