Advertisement

Quantum aspects of a quantum particle in a cylindrical wire in the presence of a screw dislocation

  • W. C. F. da Silva
  • K. BakkeEmail author
Regular Article
  • 27 Downloads

Abstract.

We consider an elastic medium with the distortion of a vertical line into a vertical spiral and investigate the influence of this topological defect on a spinless quantum particle confined to a cylindrical wire. In addition, we analyse the effects of rotation on this system. We show that there exists an analogue of the Aharonov-Bohm effect for bound states in both rotating and nonrotating reference frames. Furthermore, we show that the topology of the defect yields a term that plays the role of an effective radius in the spectrum of energy in both reference frames. In particular, in the rotating reference frame, a coupling between torsion and the angular velocity arises.

References

  1. 1.
    W. Tan, J.C. Inkson, G.P. Srivastava, Semicond. Sci. Technol. 9, 1305 (1994)ADSCrossRefGoogle Scholar
  2. 2.
    A.L. Silva Netto, C. Chesman, C. Furtado, Phys. Lett. A 372, 3894 (2008)ADSCrossRefGoogle Scholar
  3. 3.
    C. Filgueiras, E.O. Silva, Phys. Lett. A 379, 2110 (2015)ADSMathSciNetCrossRefGoogle Scholar
  4. 4.
    T. Ando, H. Aoki, Physica B 184, 365 (1993)ADSCrossRefGoogle Scholar
  5. 5.
    D. Loss, P.M. Goldbart, Phys. Rev. B 45, 13544 (1992)ADSCrossRefGoogle Scholar
  6. 6.
    D. Loss, P.M. Goldbart, A.V. Balatsky, Phys. Rev. Lett. 65, 1655 (1990)ADSCrossRefGoogle Scholar
  7. 7.
    L.G. Wang, Physica B 404, 143 (2009)ADSCrossRefGoogle Scholar
  8. 8.
    N.T. Bagraev et al., Physica B 378-380, 894 (2006)ADSCrossRefGoogle Scholar
  9. 9.
    Y.-C. Zhou, Y.-Z. Fang, G.-P. He, Physica B 226, 413 (1996)ADSCrossRefGoogle Scholar
  10. 10.
    W.-C. Tan, J.C. Inkson, Semiconduct. Sci. Technol. 11, 1635 (1996)ADSCrossRefGoogle Scholar
  11. 11.
    W.-C. Tan, J.C. Inkson, Phys. Rev. B 53, 6947 (1996)ADSCrossRefGoogle Scholar
  12. 12.
    W.-C. Tan, J.C. Inkson, Phys. Rev. B 60, 5626 (1996)ADSCrossRefGoogle Scholar
  13. 13.
    S.E. Pourmand, G. Rezaei, Physica B 543, 27 (2018)ADSCrossRefGoogle Scholar
  14. 14.
    D. Nasri, Physica B 540, 51 (2018)ADSCrossRefGoogle Scholar
  15. 15.
    L.F. García, R. Robayo, I.D. Mikhailov, Physica B 390, 340 (2017)ADSCrossRefGoogle Scholar
  16. 16.
    S. Klama, Physica B 191, 281 (1993)ADSCrossRefGoogle Scholar
  17. 17.
    S. Klama, Physica B 193, 295 (1994)ADSCrossRefGoogle Scholar
  18. 18.
    D.V. Bulaev, V.A. Geyler, V.A. Margulis, Phys. Rev. B 69, 195313 (2004)ADSCrossRefGoogle Scholar
  19. 19.
    E. Tsitsishvili, G.S. Lozano, A.O. Gogolin, Phys. Rev. B 70, 115316 (2004)ADSCrossRefGoogle Scholar
  20. 20.
    H.-S. Sim et al., Phys. Rev. Lett. 80, 1501 (1998)ADSCrossRefGoogle Scholar
  21. 21.
    E.V. Anda, C. Busser, G. Chiappe, M.A. Davidovich, Physica B 320, 358 (2002)ADSCrossRefGoogle Scholar
  22. 22.
    M.V. Berry, Proc. R. Soc. London A 392, 45 (1984)ADSCrossRefGoogle Scholar
  23. 23.
    Y. Aharonov, J. Anandan, Phys. Rev. Lett. 58, 1593 (1987)ADSMathSciNetCrossRefGoogle Scholar
  24. 24.
    X.-C. Gao, T.-Z. Qian, Phys. Rev. B 47, 7128 (1993)ADSCrossRefGoogle Scholar
  25. 25.
    T.-Z. Qian, Z.-B. Su, Phys. Rev. Lett. 72, 2311 (1994)ADSCrossRefGoogle Scholar
  26. 26.
    Y. Aharonov, D. Bohm, Phys. Rev. 115, 485 (1959)ADSMathSciNetCrossRefGoogle Scholar
  27. 27.
    M. Peshkin, A. Tonomura, The Aharonov-Bohm Effect, in Lecture Notes in Physics, Vol. 340 (Springer-Verlag, Berlin, 1989)Google Scholar
  28. 28.
    D.J. Griffiths, Introduction to Quantum Mechanics, second edition (Prentice Hall, 2004)Google Scholar
  29. 29.
    S. Oh, C.-M. Ryu, Phys. Rev. B 51, 13441 (1995)ADSCrossRefGoogle Scholar
  30. 30.
    H. Mathur, A.D. Stone, Phys. Rev. B 44, 10957 (1991)ADSCrossRefGoogle Scholar
  31. 31.
    H. Mathur, A.D. Stone, Phys. Rev. Lett. 68, 2964 (1992)ADSCrossRefGoogle Scholar
