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Simulations of persistent current in disordered rings with axial magnetic field

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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, dEn∕dΦ, 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.

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References

  1. M. Buettiker, Y. Imry, R. Landauer, Phys. Lett. A 96, 365 (1983)

    Article  ADS  Google Scholar 

  2. M. Buettiker, Y. Imry, M.Y. Azbel, Phys. Rev. A 30, 1982 (1984)

    Article  ADS  Google Scholar 

  3. M. Buettiker, Y. Imry, R. Landauer, S. Pinhas, Phys. Rev. B 31, 6207 (1985)

    Article  ADS  Google Scholar 

  4. Y. Gefen, Y. Imry, M.Y. Azbel, Phys. Rev. Lett. 52, 129 (1984)

    Article  ADS  Google Scholar 

  5. M. Murat, Y. Gefen, Y. Imry, Phys. Rev. B 34, 659 (1986)

    Article  ADS  Google Scholar 

  6. H.-F. Cheung, E.K. Riedel, Y. Gefen, Phys. Rev. Lett. 62, 587 (1989)

    Article  ADS  Google Scholar 

  7. E.P. Nakhmedov, H. Feldmann, R. Oppermann, Eur. Phys. J. B 16, 515 (2000)

    Article  ADS  Google Scholar 

  8. P.M. Shmakov, A.P. Dmitriev, V.Yu. Kachorovskii, Phys. Rev. B 87, 235417 (2000)

    Article  ADS  Google Scholar 

  9. H. Bary-Soroker, O. Entin-Wohlman, Y. Imry, Phys. Rev. Lett. 101, 057001 (2008)

    Article  ADS  Google Scholar 

  10. B.L. Altshuler, Y. Gefen, Y. Imry, Phys. Rev. Lett. 66, 88 (1991)

    Article  ADS  Google Scholar 

  11. H. Bouchiat, G. Montambaux, D. Sigeti, Phys. Rev. B 44, 1682 (1991)

    Article  ADS  Google Scholar 

  12. E.K. Riedel, F.v. Oppen, Phys. Rev. B 47, 15449 (1993)

    Article  ADS  Google Scholar 

  13. V. Ambegaokar, U. Eckern, Europhys. Lett. 13, 733 (1990)

    Article  ADS  Google Scholar 

  14. V. Ambegaokar, U. Eckern, Phys. Rev. Lett. 65, 381 (1990)

    Article  ADS  Google Scholar 

  15. G. Montambaux, H. Bouchiat, D. Sigeti, R. Friesner, Phys. Rev. B 42, 7647(R) (1990)

    Article  ADS  Google Scholar 

  16. A.O. Gogolin, N.V. Prokof’ev, Phys. Rev. B 50, 4921 (1994)

    Article  ADS  Google Scholar 

  17. J.F. Weisz, R. Kishore, F.V. Kusmartsev, Phys. Rev. B49, 8126 (1994)

    Article  ADS  Google Scholar 

  18. P.W. Brouwer, P.G. Silvestrov, C.W.J. Beenakker, Phys. Rev. B 56, R4333(R) (1997)

    Article  ADS  Google Scholar 

  19. A.G. Aronov, Yu.V. Sharvin, Rev. Mod. Phys. 59, 755 (1987)

    Article  ADS  Google Scholar 

  20. D.Y. Sharvin, Y.V. Sharvin, JETP Lett. 34, 272 (1981) [Pis’ma Zh. Eksp. Teor. Fiz. 34, 285 (1981)]

    ADS  Google Scholar 

  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)]

    ADS  Google Scholar 

  22. G. Deutscher, M. Gijs, C. Van Haesendonck, Y. Bruynseraede, Phys. Rev. Lett. 52, 2069 (1984)

    Article  ADS  Google Scholar 

  23. M. Gijs, C. Van Haesendonck, Y. Bruynseraede, Phys. Rev. Lett. 52, 2069 (1984)

    Article  ADS  Google Scholar 

  24. R.A. Webb, S. Washburn, C.P. Umbach, R.B. Laibowitz, Phys. Rev. Lett. 54, 2696 (1985)

    Article  ADS  Google Scholar 

  25. B.L. Altshuler, P.A. Lee, R.A. Webb (eds.), Mesoscopic Phenomena in Solids (North Holland, Amsterdam, 1991)

  26. E.M.Q. Jariwala, P. Mohanty, M.B. Ketchen, R.A. Webb, Phys. Rev. Lett. 86, 1594 (2001)

    Article  ADS  Google Scholar 

  27. A.D. Benoit, S. Washburn, C.P. Umbach, R.B. Laibowitz, R.A. Webb, Phys. Rev. Lett. 57, 1765 (1986)

    Article  ADS  Google Scholar 

  28. V. Chandrasekhar, R.A. Webb, M.J. Brady, M.B. Ketchen, W.J. Gallagher, A. Kleinsasser, Phys. Rev. Lett. 67, 3578 (1991)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  30. A. Bachtold, C. Strunk, J.-P. Salvetat, J.-M. Bonard et al., Nature 397, 673 (1999)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  32. A. Junck, G. Refael, F.v. Oppen, Phys. Rev. B 88, 075144 (2013)

