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

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.
Authors:
 [1] ;  [2] ;  [1] ;  [3] ;  [2] ;  [4] ;  [5]
  1. Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom)
  2. (United States)
  3. (Austria)
  4. Mathematical and Computer Sciences and Engineering Division, King Abdullah University of Science and Technology, Thuwal 23955-6900 (Saudi Arabia)
  5. (United Kingdom)
Publication Date:
OSTI Identifier:
22230843
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Computational Physics; Journal Volume: 257; Journal Issue: Part A; Other Information: Copyright (c) 2013 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; 77 NANOSCIENCE AND NANOTECHNOLOGY; BEAMS; DIRAC EQUATION; GRAPHENE; LENSES; MATHEMATICAL SOLUTIONS; PARTICLES; POTENTIALS; SIMULATION; VECTORS