TY - JOUR
T1 - A convergent 2D finite-difference scheme for the Dirac-Poisson system and the simulation of graphene
AU - Brinkman, Daniel
AU - Heitzinger, Clemens Heitzinger
AU - Markowich, Peter A.
N1 - 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.
PY - 2014/1
Y1 - 2014/1
N2 - 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.
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.
UR - http://hdl.handle.net/10754/563285
UR - https://linkinghub.elsevier.com/retrieve/pii/S0021999113006700
UR - http://www.scopus.com/inward/record.url?scp=84886068809&partnerID=8YFLogxK
U2 - 10.1016/j.jcp.2013.09.052
DO - 10.1016/j.jcp.2013.09.052
M3 - Article
SN - 0021-9991
VL - 257
SP - 318
EP - 332
JO - Journal of Computational Physics
JF - Journal of Computational Physics
IS - PA
ER -