Skip to main content
SpringerLink
Log in

Time-reversal symmetry breaking and decoherence in chaotic Dirac billiards

  • Regular Article
  • Published:
The European Physical Journal B Aims and scope Submit manuscript

Abstract

In this work, we perform a statistical study on Dirac Billiards in the extreme quantum limit (a single open channel on the leads). Our numerical analysis uses a large ensemble of random matrices and demonstrates the preponderant role of dephasing mechanisms in such chaotic billiards. Physical implementations of these billiards range from quantum dots of graphene to topological insulators structures. We show, in particular, that the role of finite crossover fields between the universal symmetries quickly leaves the conductance to the asymptotic limit of unitary ensembles. Furthermore, we show that the dephasing mechanisms strikingly lead Dirac billiards from the extreme quantum regime to the semiclassical Gaussian regime.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. M.V. Berry, Some quantum-to-classical asymptotics, in Chaos and Quantum Physics: Les Houches Lecture, edited by M.-J. Giannoni, A. Voros, J. Zinn-Justin (North-Holland, Amsterdam, 1991), Series 52, p. 251

  2. O. Bohigas, Random matrix theories and chaotic dynamics, in Chaos and Quantum Physics: Les Houches Lecture, edited by M.-J. Giannoni, A. Voros, J. Zinn-Justin (North-Holland, Amsterdam, 1991), Series 52, p. 89

  3. H.J. Stöckmann, Quantum Chaos: An Introduction (Cambridge University Press, Cambridge, 2000)

  4. G.E. Mitchell, A. Richter, H.A. Weidenmüller, Rev. Mod. Phys. 82, 2845 (2010)

    Article  ADS  Google Scholar 

  5. P.A. Mello, N. Kumar, Quantum Transport in Mesoscopic Systems Complexity and Statistical Fluctuations (Academic, Oxford, 2004)

  6. C.W.J. Beenakker, Rev. Mod. Phys. 69, 731 (1997)

    Article  ADS  Google Scholar 

  7. C.W.J. Beenakker, Rev. Mod. Phys. 80, 1337 (2008)

    Article  ADS  Google Scholar 

  8. B. Dietz, A. Richter, Chaos 25, 097601 (2015)

    Article  ADS  Google Scholar 

  9. C.W.J. Beenakker, M. Kindermann, C.M. Marcus, A. Yacoby, in Fundamental Problems of Mesoscopic Physics, NATO Science, edited by I.V. Lerner, B.L. Altshuler, Y. Gefen (Kluwer, Dordrecht, 2004), Series II, Vol. 154

  10. A. Altland, M.R. Zirnbauer, Phys. Rev. B 55, 1142 (1997)

    Article  ADS  Google Scholar 

  11. P. Jacquod, R.S. Whitney, J. Meair, M. Büttiker, Phys. Rev. B 86, 155118 (2012)

    Article  ADS  Google Scholar 

  12. M.L. Mehta, Random Matrices (Academic, New York, 1991)

  13. E.V. Shuryak, J.J.M. Verbaarschot, Nucl. Phys. A 560, 306 (1993)

    Article  ADS  Google Scholar 

  14. J. Verbaarschot, Phys. Rev. Lett. 72, 2531 (1994)

    Article  ADS  MathSciNet  Google Scholar 

  15. M.V. Berry, R.J. Mondragon, Proc. R. Soc. London A 412, 53 (1987)

    Article  ADS  MathSciNet  Google Scholar 

  16. L.A. Ponomarenko, F. Schedin, M.I. Katsnelson, R. Yang, E.W. Hill, K.S. Novoselov, A.K. Geim, Science 320, 356 (2008)

    Article  ADS  Google Scholar 

  17. U. Kuhl, S. Barkhofen, T. Tudorovskiy, H.-J. Stöckmann, T. Hossain, L. de Forges de Parny, F. Mortessagne, Phys. Rev. B 82, 094308 (2010)

    Article  ADS  Google Scholar 

  18. J. Wurm, A. Rycerz, I. Adagideli, M. Wimmer, K. Richter, H.U. Baranger, Phys. Rev. Lett. 102, 056806 (2009)

    Article  ADS  Google Scholar 

  19. J.G.G.S. Ramos, M.S. Hussein, A.L.R. Barbosa, Phys. Rev. B 93, 125136 (2016)

    Article  ADS  Google Scholar 

  20. M.S.M. Barros, A.J. Nascimento Jr., A.F. Macedo-Junior, J.G.G.S. Ramos, A.L.R. Barbosa, Phys. Rev. B 88, 245133 (2013)

