Advertisement

Simulations of persistent current in disordered rings with axial magnetic field

  • Gerd BergmannEmail author
Regular Article
  • 18 Downloads

Abstract

Electrons in pure nanorings or tubes possess eigenstates with circular currents. In the presence of disorder the eigenstates become standing waves suppressing the circular current. A magnetic field parallel to the axis of the tube/ring recreates propagating electron states with circular persistent current. Numerical calculations for disordered rings are performed in the tight-binding approximation for finite disorder and magnetic field. The application of a gauge transformation contributes to an intuitive understanding of the persistent current and its absence for a flux Φ equal to a multiple of half the flux quantum and leads to a formula for the current in the disordered ring with magnetic flux. The derivative of the eigenstate energies with respect to the magnetic flux Φ through the ring, dEndΦ, yields an effective circular group velocity and represents an alternative method to calculate the circular current in disordered systems. Current and energy obey the Aharonov–Bohm effect. For large disorder a competition between persistent current and electron localization is observed. Despite the random disorder in the rings the dependence of the energy and the current on the flux is smooth and shows an interesting symmetry. For each state with negative energy there is a state with positive energy that carries exactly the opposite current.

Graphical abstract

Keywords

Mesoscopic and Nanoscale Systems 

References

  1. 1.
    M. Buettiker, Y. Imry, R. Landauer, Phys. Lett. A 96, 365 (1983) ADSCrossRefGoogle Scholar
  2. 2.
    M. Buettiker, Y. Imry, M.Y. Azbel, Phys. Rev. A 30, 1982 (1984) ADSCrossRefGoogle Scholar
  3. 3.
    M. Buettiker, Y. Imry, R. Landauer, S. Pinhas, Phys. Rev. B 31, 6207 (1985) ADSCrossRefGoogle Scholar
  4. 4.
    Y. Gefen, Y. Imry, M.Y. Azbel, Phys. Rev. Lett. 52, 129 (1984) ADSCrossRefGoogle Scholar
  5. 5.
    M. Murat, Y. Gefen, Y. Imry, Phys. Rev. B 34, 659 (1986) ADSCrossRefGoogle Scholar
  6. 6.
    H.-F. Cheung, E.K. Riedel, Y. Gefen, Phys. Rev. Lett. 62, 587 (1989) ADSCrossRefGoogle Scholar
  7. 7.
    E.P. Nakhmedov, H. Feldmann, R. Oppermann, Eur. Phys. J. B 16, 515 (2000) ADSCrossRefGoogle Scholar
  8. 8.
    P.M. Shmakov, A.P. Dmitriev, V.Yu. Kachorovskii, Phys. Rev. B 87, 235417 (2000) ADSCrossRefGoogle Scholar
  9. 9.
    H. Bary-Soroker, O. Entin-Wohlman, Y. Imry, Phys. Rev. Lett. 101, 057001 (2008) ADSCrossRefGoogle Scholar
  10. 10.
    B.L. Altshuler, Y. Gefen, Y. Imry, Phys. Rev. Lett. 66, 88 (1991) ADSCrossRefGoogle Scholar
  11. 11.
