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

Daniel Brinkman; Clemens Heitzinger Heitzinger; Peter 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

Daniel Brinkman, Clemens Heitzinger Heitzinger, Peter A. Markowich

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

25 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 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 2014

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-I1-007-43
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.

ASJC Scopus subject areas

Physics and Astronomy (miscellaneous)
Computer Science Applications

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10.1016/j.jcp.2013.09.052

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title = "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. {\textcopyright} 2013 Elsevier Inc.",

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AU - Markowich, Peter A.

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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. © 2013 Elsevier Inc.

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

Abstract

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