Advertisement

Disordered mixed transmission lines: localization behavior

  • E. LazoEmail author
  • F. Cortés-Cortés
Regular Article
  • 13 Downloads

Abstract.

We introduce a new type of transmission line: the mixed transmission line. This system is formed by the repetition of a set of p successive direct cells followed by q successive dual cells. The total number of cells N of the complete system arises from \( N=dN_{s}\), where \( N_{s}\) is the number of recurrence pattern and \( d=(p+q)\) number of cells forming the basic unit of the mixed transmission lines. Our model allows introducing the disorder in any component of the dual or direct cells of the mixed transmission line. We study the localization behavior of this new model by introducing two different non-periodic distributions on the values of \( L_{n,y}\) inductances of dual cells, namely the Aubry-André and the Fibonacci models. For random and non-periodic distributions of \( L_{n,y}\) values, states were allowed to appear only inside a set of \( d=(p+q)\) sub-bands separated by gaps in the frequency range. We study the localization behavior for the \( p > q\) and \( q > p\) cases. For \( p > q\) (greater number of direct cells than dual cells), the d sub-bands are distributed more evenly in a reduced range of frequencies compared to \( p < q\). Using the scaling analysis of the \( C_{\omega}\) average overlap amplitude, we have shown that for random distribution of q values of inductances \( L_{n,y}\) of the dual cells, the extended states can appear in any of the d sub-band bands, but only for the small N -size system. We have further shown that the case \( p\geq 1\), q = 1 for random distribution of q inductances \( L_{n,y}\), cannot be regarded as a model of Anderson diluted, because the localization behavior of both models is completely different.