    H. Bouchiat, G. Montambaux, D. Sigeti, Phys. Rev. B 44, 1682 (1991) ADSCrossRefGoogle Scholar
  12. 12.
    E.K. Riedel, F.v. Oppen, Phys. Rev. B 47, 15449 (1993) ADSCrossRefGoogle Scholar
  13. 13.
    V. Ambegaokar, U. Eckern, Europhys. Lett. 13, 733 (1990) ADSCrossRefGoogle Scholar
  14. 14.
    V. Ambegaokar, U. Eckern, Phys. Rev. Lett. 65, 381 (1990) ADSCrossRefGoogle Scholar
  15. 15.
    G. Montambaux, H. Bouchiat, D. Sigeti, R. Friesner, Phys. Rev. B 42, 7647(R) (1990) ADSCrossRefGoogle Scholar
  16. 16.
    A.O. Gogolin, N.V. Prokof’ev, Phys. Rev. B 50, 4921 (1994) ADSCrossRefGoogle Scholar
  17. 17.
    J.F. Weisz, R. Kishore, F.V. Kusmartsev, Phys. Rev. B49, 8126 (1994) ADSCrossRefGoogle Scholar
  18. 18.
    P.W. Brouwer, P.G. Silvestrov, C.W.J. Beenakker, Phys. Rev. B 56, R4333(R) (1997) ADSCrossRefGoogle Scholar
  19. 19.
    A.G. Aronov, Yu.V. Sharvin, Rev. Mod. Phys. 59, 755 (1987) ADSCrossRefGoogle Scholar
  20. 20.
    D.Y. Sharvin, Y.V. Sharvin, JETP Lett. 34, 272 (1981) [Pis’ma Zh. Eksp. Teor. Fiz. 34, 285 (1981)] ADSGoogle Scholar
  21. 21.
    B.L. Altshuler, A.G. Aronov, B.Z. Spivak, D.Y. Sharvin, Y.V. Sharvin, JETP Lett. 35, 588 (1982) [Pis’ma Zh. Eksp. Teor. Fiz. 35, 476 (1982)] ADSGoogle Scholar
  22. 22.
    G. Deutscher, M. Gijs, C. Van Haesendonck, Y. Bruynseraede, Phys. Rev. Lett. 52, 2069 (1984) ADSCrossRefGoogle Scholar
  23. 23.
    M. Gijs, C. Van Haesendonck, Y. Bruynseraede, Phys. Rev. Lett. 52, 2069 (1984) ADSCrossRefGoogle Scholar
  24. 24.
    R.A. Webb, S. Washburn, C.P. Umbach, R.B. Laibowitz, Phys. Rev. Lett. 54, 2696 (1985) ADSCrossRefGoogle Scholar
  25. 25.
    B.L. Altshuler, P.A. Lee, R.A. Webb (eds.), Mesoscopic Phenomena in Solids (North Holland, Amsterdam, 1991) Google Scholar
  26. 26.
    E.M.Q. Jariwala, P. Mohanty, M.B. Ketchen, R.A. Webb, Phys. Rev. Lett. 86, 1594 (2001) ADSCrossRefGoogle Scholar
  27. 27.
    A.D. Benoit, S. Washburn, C.P. Umbach, R.B. Laibowitz, R.A. Webb, Phys. Rev. Lett. 57, 1765 (1986) ADSCrossRefGoogle Scholar
  28. 28.
    V. Chandrasekhar, R.A. Webb, M.J. Brady, M.B. Ketchen, W.J. Gallagher, A. Kleinsasser, Phys. Rev. Lett. 67, 3578 (1991) ADSCrossRefGoogle Scholar
  29. 29.
    A.C. Bleszynski-Jayich, W.E. Shanks, B. Peaudecerf, E. Ginossar, F. von Oppen, L. Glazman, J.G.E. Harris, Science 326, 272 (2009) ADSCrossRefGoogle Scholar
  30. 30.
    A. Bachtold, C. Strunk, J.-P. Salvetat, J.-M. Bonard et al., Nature 397, 673 (1999) ADSCrossRefGoogle Scholar
  31. 31.
    D. Hsieh, Y. Xia, D. Qian, L. Wray, J.H. Dil, F. Meier, J. Osterwalder, L. Patthey, J.G. Checkelsky, N.P. Ong, A.V. Fedorov, H. Lin, A. Bansil, D. Grauer, Y.S. Hor, R.J. Cava, M.Z. Hasan, Nature 460, 1101 (2009) ADSCrossRefGoogle Scholar