  32. 32.
    A.V. Balatsky, B.L. Altshuler, Phys. Rev. Lett. 70, 1678 (1993)ADSCrossRefGoogle Scholar
  33. 33.
    K. Bakke, C. Furtado, J. Math. Phys. 53, 023514 (2012)ADSMathSciNetCrossRefGoogle Scholar
  34. 34.
    K. Bakke, C. Furtado, Mod. Phys. Lett. A 26, 1331 (2011)ADSCrossRefGoogle Scholar
  35. 35.
    Y. Aharonov, A. Casher, Phys. Rev. Lett. 53, 319 (1984)ADSMathSciNetCrossRefGoogle Scholar
  36. 36.
    R. Merlin, Phys. Lett. A 181, 421 (1993)ADSCrossRefGoogle Scholar
  37. 37.
    G. Vignale, B. Mashhoon, Phys. Lett. A 197, 444 (1995)ADSCrossRefGoogle Scholar
  38. 38.
    I.C. Fonseca, K. Bakke, Eur. Phys. J. Plus 131, 67 (2016)CrossRefGoogle Scholar
  39. 39.
    L. Dantas, C. Furtado, Phys. Lett. A 377, 2926 (2013)ADSMathSciNetCrossRefGoogle Scholar
  40. 40.
    C. Furtado, V.B. Bezerra, F. Moraes, Phys. Lett. A 289, 160 (2001)ADSCrossRefGoogle Scholar
  41. 41.
    C. Furtado, C.A. de Lima Ribeiro, S. Azevedo, Phys. Lett. A 296, 171 (2002)ADSCrossRefGoogle Scholar
  42. 42.
    L. Dantas, C. Furtado, A.L. Silva Netto, Phys. Lett. A 379, 11 (2015)ADSMathSciNetCrossRefGoogle Scholar
  43. 43.
    H. Kleinert, Gauge Fields in Condensed Matter, Vol. 2 (World Scientific, Singapore, 1989)Google Scholar
  44. 44.
    K.C. Valanis, V.P. Panoskaltsis, Acta Mech. 175, 77 (2005)CrossRefGoogle Scholar
  45. 45.
    R.A. Puntigam, H.H. Soleng, Class. Quantum Grav. 14, 1129 (1997)ADSCrossRefGoogle Scholar
  46. 46.
    M.O. Katanaev, I.V. Volovich, Ann. Phys. (N.Y.) 216, 1 (1992)ADSCrossRefGoogle Scholar
  47. 47.
    G. de A. Marques et al., J. Phys. A 34, 5945 (2001)ADSMathSciNetCrossRefGoogle Scholar
  48. 48.
    C. Furtado, F. Moraes, Europhys. Lett. 45, 279 (1999)ADSCrossRefGoogle Scholar
  49. 49.
    A.L. Silva Netto, C. Furtado, J. Phys.: Condens. Matter 20, 125209 (2008)ADSGoogle Scholar
  50. 50.
    C. Furtado, F. Moraes, J. Phys. A 33, 5513 (2000)ADSMathSciNetCrossRefGoogle Scholar
  51. 51.
    M.J. Bueno, C. Furtado, K. Bakke, Physica B 496, 45 (2016)ADSCrossRefGoogle Scholar
  52. 52.
    A.V.D.M. Maia, K. Bakke, Physica B 531, 213 (2018)ADSCrossRefGoogle Scholar
  53. 53.
    K. Bakke, Physica B 537, 346 (2018)ADSCrossRefGoogle Scholar
  54. 54.
    M.J. Bueno, C. Furtado, A.M. de M. Carvalho, Eur. Phys. J. B 85, 53 (2012)ADSCrossRefGoogle Scholar
  55. 55.
    J. Amaro Neto, M.J. Bueno, C. Furtado, Ann. Phys. (N.Y.) 373, 273 (2016)ADSCrossRefGoogle Scholar
  56. 56.
    J. Amaro Neto, J.R. de S. Oliveira, C. Furtado, S. Sergeenkov, Eur. Phys. J. Plus 133, 185 (2008)CrossRefGoogle Scholar
  57. 57.
    M.J. Bueno, J. Lemos de Melo, C. Furtado, A.M. de M. Carvalho, Eur. Phys. J. Plus 129, 201 (2014)CrossRefGoogle Scholar
  58. 58.
    L.D. Landau, E.M. Lifshitz, Mechanics, third edition (Pergamon Press, Oxford, 1980)Google Scholar
  59. 59.
    L.D. Landau, E.M. Lifshitz, Statistical Physics - Part 1, 3rd. ed. (Pergamon Press, New York, 1980)Google Scholar
  60. 60.
    J. Anandan, J. Suzuki, in Relativity in Rotating Frames, Relativistic Physics in Rotating Reference Frame, edited by G. Rizzi, M.L. Ruggiero (Kluwer Academic Publishers, Dordrecht, 2004) pp. 361--369, arXiv:quant-ph/0305081Google Scholar
  61. 61.
    C.-H. Tsai, D. Neilson, Phys. Rev. A 37, 619 (1988)ADSCrossRefGoogle Scholar
  62. 62.
    V.B. Bezerra, J. Math. Phys. 38, 2553 (1997)ADSMathSciNetCrossRefGoogle Scholar
  63. 63.
    L.A. Page, Phys. Rev. Lett. 35, 543 (1975)ADSCrossRefGoogle Scholar
  64. 64.
    S.A. Werner, J.-L. Staudenmann, R. Colella, Phys. Rev. Lett. 42, 1103 (1979)ADSCrossRefGoogle Scholar
  65. 65.
    F.W. Hehl, W.-T. Ni, Phys. Rev. D 42, 2045 (1990)ADSCrossRefGoogle Scholar

Copyright information

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

Authors and Affiliations

  1. 1.Departamento de FísicaUniversidade Federal da ParaíbaJoão PessoaBrazil

Personalised recommendations