References

  1. 1.
    P.W. Anderson, Phys. Rev. 109, 1492 (1958)ADSCrossRefGoogle Scholar
  2. 2.
    N.F. Mott, W.D. Twose, Adv. Phys. 10, 107 (1961)ADSCrossRefGoogle Scholar
  3. 3.
    R. Landauer, Philos. Mag. 21, 863 (1970)ADSCrossRefGoogle Scholar
  4. 4.
    R. Abou-Chacra, P.W. Anderson, D.J. Thouless, J. Phys. C 6, 1734 (1973)ADSCrossRefGoogle Scholar
  5. 5.
    J.C. Flores, J. Phys.: Condens. Matter 1, 8471 (1989)ADSGoogle Scholar
  6. 6.
    D.H. Dunlap, H.L. Wu, P.W. Philips, Phys. Rev. Lett. 65, 88 (1990)ADSCrossRefGoogle Scholar
  7. 7.
    H.-L. Wu, P. Phillips, Phys. Rev. Lett. 66, 1366 (1991)ADSCrossRefGoogle Scholar
  8. 8.
    P.W. Philips, H.-L. Wu, Science 252, 1805 (1991)ADSCrossRefGoogle Scholar
  9. 9.
    F.A.B.F. de Moura, M.L. Lyra, Phys. Rev. Lett. 81, 3735 (1998)ADSCrossRefGoogle Scholar
  10. 10.
    F.M. Izrailev, A.A. Krokhin, Phys. Rev. Lett. 82, 4062 (1999)ADSCrossRefGoogle Scholar
  11. 11.
    V. Bellani, E. Diez, R. Hey, L. Toni, L. Tarricone, G.B. Parravicini, F. Domínguez-Adame, R. Gómez-Alcalá, Phys. Rev. Lett. 82, 2159 (1999)ADSCrossRefGoogle Scholar
  12. 12.
    E. Lazo, M.E. Onell, Physica B 299, 173 (2001)ADSCrossRefGoogle Scholar
  13. 13.
    W. Zhang, S.E. Ulloa, Phys. Rev. B 69, 153203 (2004)ADSCrossRefGoogle Scholar
  14. 14.
    H. Shima, T. Nomura, T. Nakayama, Phys. Rev. B 70, 075116 (2004)ADSCrossRefGoogle Scholar
  15. 15.
    T. Kaya, Eur. Phys. J. B 55, 49 (2007)ADSCrossRefGoogle Scholar
  16. 16.
    F.M. Izrailev, A.A. Krokhin, N.M. Makarov, Phys. Rep. 512, 125 (2012)ADSMathSciNetCrossRefGoogle Scholar
  17. 17.
    A.A. Krokhin, F.M. Izrailev, U. Kuhl, H.-J. Stöckmann, S.E. Ulloa, Physica E 13, 695 (2002)ADSCrossRefGoogle Scholar
  18. 18.
    U. Kuhl, F.M. Izrailev, A.A. Krokhin, H.-J. Stöckmann, Appl. Phys. Lett. 77, 633 (2000)ADSCrossRefGoogle Scholar
  19. 19.
    G.M.A. Almeida, C.V.C. Mendes, M.L. Lyra, F.A.B.F. de Moura, Ann. Phys. 398, 180 (2018)ADSCrossRefGoogle Scholar
  20. 20.
    T.F. Assunção, M.L. Lyraa, F.A.B.F. de Moura, F. Domínguez-Adame, Phys. Lett. A 375, 1048 (2011)ADSCrossRefGoogle Scholar
  21. 21.
    Y. Zhao, S. Duan, W. Zhang, J. Phys.: Condens. Matter 24, 245502 (2012)ADSGoogle Scholar
  22. 22.
    G.P. Zhang, M. Gao, Y.Y. Zhang, N. Liu, Z.J. Qin, M.H. Shangguan, J. Phys.: Condens. Matter 24, 235303 (2012)ADSGoogle Scholar
  23. 23.
    P. Thiessen, E. Díaz, R.A. Römer, F. Domínguez-Adame, Phys. Rev. B 95, 195431 (2017)ADSCrossRefGoogle Scholar
  24. 24.
    A. Nandy, B. Pal, A. Chakrabarti, EPL 115, 37004 (2016)ADSCrossRefGoogle Scholar
  25. 25.
    H. Dong-Sheng, L. Xiu-Juan, Z. Yong-Mei, Z. Chen-Ping, Chin. Phys. B 18, 1674 (2009)ADSCrossRefGoogle Scholar
  26. 26.
    E. Diez, F. Izrailev, A. Krokhin, A. Rodriguez, Phys. Rev. B 78, 035118 (2008)ADSCrossRefGoogle Scholar
  27. 27.
    E. Lazo, E. Diez, Phys. Lett. A 374, 3538 (2010)ADSCrossRefGoogle Scholar
  28. 28.
    E. Lazo, E. Diez, Phys. Lett. A 375, 2122 (2011)ADSCrossRefGoogle Scholar
  29. 29.
    E. Lazo, E. Diez, Physica B 419, 19 (2013)ADSCrossRefGoogle Scholar
  30. 30.
    E. Lazo, F.R. Humire, E. Saavedra, Physica B 452, 74 (2014)ADSCrossRefGoogle Scholar
  31. 31.
    E. Lazo, Phys. Lett. A 432, 121 (2014)Google Scholar
  32. 32.
    E. Lazo, E. Saavedra, F.R. Humire, C.E. Castro, F. Cortés, Eur. Phys. J. B 88, 216 (2015)ADSCrossRefGoogle Scholar
