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Self-trapping phase diagram for the strongly correlated extended Holstein-Hubbard model in two-dimensions

  • I. V. Sankar
  • Ashok Chatterjee
Regular Article

Abstract

The two-dimensional extended Holstein-Hubbard model is investigated in the strong correlation regime to study the nature of self-trapping transition and the polaron phase diagram in the absence of superconductivity. Using a series of canonical transformations followed by zero-phonon averaging the extended Holstein-Hubbard model is converted into an effective extended Hubbard model which is subsequently transformed into an effective t-J model in the strong correlation limit. This effective t-J model is finally solved using the mean-field Hartree-Fock approximation to show that the self-trapping transition is continuous in the anti-adiabatic limit while it is discontinuous in the adiabatic limit. The phase diagrams for the localization-delocalization transition, namely the phase line and the phase surface separating the small polaron and large polaron states are also shown.

Keywords

Solid State and Materials 

References

  1. 1.
    J.G. Bednorz, K.A. Müller, Z. Phys. B 64, 189 (1986)ADSCrossRefGoogle Scholar
  2. 2.
    S. Jin et al., Science 264, 413 (1994)ADSCrossRefGoogle Scholar
  3. 3.
    T.K. Mitra, A. Chatterjee, S. Mukhopadhyay, Phys. Rep. 153, 91 (1987)ADSCrossRefGoogle Scholar
  4. 4.
    B. Gerlach, H. Löwen, Phys. Rev. B 35, 4291 (1987)ADSCrossRefGoogle Scholar
  5. 5.
    B. Gerlach, H. Löwen, Phys. Rev. B 35, 4297 (1987)ADSCrossRefGoogle Scholar
  6. 6.
    A. Chatterjee, S. Sil, Phys. Rev. B 51, 2223 (1995)ADSCrossRefGoogle Scholar
  7. 7.
    J. Bonča, T. Katrašnik, S.A. Trugman, Phys. Rev. Lett. 84, 3153 (2000)ADSCrossRefGoogle Scholar
  8. 8.
    A.S. Alexandrov, P.E. Kornilovitch, Phys. Rev. Lett. 82, 807 (1999)ADSCrossRefGoogle Scholar
  9. 9.
    Y. Toyozawa, Prog. Theor. Phys. 16, 1301 (1961)Google Scholar
  10. 10.
    K. Cho, Y. Toyozawa, J. Phys. Soc. Jpn 30, 1555 (1971)ADSCrossRefGoogle Scholar
  11. 11.
    K. Cho, Y. Toyozawa, J. Phys. Soc. Jpn 46, 505 (1979)CrossRefGoogle Scholar
  12. 12.
    D. Emin, Adv. Phys. 22, 57 (1973)ADSCrossRefGoogle Scholar
  13. 13.
    D. Yarkony, R. Silbey, J. Chem. Phys. 65, 1042 (1976)ADSCrossRefGoogle Scholar
  14. 14.
    D. Yarkony, R. Silbey, J. Chem. Phys. 67, 5818 (1977)ADSCrossRefGoogle Scholar
  15. 15.
    H. De Raedt, A. Lagendijk, Phys. Rep. 127, 233 (1985)ADSCrossRefMathSciNetGoogle Scholar
  16. 16.
    P.O.J. Scherer, E.W. Knapp, S.F. Fischer, Chem. Phys. Lett. 106, 191 (1984)ADSCrossRefGoogle Scholar
  17. 17.
    G. Venzl, S.F. Fisher, Phys. Rev. B 32, 6437 (1985)ADSCrossRefGoogle Scholar
  18. 18.
    H. Löwen, Phys. Rev. B 37, 8667 (1988)CrossRefGoogle Scholar
  19. 19.
    B. Gerlach, H. Löwen, Rev. Mod. Phys. 63, 6208 (1991)CrossRefGoogle Scholar
  20. 20.
    A.H. Romero, D.W. Brown, K. Lindenberg, Phys. Rev. B 60, 4618 (1999)ADSCrossRefGoogle Scholar
  21. 21.
    A.H. Romero, D.W. Brown, K. Lindenberg, Phys. Lett. A 260, 414 (2000)ADSCrossRefGoogle Scholar
  22. 22.
    A. Alvermann, H. Fehske, S.A. Trugman, Phys. Rev. B 81, 165113 (2010)ADSCrossRefGoogle Scholar
  23. 23.
    A. Alvermann, H. Fehske, S.A. Trugman, Phys. Rev. B 78, 165108 (2008)ADSCrossRefGoogle Scholar
  24. 24.
    A.S. Alexandrov, N.F. Mott, Rep. Prog. Phys. 57, 1197 (1994)ADSCrossRefGoogle Scholar
  25. 25.
    K.H. Kim, J.Y. Gu, H.S. Choi, G.W. Park, T.W. Noh, Phys. Rev. Lett. 77, 1877 (1996)ADSCrossRefGoogle Scholar
  26. 26.
    W. Koller, A.C. Hewson, D.M. Edwards, Phys. Rev. Lett. 95, 256401 (2005)ADSCrossRefGoogle Scholar