    Article  ADS  Google Scholar 

  21. B. Dietz, T. Klaus, M. Miski-Oglu, A. Richter, Phys. Rev. B 91, 035411 (2015)

    Article  ADS  Google Scholar 

  22. C.W.J. Beenakker, Lect. Notes Phys. 667, 131 (2005)

    Article  ADS  Google Scholar 

  23. H.U. Baranger, P.A. Mello, Phys. Rev. Lett. 73,142 (1994)

    Article  ADS  Google Scholar 

  24. G. Lenz, F. Haake, Phys. Rev. Lett. 65, 2325 (1990)

    Article  ADS  MathSciNet  Google Scholar 

  25. A.G. Huibers, S.R. Patel, C.M. Marcus, P.W. Brouwer, C.I. Duruöz, J.S. Harris Jr., Phys. Rev. Lett. 81, 1917 (1998)

    Article  ADS  Google Scholar 

  26. P. Vidal, E. Kanzieper, Phys. Rev. Lett. 108, 206806 (2012)

    Article  ADS  Google Scholar 

  27. A. Jarosz, P. Vidal, E. Kanzieper, Phys. Rev. B 91, 180203(R) (2015)

    Article  ADS  Google Scholar 

  28. A.M.C. Souza, A.M.S. Macêdo, Physica A 344, 677 (2004)

    Article  ADS  Google Scholar 

  29. J.G.G.S. Ramos, D. Bazeia, M.S. Hussein, C.H. Lewenkopf, Phys. Rev. Lett. 107, 176807 (2011)

    Article  ADS  Google Scholar 

  30. A.L.R. Barbosa, M.S. Hussein, J.G.G.S. Ramos, Phys. Rev. E 88, 010901(R) (2013)

    Article  ADS  Google Scholar 

  31. B. Dietz, A. Richter, R. Samajdar, Phys. Rev. B 92, 0229004 (2015)

    Google Scholar 

  32. A.L.R. Barbosa, D. Bazeia, J.G.G.S. Ramos, Phys. Rev. E 90, 042915 (2014)

    Article  ADS  Google Scholar 

  33. A.L.R. Barbosa, J.G.G.S. Ramos, A.M.S. Macêdo, J. Phys. A 43, 075101 (2010)

    Article  ADS  Google Scholar 

  34. J.G.G.S. Ramos, A.L.R. Barbosa, A.M.S. Macêdo, Phys. Rev. B 78, 235305 (2008)

    Article  ADS  Google Scholar 

  35. M. Novaes, Ann. Phys. 361, 51 (2015)

    Article  MathSciNet  Google Scholar 

  36. V.A. Gopar, D. Frustaglia, Phys. Rev. B 77, 153403 (2008)

    Article  ADS  Google Scholar 

  37. F.A.G. Almeida, A.M.C. Souza, Phys. Rev. B 82, 115422 (2010)

    Article  ADS  Google Scholar 

  38. M.V. Berry, M. Robnik, J. Phys. A 19, 649 (1986)

    Article  ADS  MathSciNet  Google Scholar 

  39. H. Schanze, E.R.P. Alves, C.H. Lewenkopf, H.-J. Stöckmann, Phys. Rev. E 64, 065201 (2001)

    Article  ADS  Google Scholar 

  40. B. Dietz, T. Friedrich, H.L. Harney, M. Miski-Oglu, A. Richter, F. Schfer, J. Verbaarschot, H.A. Weidenmüller, Phys. Rev. Lett. 103, 064101 (2009)

