Transport in a disordered tight-binding chain with dephasing

Regular Article

Abstract

We studied transport properties of a disordered tight-binding model (XX spin chain) in the presence of dephasing. Focusing on diffusive behaviour in the thermodynamic limit at high energies, we analytically derived the dependence of conductivity on dephasing and disorder strengths. As a function of dephasing, conductivity exhibits a single maximum at the optimal dephasing strength. The scaling of the position of this maximum with disorder strength is different for small and large disorders. In addition, we studied periodic disorder for which we found a resonance phenomenon, with conductivity having two maxima as a function of dephasing strength. If the disorder is non-zero only at a random fraction of all sites, conductivity is approximately the same as in the case of a disorder on all sites but with a rescaled disorder strength.

Keywords

Mesoscopic and Nanoscale Systems 

References

  1. 1.
    D.J. Thouless, S. Kirkpatrick, J. Phys. C 14, 235 (1981)ADSCrossRefGoogle Scholar
  2. 2.
    S. Datta, Electronic Transport in Mesoscopic Systems (Cambridge University Press, Cambridge, 1995)Google Scholar
  3. 3.
    M. Büttiker, Phys. Rev. B 32, 1846 (1985)ADSCrossRefGoogle Scholar
  4. 4.
    J.L. D’Amato, H.M. Pastawski, Phys. Rev. B 41, 7411 (1990)ADSCrossRefGoogle Scholar
  5. 5.
    J. Maassen, F. Zahid, H. Guo, Phys. Rev. B 80, 125423 (2009)ADSCrossRefGoogle Scholar
  6. 6.
    D. Nozaki, Y. Girard, K. Yoshizawa, J. Chem. Phys. 112, 17408 (2008)Google Scholar
  7. 7.
    C.J. Cattena, R.A. Bustos-Marún, H.M. Pastawski, Phys. Rev. B 82, 144201 (2010)ADSCrossRefGoogle Scholar
  8. 8.
    D. Nozaki, C. Gomes da Rocha, H.M. Pastawski, G. Cuniberti, Phys. Rev. B 85, 155327 (2012)ADSCrossRefGoogle Scholar
  9. 9.
    R. Golizadeh-Mojarad, S. Datta, Phys. Rev. B 75, 081301(R) (2007)ADSCrossRefGoogle Scholar
  10. 10.
    M. Zilly, O. Ujsághy, D.E. Wolf, Eur. Phys. J. B 68, 237 (2009)ADSCrossRefGoogle Scholar
  11. 11.
    M. Zilly, O. Ujsághy, M. Woelki, D.E. Wolf, Phys. Rev. B 85, 075110 (2012)ADSCrossRefGoogle Scholar
  12. 12.
    T. Stegmann, M. Zilly, O. Ujsághy, D.E. Wolf, Eur. Phys. J. B 85, 264 (2012)ADSCrossRefGoogle Scholar
  13. 13.
    E. Kogan, Eur. Phys. J. B 61, 181 (2008)ADSCrossRefGoogle Scholar
  14. 14.
    H. Ishii, S. Roche, N. Kobayashi, K. Hirose, Phys. Rev. Lett. 104, 116801 (2010)ADSCrossRefGoogle Scholar
  15. 15.
    G. Lindblad, Commun. Math. Phys. 48, 119 (1976)MathSciNetADSMATHCrossRefGoogle Scholar
  16. 16.
    V. Gorini, A. Kossakowski, E.C.G. Sudarshan, J. Math. Phys. 17, 821 (1976)MathSciNetADSCrossRefGoogle Scholar
  17. 17.
    M. Žnidarič, J. Stat. Mech. 2010, L05002 (2010)CrossRefGoogle Scholar
  18. 18.
    H.-P. Breuer, F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, Oxford, 2002)Google Scholar
  19. 19.
    C. Timm, Phys. Rev. B 77, 195416 (2008)ADSCrossRefGoogle Scholar
  20. 20.
    M.B. Plenio, S.F. Huelga, New J. Phys. 10, 113019 (2008)ADSCrossRefGoogle Scholar
  21. 21.
    P. Rebentrost, M. Mohseni, I. Kassal, S. Lloyd, A. Aspuru-Guzik, New J. Phys. 11, 033003 (2009)ADSCrossRefGoogle Scholar
