Russian Physics Journal

, Volume 59, Issue 11, pp 1875–1880 | Cite as

Numerical Computation of Dynamical Schwinger-like Pair Production in Graphene

  • F. Fillion-Gourdeau
  • P. Blain
  • D. Gagnon
  • C. Lefebvre
  • S. Maclean

The density of electron-hole pairs produced in a graphene sample immersed in a homogeneous time-dependent electric field is evaluated. Because low energy charge carriers in graphene are described by relativistic quantum mechanics, the calculation is performed within the strong field quantum electrodynamics formalism, requiring a solution of the Dirac equation in momentum space. The equation is solved using a split-operator numerical scheme on parallel computers, allowing for the investigation of several field configurations. The strength of the method is illustrated by computing the electron momentum density generated from a realistic laser pulse model. We observe quantum interference patterns reminiscent of Landau–Zener–Stückelberg interferometry.


graphene pair production Dirac equation Schwinger mechanism 


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  1. 1.
    V. Gusynin, S. Sharapov, and J. Carbotteб Int. J. Mod. Phys., B21, 4611 (2007).Google Scholar
  2. 2.
    S. Teber, Phys. Rev., D86, 025005 (2012).ADSGoogle Scholar
  3. 3.
    N. Stander, B. Huard, and D. Goldhaber-Gordon, Phys. Rev. Lett., 102, 026807 (2009).ADSCrossRefGoogle Scholar
  4. 4.
    I. V. Fialkovsky, V. N. Marachevsky, and D. V. Vassilevich, Phys. Rev., B84, 035446 (2011).ADSCrossRefGoogle Scholar
  5. 5.
    D . Allor, T. D. Cohen, and D. A. McGady, Phys. Rev., D78, 096009 (2008).ADSGoogle Scholar
  6. 6.
    S. P. Gavrilov, D. M. Gitman, and N. Yokomizo, Phys. Rev., D86, 125022 (2012).ADSGoogle Scholar
  7. 7.
    T. C. Adorno, S. P. Gavrilov, and D. M. Gitman, Phys. Scr., 90, 074005 (2015).ADSCrossRefGoogle Scholar
  8. 8.
    F. Hebenstreit, R. Alkofer, and H. Gies, Phys. Rev., D82, 105026 (2010).ADSGoogle Scholar
  9. 9.
    C. K. Dumlu and G. V. Dunne, Phys. Rev. Lett., 104, 250402 (2010).ADSCrossRefGoogle Scholar
  10. 10.
    F. Gelis and N. Tanji, Progr. Part. Nucl. Phys., 87, 1 (2016).ADSCrossRefGoogle Scholar
  11. 11.
    F. Hebenstreit, R. Alkofer, and H. Gies, Phys. Rev., D78, 061701 (2008).ADSGoogle Scholar
  12. 12.
    F. Hebenstreit, A. Ilderton, M. Marklund, and J. Zamanian, Phys. Rev., D83, 065007 (2011).ADSGoogle Scholar
  13. 13.
    F. Fillion-Gourdeau, E. Lorin, and A. D. Bandrauk, Phys. Rev., A86, 032118 (2012).ADSCrossRefGoogle Scholar
  14. 14.
    F. fillion-gourdeau and s. maclean, Phys. Rev., B92, 035401 (2015).Google Scholar
  15. 15.
    J. W. Braun, Q. Su, and R. Grobe , Phys. Rev., A59, 604 (1999).ADSCrossRefGoogle Scholar
  16. 16.
    G. R. Mocken and C. H. Keitel, J. Comp. Phys., 199, 558 (2004).ADSCrossRefGoogle Scholar
  17. 17.
    H. Bauke and C. H. Keitel, Comp. Phys. Comm., 182, 2454 (2011).ADSCrossRefGoogle Scholar
  18. 18.
    G. R. Mocken and C. H. Keitel, Comp. Phys. Comm., 178, 868 (2008).ADSCrossRefGoogle Scholar
  19. 19.
    R. I. McLachlan and G. R. W. Quispel, Acta Num., 11, 341 (2002).CrossRefGoogle Scholar
  20. 20.
    M. Suzuki, Proc. Jpn. Acad. Ser., B69, 161 (1993).CrossRefGoogle Scholar
  21. 21.
    F. Fillion-Gourdeau, E. Lorin, and A. D. Bandrauk, Comp. Phys. Comm., 183, 1403 (2012).ADSCrossRefGoogle Scholar
  22. 22.
    F. Fillion-Gourdeau, D. Gagnon, C. Lefebvre, and S. Maclean, arXiv:1607.02055 (2015).Google Scholar
  23. 23.
    S. Shevchenko, S. Ashhab, and F. Nori, Phys. Rep., 492, 1 (2010).ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  • F. Fillion-Gourdeau
    • 1
    • 2
  • P. Blain
    • 1
  • D. Gagnon
    • 1
    • 2
  • C. Lefebvre
    • 1
    • 2
  • S. Maclean
    • 1
    • 2
  1. 1.Université du Québec, Inrs-Énergie, Matériaux et TélécommunicationsVarennesCanada
  2. 2.Institute for Quantum ComputingUniversity of WaterlooWaterlooCanada

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