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

Journal Article · Wed Jan 15 00:00:00 EST 2014 · Journal of Computational Physics

DOI:https://doi.org/10.1016/J.JCP.2013.09.052· OSTI ID:22230843

Brinkman, D., E-mail: [e-mail] ^[1]; School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287 ^[2]; Heitzinger, C., E-mail: [e-mail] ^[1]; AIT Austrian Institute of Technology, A-1220 Vienna ^[3]; School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287 ^[2]; Markowich, P.A., E-mail: [e-mail] ^[4]; Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA ^[5]

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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)

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.

• OSTI ID: 22230843
• Journal Information: Journal of Computational Physics, Vol. 257, 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); ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
77 NANOSCIENCE AND NANOTECHNOLOGY
BEAMS
DIRAC EQUATION
GRAPHENE
LENSES
MATHEMATICAL SOLUTIONS
PARTICLES
POTENTIALS
SIMULATION
VECTORS