  32. 32.
    A. Junck, G. Refael, F.v. Oppen, Phys. Rev. B 88, 075144 (2013) ADSCrossRefGoogle Scholar
  33. 33.
    Z.-H. Zhu et al., Phys. Rev. Lett. 110, 216401 (2013) ADSCrossRefGoogle Scholar
  34. 34.
    C.H. Li, O.M.J. Erve, J.T. Robinson, Y. Liu, L. Li, B.T. Jonker, Nat. Nanotechnol. 9, 218 (2014) ADSCrossRefGoogle Scholar
  35. 35.
    J. Tang, Nano Lett. 14, 5423 (2014) ADSCrossRefGoogle Scholar
  36. 36.
    A. Dankert, J. Geurs, M.V. Kamalakar, S. Charpentier, S.P. Dash, Nano Lett. 15, 7976 (2015) ADSCrossRefGoogle Scholar
  37. 37.
    J. Tian, S. Hong, I. Miotkowski, S. Datta, Sci. Adv. 3, e1602531 (2017) ADSCrossRefGoogle Scholar
  38. 38.
    F. Kuemmeth, S. Ilani, D.C. Ralph, P.L. McEuen, Nature 452, 448 (2008) ADSCrossRefGoogle Scholar
  39. 39.
    G.A. Steele, F. Pei, E.A. Laird, J.M. Jol, H.B. Meerwaldt, L.P. Kouwenhoven, Nat. Commun. 4, 1573 (2013) ADSCrossRefGoogle Scholar
  40. 40.
    W. Izumida, K. Sato, R. Saito, J. Phys. Soc. Jpn. 78, 074707 (2009) ADSCrossRefGoogle Scholar
  41. 41.
    R. Peierls, Z. Phys. 80, 763 (1933) ADSCrossRefGoogle Scholar
  42. 42.
    J. Alicea, Y. Oreg, G. Refael, F.V. Oppen, M.P.A. Fisher, Nat. Phys. 7, 412 (2011) CrossRefGoogle Scholar
  43. 43.
    M.Y. Azbel, Phys. Rev. Lett. 46, 675 (1981) ADSCrossRefGoogle Scholar
  44. 44.
    P.W. Brouwer, P.G. Silvestrov, C.W.J. Beenakker, Phys. Rev. B 56, R4333 (1997) ADSCrossRefGoogle Scholar
  45. 45.
    R.E. Borland, N.F. Bird, Proc. Phys. Soc. 83, 23 (1964) ADSCrossRefGoogle Scholar
  46. 46.
    B. Doucot, R. Rammel, Physique 47, 973 (1986) CrossRefGoogle Scholar
  47. 47.
    E.N. Economou, C.M. Soukoulis, Phys. Rev. Lett. 46, 618 (1981) ADSCrossRefGoogle Scholar
  48. 48.
    Y. Gefen, G. Schoen, Phys. Rev. B 30, 7323(R) (1984) ADSCrossRefGoogle Scholar
  49. 49.
    R. Landauer, Phil. Mag. 21, 863 (1970) ADSCrossRefGoogle Scholar
  50. 50.
    J.B. Pendry, J. Phys. C: Solid State Phys. 15, 4821 (1982) ADSCrossRefGoogle Scholar
  51. 51.
    J. Sirker, Phys. Rev. Lett. 105, 117203 (2010) ADSCrossRefGoogle Scholar
  52. 52.
    C.M. Soukoulis, J.V. Jose, E.N. Economou, P. Sheng, Phys. Rev. Lett. 50, 764 (1983) ADSCrossRefGoogle Scholar
  53. 53.
    D.J. Thouless, Phys. Rev. Lett. 39, 1167 (1977) ADSCrossRefGoogle Scholar
  54. 54.
    C.W.J. Beenakker, Rev. Mod. Phys. 80, 1337 (2008) ADSCrossRefGoogle Scholar
  55. 55.
    P. LaFarge, P. Joyez, D. Esteve, C. Urbina, M.H. Devoret, Nature 365, 422 (1993) ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences / Società Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Physics and AstronomyUniversity of Southern CaliforniaLos AngelesUSA

Personalised recommendations