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

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    Type
    Article
    Authors
    Brinkman, Daniel
    Heitzinger, Clemens Heitzinger
    Markowich, Peter A. cc
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Applied Mathematics and Computational Science Program
    KAUST Grant Number
    KUK-I1-007-43
    Date
    2014-01
    Permanent link to this record
    http://hdl.handle.net/10754/563285
    
    Metadata
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    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
    Sponsors
    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
    ae974a485f413a2113503eed53cd6c53
    10.1016/j.jcp.2013.09.052
    Scopus Count
    Collections
    Articles; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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