  27. 27.
    G. Sangiovanni, O. Gunnarsson, E. Koch, C. Castellani, M. Capone, Phys. Rev. Lett. 97, 046404 (2006)ADSCrossRefGoogle Scholar
  28. 28.
    H. Fehske, D. Ihle, J. Loos, U. Trapper, H. Büttner, Z. Phys. B 94, 91 (1994)ADSCrossRefGoogle Scholar
  29. 29.
    A.N. Das, S. Sil, J. Phys.: Condens. Matter 5, 8265 (1993)ADSGoogle Scholar
  30. 30.
    I. Lang, Y.A. Firsov, Sov. Phys. J. Exp. Theor. Phys. 16, 1301 (1963)ADSGoogle Scholar
  31. 31.
    Z. Hang, Phys. Rev. B 36, 8736 (1987)ADSCrossRefGoogle Scholar
  32. 32.
    Z. Hang, Phys. Rev. B 37, 7419 (1988)ADSCrossRefGoogle Scholar
  33. 33.
    R.P.M. Krishna, S. Mukhopadhyay, A. Chatterjee, Phys. Lett. A 327, 67 (2004)ADSCrossRefMATHGoogle Scholar
  34. 34.
    E.H. Lieb, F.Y. Wu, Phys. Rev. Lett. 20, 1445 (1968)ADSCrossRefGoogle Scholar
  35. 35.
    I.V. Sankar, S. Mukhopadhyay, A. Chatterjee, J. Phys. C 480, 55 (2012)CrossRefGoogle Scholar
  36. 36.
    A.N. Das, S. Sil, Physica C 161, 325 (1989)ADSCrossRefGoogle Scholar
  37. 37.
    C.F. Lo, R. Sollie, Phys. Rev. B 48, 10183 (1993)ADSCrossRefGoogle Scholar
  38. 38.
    J. Solyom, in Fundamentals of the Physics of Solids, vol. III-Normal, Broken-Symmetry and Correlated Systems (Springer-Verlag, Berlin, Heidelberg, 2010), p. 340Google Scholar
  39. 39.
    K.A. Chao, J. Spalek, A.M. Oles, J. Phys. C 10, L271 (1977)ADSCrossRefGoogle Scholar
  40. 40.
    K.A. Chao, J. Spalek, A.M. Oles, Phys. Rev. B 18, 3453 (1978)ADSCrossRefGoogle Scholar
  41. 41.
    M.C. Gutzwiller, Phys. Rev. Lett. 10, 159 (1963)ADSCrossRefGoogle Scholar
  42. 42.
    M.C. Gutzwiller, Phys. Rev. 137, A1726 (1965)ADSCrossRefMathSciNetGoogle Scholar
  43. 43.
    D. Vollhardt, Rev. Mod. Phys. 56, 1 (1984)CrossRefGoogle Scholar
  44. 44.
    F.C. Zhang, C. Gros, T.M. Rice, H. Shiba, Supercond. 1, 36 (1988)Google Scholar
  45. 45.
    A.N. Das, J. Konior, D.K. Ray, A.M. Oles, Phys. Rev. B 44, 7680 (1991)ADSCrossRefGoogle Scholar
  46. 46.
    E. Cappelluti, S. Ciuchi, Phys. Rev. B 66, 165102 (2002)ADSCrossRefGoogle Scholar
  47. 47.
    D.N. Zubarev, Sov. Phys. Usp. 3, 3 (1960)CrossRefMathSciNetGoogle Scholar
  48. 48.
    J. Hubbard, Proc. R. Soc. Lond. Ser. A 276, 238 (1963)ADSCrossRefGoogle Scholar
  49. 49.
    S. Patra, J. Surf. Sci. Technol. 22, 3 (2006)Google Scholar
  50. 50.
    H. Fehske, H. Roder, G. Wellein, A. Mistriotis, Phys. Rev. B 51, 16581 (1995)ADSCrossRefGoogle Scholar
  51. 51.
    Y. Takada, A. Chatterjee, Phys. Rev. B 67, 081102(R) (2003)ADSCrossRefGoogle Scholar
  52. 52.
    A. Chatterjee, Y. Takada, J. Phys. Soc. Jpn 73, 964 (2004)ADSCrossRefGoogle Scholar
  53. 53.
    T.T. Clay, R.P. Hardikar, Phys. Rev. Lett. 95, 096401 (2005)ADSCrossRefGoogle Scholar
  54. 54.
    M. Tezuka, R. Arita, H. Aoki, Phys. Rev. Lett. 95, 226401 (2005)ADSCrossRefGoogle Scholar
  55. 55.
    P.M. Krishna, A. Chatterjee, Physica C 457, 55 (2007)ADSCrossRefGoogle Scholar
  56. 56.
    R.P. Hardikar, R.T. Clay, Phys. Rev. B 75, 245103 (2007)ADSCrossRefGoogle Scholar
  57. 57.
    M. Tezuka, R. Arita, H. Aoki, Phys. Rev. B 76, 155114 (2007)ADSCrossRefGoogle Scholar
  58. 58.
    A. Chatterjee, Adv. Condens. Matter Phys. 2010, 350787 (2010)CrossRefGoogle Scholar
  59. 59.
    S. Ejima, H. Fehske, J. Phys.: Conf. Ser. 200, 012031 (2010)ADSGoogle Scholar
  60. 60.
    A. Payeur, D. Senechal, Phys. Rev. B 83, 033104 (2011)ADSCrossRefGoogle Scholar
  61. 61.
    Y. Murakami, P. Werner, N. Tsuji, H. Aoki, Phys. Rev. B 88, 125126 (2013)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.School of PhysicsUniversity of HyderabadHyderabadIndia

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