  22. 22.
    F. Caruso, A.W. Chin, A. Datta, S.F. Huelga, M.B. Plenio, J. Chem. Phys. 131, 105106 (2009)ADSCrossRefGoogle Scholar
  23. 23.
    S. Hoyer, M. Sarovar, K.B. Whaley, New J. Phys. 12, 065041 (2010)ADSCrossRefGoogle Scholar
  24. 24.
    I. Kassal, A. Aspuru-Guzik, New J. Phys. 14, 053041 (2012)ADSCrossRefGoogle Scholar
  25. 25.
    M. Žnidarič, Phys. Rev. E 83, 011108 (2011)MathSciNetADSCrossRefGoogle Scholar
  26. 26.
    V. Eisler, J. Stat. Mech. 2011, P06007 (2011)CrossRefGoogle Scholar
  27. 27.
    K. Temme, M.M. Wolf, F. Verstraete, New J. Phys. 14, 075004 (2012)ADSCrossRefGoogle Scholar
  28. 28.
    B. Horstmann, J.I. Cirac, G. Giedke, arXiv:1207.1653 [quant-ph] (2012)Google Scholar
  29. 29.
    B. Žunkovič, T. Prosen, J. Stat. Mech. 2010, P08016 (2010)CrossRefGoogle Scholar
  30. 30.
    T. Prosen, J. Stat. Mech. 2010, P07020 (2010)MathSciNetCrossRefGoogle Scholar
  31. 31.
    M. Žnidarič, T. Prosen, G. Benenti, G. Casati, D. Rossini, Phys. Rev. E 81, 051135 (2010)ADSCrossRefGoogle Scholar
  32. 32.
    P. Jordan, E. Wigner, Z. Phys. 47, 631 (1928)ADSMATHCrossRefGoogle Scholar
  33. 33.
    P.W. Anderson, Rev. Mod. Phys. 50, 191 (1978)ADSCrossRefGoogle Scholar
  34. 34.
    M. Žnidarič, New J. Phys. 12, 043001 (2010)CrossRefGoogle Scholar
  35. 35.
    B. Kramer, A. MacKinnon, Rep. Prog. Phys. 56, 1469 (1993)ADSCrossRefGoogle Scholar
  36. 36.
    P.W. Anderson, D.J. Thouless, E. Abrahams, D.S. Fisher, Phys. Rev. B 22, 3519 (1980)MathSciNetADSCrossRefGoogle Scholar
  37. 37.
    H. Schomerus, M. Titov, Phys. Rev. B 67, 100201(R) (2003)ADSCrossRefGoogle Scholar
  38. 38.
    L.I. Deych, M.V. Erementchouk, A.A. Lisyansky, B.L. Altshuler, Phys. Rev. Lett. 91, 096601 (2003)ADSCrossRefGoogle Scholar
  39. 39.
    D.H. Dunlap, V.M. Kenkre, Phys. Rev. B 37, 6622 (1988)ADSCrossRefGoogle Scholar
  40. 40.
    A.R. Kolovsky, A.V. Ponomarev, H.J. Korsch, Phys. Rev. A 66, 053405 (2002)ADSCrossRefGoogle Scholar
  41. 41.
    D. Segal, A. Nitzan, W.B. Davis, M.R. Wasielewski, M.A. Ratner, J. Phys. Chem. B 104, 3817 (2000)CrossRefGoogle Scholar
  42. 42.
    M. Kappus, F. Wegner, Z. Phys. B 45, 15 (1981)ADSCrossRefGoogle Scholar
  43. 43.
    B. Derrida, E. Gardner, J. Phys. 45, 1283 (1984)MathSciNetCrossRefGoogle Scholar
  44. 44.
    J.C. Flores, J. Phys.: Condens. Matter 1, 8471 (1989)ADSCrossRefGoogle Scholar
  45. 45.
    D.H. Dunlap, H.-L. Wu, P.W. Phillips, Phys. Rev. Lett. 65, 88 (1990)ADSCrossRefGoogle Scholar
  46. 46.
    G. Theodorou, M.H. Cohen, Phys. Rev. B 13, 4597 (1976)ADSCrossRefGoogle Scholar
  47. 47.
    F. Delyon, H. Kunz, B. Souillard, J. Phys. A 16, 25 (1983)MathSciNetADSMATHCrossRefGoogle Scholar
  48. 48.
    M. Hilke, J. Phys. A 30, L367 (1997)ADSMATHCrossRefGoogle Scholar
  49. 49.
    N. Hlubek, P. Ribeiro, R. Saint-Martin, S. Nishimoto, A. Revcolevschi, S.-L. Drechsler, G. Behr, J. Trinckauf, J.E. Hamann-Borrero, J. Geck, B. Büchner, C. Hess, Phys. Rev. B 84, 214419 (2011)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Physics Department, Faculty of Mathematics and PhysicsUniversity of LjubljanaLjubljanaSlovenia

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