  33. 33.
    E. Lazo, C. Castro, F. Cortés-Cortés, Phys. Lett. A 380, 3284 (2016)ADSCrossRefGoogle Scholar
  34. 34.
    E. Lazo, A. Garrido, F. Neira, Eur. Phys. J. B 89, 249 (2016)ADSCrossRefGoogle Scholar
  35. 35.
    A.A. Asatryan, L.C. Botten, M.A. Byrne, V.D. Freilikher, S.A. Gredeskul, I.V. Shadrivov, R.C. McPhedran, Y.S. Kivshar, Phys. Rev. Lett. 99, 193902 (2007)ADSCrossRefGoogle Scholar
  36. 36.
    O. del Barco, M. Ortuño, Phys. Rev. A 86, 023846 (2012)ADSCrossRefGoogle Scholar
  37. 37.
    O. del Barco, V. Gasparian, Z. Gevorkian, Phys. Rev. A 91, 063822 (2015)ADSCrossRefGoogle Scholar
  38. 38.
    M. Hilke, J. Phys. A 30, L367 (1997)ADSCrossRefGoogle Scholar
  39. 39.
    F. Domínguez-Adame, I. Gomez, A. Avakyan, D. Sedrakyan, A. Sedrakyan, Phys. Status Solidi B 221, 633 (2000)ADSCrossRefGoogle Scholar
  40. 40.
    W. Deng, Physica B 279, 224 (2000)ADSCrossRefGoogle Scholar
  41. 41.
    E. Lazo, M.E. Onell, Phys. Lett. A 283, 376 (2001)ADSMathSciNetCrossRefGoogle Scholar
  42. 42.
    M. Hilke, Phys. Rev. Lett. 91, 226403 (2003)ADSCrossRefGoogle Scholar
  43. 43.
    F.A.B.F. de Moura, N.M.B. Santos, U.L. Fulco, M.L. Lyra, E. Lazo, M.E. Onell, Eur. Phys. J. B 36, 81 (2003)ADSCrossRefGoogle Scholar
  44. 44.
    S.S. Albuquerque, F.A.B.F. de Moura, M.L. Lyra, Physica A 357, 165 (2005)ADSCrossRefGoogle Scholar
  45. 45.
    S.S. Albuquerque, F.A.B.F. de Moura, M.L. Lyra, E. Lazo, Phys. Lett. A 355, 468 (2006)ADSCrossRefGoogle Scholar
  46. 46.
    F.A.B.F. de Moura, M.L. Lyra, S.S. Albuquerque, J. Phys.: Condens. Matter 20, 075109 (2008)ADSGoogle Scholar
  47. 47.
    A.P. Ribbeiro, E.M. Nascimento, M.L. Lyra, Photon. Nanostruct. 10, 463 (2012)ADSCrossRefGoogle Scholar
  48. 48.
    E. Lazo, Physica B 432, 121 (2014)ADSCrossRefGoogle Scholar
  49. 49.
    E. Lazo, F.R. Humire, E. Saavedra, Int. J. Mod. Phys. C 25, 1450023 (2014)ADSCrossRefGoogle Scholar
  50. 50.
    E. Lazo, C.E. Castro, F. Cortés-Cortés, Phys. Lett. A 380, 3284 (2016)ADSCrossRefGoogle Scholar
  51. 51.
    A. Lakshminarayan, V. Subrahmanyam, Phys. Rev. A 67, 052304 (2003)ADSCrossRefGoogle Scholar
  52. 52.
    E. Lazo, Eur. Phys. J. D 71, 144 (2017)ADSCrossRefGoogle Scholar
  53. 53.
    S. Aubry, G. André, Ann. Isr. Phys. Soc. 3, 133 (1980)Google Scholar
  54. 54.
    W.W. Cheng, L.Y. Gong, C.J. Shan, Y.B. Sheng, S.M. Zhao, Eur. Phys. J. D 67, 121 (2013)ADSCrossRefGoogle Scholar
  55. 55.
    W.W. Cheng, C.J. Shan, L.Y. Gong, S.M. Zhao, J. Phys. B: At. Mol. Opt. Phys. 47, 175503 (2014)ADSCrossRefGoogle Scholar
  56. 56.
    L. Gong, W. Li, S. Zhao, W. Cheng, Phys. Lett. A 380, 59 (2016)ADSCrossRefGoogle Scholar
  57. 57.
    E. Maciá, ISRN Condens. Matter Phys. 2014, 165943 (2014)MathSciNetCrossRefGoogle Scholar
  58. 58.
    M. Kohmoto, L.P. Kadanoff, C. Tang, Phys. Rev. Lett. 50, 1870 (1983)ADSMathSciNetCrossRefGoogle Scholar
  59. 59.
    M. Kohmoto, J.R. Banavar, Phys. Rev. B 34, 563 (1986)ADSCrossRefGoogle Scholar
  60. 60.
    Y. Liu, R. Riklund, Phys. Rev. B 35, 6034 (1987)ADSCrossRefGoogle Scholar
  61. 61.
    E. Lazo, M.E. Onell, Rev. Mex. Fis. 44, 46 (1998) (Sup. I)Google Scholar
  62. 62.
    E. Lazo, F. Mellado, E. Saavedra, Phys. Lett. A 376, 3423 (2012)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 Física, Facultad de CienciasUniversidad de TarapacáAricaChile

Personalised recommendations