Advertisement

Darboux transformations for the massless Dirac equation with matrix potential: Construction of zero-energy states

  • Axel Schulze-HalbergEmail author
  • Mahmoud Ojel
Regular Article
First Online:
  • 14 Downloads

Abstract.

We develop a new method for constructing zero-energy states of the massless Dirac equation with a matrix potential. Our method is based on a Darboux transformation for Schrödinger-type equations featuring quadratically energy-dependent potentials.

This is a preview of subscription content, log in to check access.

References

  1. 1.
    K.S. Novoselov, A.K. Geim, S.M. Morozov, Y. Zhang, S.V. Dubonos, I.V. Grigorieva, A.A. Firsov, Science 306, 666 (2004)ADSCrossRefGoogle Scholar
  2. 2.
    A.K. Geim, K.S. Novoselov, Nat. Mater. 6, 183 (2007)ADSCrossRefGoogle Scholar
  3. 3.
    A.H. Castro Neto, F. Guinea, N.M.R. Peres, K.S. Novoselov, A.K. Geim, Rev. Mod. Phys. 81, 109 (2009)ADSCrossRefGoogle Scholar
  4. 4.
    M. Ramezani Masir, A. Matulis, F.M. Peeters, Phys. Rev. B 79, 155451 (2009)ADSCrossRefGoogle Scholar
  5. 5.
    V. Jakubsky, Phys. Rev. D 91, 045039 (2015)ADSMathSciNetCrossRefGoogle Scholar
  6. 6.
    J.G. Checkelsky, L. Li, N.P. Ong, Phys. Rev. Lett. 100, 206801 (2008)ADSCrossRefGoogle Scholar
  7. 7.
    P. Roy, T.K. Ghosh, K. Bhattacharya, J. Phys.: Condens. Matter 24, 055301 (2012)ADSGoogle Scholar
  8. 8.
    P. Ghosh, P. Roy, Phys. Lett. A 380, 567 (2016)ADSCrossRefGoogle Scholar
  9. 9.
    C.L. Ho, P. Roy, EPL 108, 20004 (2014)ADSCrossRefGoogle Scholar
  10. 10.
    C.A. Downing, M.E. Portnoi, J. Phys.: Condens. Matter 29, 315301 (2017)Google Scholar
  11. 11.
    R.R. Hartmann, M.E. Portnoi, Sci. Rep. 7, 11599 (2017)ADSCrossRefGoogle Scholar
  12. 12.
    R.R. Hartmann, M.E. Portnoi, Phys. Rev. A 95, 062110 (2017)ADSCrossRefGoogle Scholar
  13. 13.
    M. Erementchouk, P. Mazumder, M.A. Khan, M.N. Leuenberger, J. Phys.: Condens. Matter 28, 115501 (2016)ADSGoogle Scholar
  14. 14.
    C.A. Downing, M.E. Portnoi, Nat. Commun. 8, 897 (2017)ADSCrossRefGoogle Scholar
  15. 15.
    F. Correa, V. Jakubsky, Phys. Rev. A 95, 033807 (2017)ADSCrossRefGoogle Scholar
  16. 16.
    E. Pozdeeva, A. Schulze-Halberg, J. Math. Phys. 51, 113501 (2010)ADSMathSciNetCrossRefGoogle Scholar
  17. 17.
    A.V. Yurov, Phys. Lett. A 225, 51 (1997)ADSMathSciNetCrossRefGoogle Scholar
  18. 18.
    G. Darboux, C. R. Acad. Sci. 94, 1456 (1882)Google Scholar
  19. 19.
    F. Cooper, A. Khare, U. Sukhatme, Phys. Rep. 251, 267 (1995)ADSMathSciNetCrossRefGoogle Scholar
  20. 20.
    A. Contreras-Astorga, A. Schulze-Halberg, J. Math. Phys. 55, 103506 (2014)ADSMathSciNetCrossRefGoogle Scholar
  21. 21.
    A. Schulze-Halberg, P. Roy, J. Phys. A 50, 365205 (2017)MathSciNetCrossRefGoogle Scholar
  22. 22.
    A. Bergvall, T. Lofwander, Phys. Rev. B 87, 205431 (2013)ADSCrossRefGoogle Scholar
  23. 23.
    R. Olsen, R. van Gelderen, C.M. Smith, Phys. Rev. B 87, 115414 (2013)ADSCrossRefGoogle Scholar
  24. 24.
    J. Lin, Y.-S. Li, X.-M. Qian, Phys. Lett. A 362, 212 (2007)ADSMathSciNetCrossRefGoogle Scholar

Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematics and Actuarial Science and Department of PhysicsIndiana University NorthwestGaryUSA

Personalised recommendations

Cite article

Buy options