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

Handle URI:
http://hdl.handle.net/10754/563285
Title:
A convergent 2D finite-difference scheme for the Dirac-Poisson system and the simulation of graphene
Authors:
Brinkman, Daniel; Heitzinger, Clemens Heitzinger; Markowich, Peter A. ( 0000-0002-3704-1821 )
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.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Applied Mathematics and Computational Science Program
Publisher:
Elsevier BV
Journal:
Journal of Computational Physics
Issue Date:
Jan-2014
DOI:
10.1016/j.jcp.2013.09.052
Type:
Article
ISSN:
00219991
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.
Appears in Collections:
Articles; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorBrinkman, Danielen
dc.contributor.authorHeitzinger, Clemens Heitzingeren
dc.contributor.authorMarkowich, Peter A.en
dc.date.accessioned2015-08-03T11:44:52Zen
dc.date.available2015-08-03T11:44:52Zen
dc.date.issued2014-01en
dc.identifier.issn00219991en
dc.identifier.doi10.1016/j.jcp.2013.09.052en
dc.identifier.urihttp://hdl.handle.net/10754/563285en
dc.description.abstractWe 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.en
dc.description.sponsorshipThe 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.en
dc.publisherElsevier BVen
dc.subjectBeam splitteren
dc.subjectDirac equationen
dc.subjectDirac-Poisson systemen
dc.subjectFinite differencesen
dc.subjectGrapheneen
dc.subjectVeselago lensen
dc.titleA convergent 2D finite-difference scheme for the Dirac-Poisson system and the simulation of grapheneen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.identifier.journalJournal of Computational Physicsen
dc.contributor.institutionDepartment of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdomen
dc.contributor.institutionSchool of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287, United Statesen
dc.contributor.institutionAIT Austrian Institute of Technology, A-1220 Vienna, Austriaen
kaust.authorMarkowich, Peter A.en
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