Skip to main content
SpringerLink
Log in

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

  • Regular Article
  • Published:
The European Physical Journal B Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J.G. Bednorz, K.A. Müller, Z. Phys. B 64, 189 (1986)

    Article  ADS  Google Scholar 

  2. S. Jin et al., Science 264, 413 (1994)

    Article  ADS  Google Scholar 

  3. T.K. Mitra, A. Chatterjee, S. Mukhopadhyay, Phys. Rep. 153, 91 (1987)

    Article  ADS  Google Scholar 

  4. B. Gerlach, H. Löwen, Phys. Rev. B 35, 4291 (1987)

    Article  ADS  Google Scholar 

  5. B. Gerlach, H. Löwen, Phys. Rev. B 35, 4297 (1987)

    Article  ADS  Google Scholar 

  6. A. Chatterjee, S. Sil, Phys. Rev. B 51, 2223 (1995)

    Article  ADS  Google Scholar 

  7. J. Bonča, T. Katrašnik, S.A. Trugman, Phys. Rev. Lett. 84, 3153 (2000)

    Article  ADS  Google Scholar 

  8. A.S. Alexandrov, P.E. Kornilovitch, Phys. Rev. Lett. 82, 807 (1999)

    Article  ADS  Google Scholar 

  9. Y. Toyozawa, Prog. Theor. Phys. 16, 1301 (1961)

    Google Scholar 

  10. K. Cho, Y. Toyozawa, J. Phys. Soc. Jpn 30, 1555 (1971)

    Article  ADS  Google Scholar 

  11. K. Cho, Y. Toyozawa, J. Phys. Soc. Jpn 46, 505 (1979)

    Article  Google Scholar 

  12. D. Emin, Adv. Phys. 22, 57 (1973)

    Article  ADS  Google Scholar 

  13. D. Yarkony, R. Silbey, J. Chem. Phys. 65, 1042 (1976)

    Article  ADS  Google Scholar 

  14. D. Yarkony, R. Silbey, J. Chem. Phys. 67, 5818 (1977)

    Article  ADS  Google Scholar 

  15. H. De Raedt, A. Lagendijk, Phys. Rep. 127, 233 (1985)

    Article  ADS  MathSciNet  Google Scholar 

  16. P.O.J. Scherer, E.W. Knapp, S.F. Fischer, Chem. Phys. Lett. 106, 191 (1984)

    Article  ADS  Google Scholar 

  17. G. Venzl, S.F. Fisher, Phys. Rev. B 32, 6437 (1985)

    Article  ADS  Google Scholar 

  18. H. Löwen, Phys. Rev. B 37, 8667 (1988)

    Article  Google Scholar 

  19. B. Gerlach, H. Löwen, Rev. Mod. Phys. 63, 6208 (1991)

    Article  Google Scholar 

  20. A.H. Romero, D.W. Brown, K. Lindenberg, Phys. Rev. B 60, 4618 (1999)

    Article  ADS  Google Scholar 

  21. A.H. Romero, D.W. Brown, K. Lindenberg, Phys. Lett. A 260, 414 (2000)

    Article  ADS  Google Scholar 

  22. A. Alvermann, H. Fehske, S.A. Trugman, Phys. Rev. B 81, 165113 (2010)

    Article  ADS  Google Scholar 

  23. A. Alvermann, H. Fehske, S.A. Trugman, Phys. Rev. B 78, 165108 (2008)

    Article  ADS  Google Scholar 

  24. A.S. Alexandrov, N.F. Mott, Rep. Prog. Phys. 57, 1197 (1994)

    Article  ADS  Google Scholar 

  25. K.H. Kim, J.Y. Gu, H.S. Choi, G.W. Park, T.W. Noh, Phys. Rev. Lett. 77, 1877 (1996)

    Article  ADS  Google Scholar 

  26. W. Koller, A.C. Hewson, D.M. Edwards, Phys. Rev. Lett. 95, 256401 (2005)

    Article  ADS  Google Scholar 

  27. G. Sangiovanni, O. Gunnarsson, E. Koch, C. Castellani, M. Capone, Phys. Rev. Lett. 97, 046404 (2006)

    Article  ADS  Google Scholar 

  28. H. Fehske, D. Ihle, J. Loos, U. Trapper, H. Büttner, Z. Phys. B 94, 91 (1994)

    Article  ADS  Google Scholar 

  29. A.N. Das, S. Sil, J. Phys.: Condens. Matter 5, 8265 (1993)

    ADS  Google Scholar 

  30. I. Lang, Y.A. Firsov, Sov. Phys. J. Exp. Theor. Phys. 16, 1301 (1963)

    ADS  Google Scholar 

  31. Z. Hang, Phys. Rev. B 36, 8736 (1987)

    Article  ADS  Google Scholar 

  32. Z. Hang, Phys. Rev. B 37, 7419 (1988)

    Article  ADS  Google Scholar 

  33. R.P.M. Krishna, S. Mukhopadhyay, A. Chatterjee, Phys. Lett. A 327, 67 (2004)

    Article  ADS  MATH  Google Scholar 

  34. E.H. Lieb, F.Y. Wu, Phys. Rev. Lett. 20, 1445 (1968)

    Article  ADS  Google Scholar 

  35. I.V. Sankar, S. Mukhopadhyay, A. Chatterjee, J. Phys. C 480, 55 (2012)

    Article  Google Scholar 

  36. A.N. Das, S. Sil, Physica C 161, 325 (1989)

    Article  ADS  Google Scholar 

  37. C.F. Lo, R. Sollie, Phys. Rev. B 48, 10183 (1993)

    Article  ADS  Google Scholar 

  38. J. Solyom, in Fundamentals of the Physics of Solids, vol. III-Normal, Broken-Symmetry and Correlated Systems (Springer-Verlag, Berlin, Heidelberg, 2010), p. 340

  39. K.A. Chao, J. Spalek, A.M. Oles, J. Phys. C 10, L271 (1977)

    Article  ADS  Google Scholar 

  40. K.A. Chao, J. Spalek, A.M. Oles, Phys. Rev. B 18, 3453 (1978)

    Article  ADS  Google Scholar 

  41. M.C. Gutzwiller, Phys. Rev. Lett. 10, 159 (1963)

    Article  ADS  Google Scholar 

  42. M.C. Gutzwiller, Phys. Rev. 137, A1726 (1965)

    Article  ADS  MathSciNet  Google Scholar 

  43. D. Vollhardt, Rev. Mod. Phys. 56, 1 (1984)

    Article  Google Scholar 

  44. F.C. Zhang, C. