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dc.contributor.authorBrinkman, Daniel
dc.contributor.authorHeitzinger, Clemens Heitzinger
dc.contributor.authorMarkowich, Peter A.
dc.date.accessioned2015-08-03T11:44:52Z
dc.date.available2015-08-03T11:44:52Z
dc.date.issued2014-01
dc.identifier.issn00219991
dc.identifier.doi10.1016/j.jcp.2013.09.052
dc.identifier.urihttp://hdl.handle.net/10754/563285
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.
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.
dc.publisherElsevier BV
dc.subjectBeam splitter
dc.subjectDirac equation
dc.subjectDirac-Poisson system
dc.subjectFinite differences
dc.subjectGraphene
dc.subjectVeselago lens
dc.titleA convergent 2D finite-difference scheme for the Dirac-Poisson system and the simulation of graphene
dc.typeArticle
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.identifier.journalJournal of Computational Physics
dc.contributor.institutionDepartment of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
dc.contributor.institutionSchool of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287, United States
dc.contributor.institutionAIT Austrian Institute of Technology, A-1220 Vienna, Austria
kaust.personMarkowich, Peter A.
kaust.grant.numberKUK-I1-007-43


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