    Article  ADS  Google Scholar 

  33. Z.-H. Zhu et al., Phys. Rev. Lett. 110, 216401 (2013)

    Article  ADS  Google Scholar 

  34. C.H. Li, O.M.J. Erve, J.T. Robinson, Y. Liu, L. Li, B.T. Jonker, Nat. Nanotechnol. 9, 218 (2014)

    Article  ADS  Google Scholar 

  35. J. Tang, Nano Lett. 14, 5423 (2014)

    Article  ADS  Google Scholar 

  36. A. Dankert, J. Geurs, M.V. Kamalakar, S. Charpentier, S.P. Dash, Nano Lett. 15, 7976 (2015)

    Article  ADS  Google Scholar 

  37. J. Tian, S. Hong, I. Miotkowski, S. Datta, Sci. Adv. 3, e1602531 (2017)

    Article  ADS  Google Scholar 

  38. F. Kuemmeth, S. Ilani, D.C. Ralph, P.L. McEuen, Nature 452, 448 (2008)

    Article  ADS  Google Scholar 

  39. G.A. Steele, F. Pei, E.A. Laird, J.M. Jol, H.B. Meerwaldt, L.P. Kouwenhoven, Nat. Commun. 4, 1573 (2013)

    Article  ADS  Google Scholar 

  40. W. Izumida, K. Sato, R. Saito, J. Phys. Soc. Jpn. 78, 074707 (2009)

    Article  ADS  Google Scholar 

  41. R. Peierls, Z. Phys. 80, 763 (1933)

    Article  ADS  Google Scholar 

  42. J. Alicea, Y. Oreg, G. Refael, F.V. Oppen, M.P.A. Fisher, Nat. Phys. 7, 412 (2011)

    Article  Google Scholar 

  43. M.Y. Azbel, Phys. Rev. Lett. 46, 675 (1981)

    Article  ADS  Google Scholar 

  44. P.W. Brouwer, P.G. Silvestrov, C.W.J. Beenakker, Phys. Rev. B 56, R4333 (1997)

    Article  ADS  Google Scholar 

  45. R.E. Borland, N.F. Bird, Proc. Phys. Soc. 83, 23 (1964)

    Article  ADS  Google Scholar 

  46. B. Doucot, R. Rammel, Physique 47, 973 (1986)

    Article  Google Scholar 

  47. E.N. Economou, C.M. Soukoulis, Phys. Rev. Lett. 46, 618 (1981)

    Article  ADS  Google Scholar 

  48. Y. Gefen, G. Schoen, Phys. Rev. B 30, 7323(R) (1984)

    Article  ADS  Google Scholar 

  49. R. Landauer, Phil. Mag. 21, 863 (1970)

    Article  ADS  Google Scholar 

  50. J.B. Pendry, J. Phys. C: Solid State Phys. 15, 4821 (1982)

    Article  ADS  Google Scholar 

  51. J. Sirker, Phys. Rev. Lett. 105, 117203 (2010)

    Article  ADS  Google Scholar 

  52. C.M. Soukoulis, J.V. Jose, E.N. Economou, P. Sheng, Phys. Rev. Lett. 50, 764 (1983)

    Article  ADS  Google Scholar 

  53. D.J. Thouless, Phys. Rev. Lett. 39, 1167 (1977)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  55. P. LaFarge, P. Joyez, D. Esteve, C. Urbina, M.H. Devoret, Nature 365, 422 (1993)

    Article  ADS  Google Scholar 

Download references

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  1. Department of Physics and Astronomy, University of Southern California, Los Angeles, CA, 90089-0484, USA

    Gerd Bergmann

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Bergmann, G. Simulations of persistent current in disordered rings with axial magnetic field. Eur. Phys. J. B 92, 79 (2019). https://doi.org/10.1140/epjb/e2019-90577-0

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  • DOI: https://doi.org/10.1140/epjb/e2019-90577-0

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