    Article  ADS  Google Scholar 

  41. M. Büttiker, Phys. Rev. Lett. 57, 1761 (1986)

    Article  ADS  Google Scholar 

  42. M. Büttiker, Phys. Rev. B 33, 3020 (1986)

    Article  ADS  Google Scholar 

  43. C.M. Marcus, R.M. Westervelt, P.F. Hopkins, A.C. Gossard, Phys. Rev. B 48, 2460 (1993)

    Article  ADS  Google Scholar 

  44. H.U. Baranger, P.A. Mello, Phys. Rev. B 51, 4703 (1995).

    Article  ADS  Google Scholar 

  45. P.W. Brouwer, C.W.J. Beenakker, Phys. Rev. B 51, 7739 (1995)

    Article  ADS  Google Scholar 

  46. R.S. Whitney, P. Jacquod, C. Petitjean, Phys. Rev. B 77, 045315 (2008)

    Article  ADS  Google Scholar 

  47. H. Schanze, H.-J. Stckmann, M. Martnez-Mares, C.H. Lewenkopf, Phys. Rev. E 71, 016223 (2005)

    Article  ADS  Google Scholar 

  48. T.O. Wehling, A.M. Black-Schaffer, A.V. Balatsky, Adv. Phys. 76, 1 (2014)

    Article  ADS  Google Scholar 

  49. J.G.G.S. Ramos, I.M.L. da Silva, A.L.R. Barbosa, Phys. Rev. B 90, 245107 (2014)

    Article  ADS  Google Scholar 

  50. J. Wurm, M. Wimmer, I. Adagideli, K. Richter, H.U. Baranger, New J. Phys. 11 095022 (2009)

    Article  ADS  Google Scholar 

  51. J. Wurm, K. Richter, I. Adagideli, Phys. Rev. B 84, 075468 (2011)

    Article  ADS  Google Scholar 

  52. J. Wurm, K. Richter, I. Adagideli, Phys. Rev. B 84, 205421 (2011)

    Article  ADS  Google Scholar 

  53. J. Wurm, M. Wimmer, K. Richter, Phys. Rev. B 85, 245418 (2012)

    Article  ADS  Google Scholar 

  54. L. Hee, K. Richter, Phys. Rev. B 90, 205424 (2014)

    Article  ADS  Google Scholar 

  55. F. Libisch, C. Stampfer, J. Burgdörfer, Phys. Rev. B 79, 115423 (2009)

    Article  ADS  Google Scholar 

  56. R. Yang, L. Huang, Ying-Cheng Lai, C. Grebogi, Europhys. Lett. 94, 40004 (2011)

    Article  ADS  Google Scholar 

  57. A. Rycerz, Phys. Rev. B 85, 245424 (2012)

    Article  ADS  Google Scholar 

  58. A. Rycerz, Phys. Rev. B 87, 195431 (2013)

    Article  ADS  Google Scholar 

  59. B. Dietz, A. Richter, R. Samajda, Phys. Rev. E 92, 022904 (2015)

    Article  ADS  Google Scholar 

  60. B. Dietz, T. Klaus, M. Miski-Oglu, A. Richter, M. Wunderle, C. Bouazza, Phys. Rev. Lett. 116, 023901 (2016)

    Article  ADS  Google Scholar 

  61. Lei Ying, Ying-Cheng Lai, Phys. Rev. B 93, 085408 (2016)

    Article  ADS  Google Scholar 

  62. P. Markos, L. Schweitzer, Physica B 407, 4016, (2012)

    Article  ADS  Google Scholar 

  63. A.F. Macedo Jr., A.M.S. Macêdo, Phys. Rev. B 77, 165313 (2008)

    Article  ADS  Google Scholar 

  64. A.F. Macedo Jr., A.M.S. Macêdo, Phys. Rev. B 66, 041307 (2002)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departamento de Física, Universidade Federal Rural de Pernambuco, 52171-900, Recife-PE, Brazil

    Agnaldo J. Nascimento Júnior & Anderson L.R. Barbosa

  2. Departamento de Física, Universidade Federal da Paraíba, 58051-970, João Pessoa, Paraíba, Brazil

    Marilia S.M. Barros & Jorge G.G.S. Ramos

Authors
  1. Agnaldo J. Nascimento Júnior
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Marilia S.M. Barros
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jorge G.G.S. Ramos
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Anderson L.R. Barbosa
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jorge G.G.S. Ramos.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Nascimento Júnior, A., Barros, M., Ramos, J. et al. Time-reversal symmetry breaking and decoherence in chaotic Dirac billiards. Eur. Phys. J. B 89, 194 (2016). https://doi.org/10.1140/epjb/e2016-70147-x

Download citation

  • Received:

  • Revised:

  • Published:

  • DOI: https://doi.org/10.1140/epjb/e2016-70147-x

Keywords

Search

Navigation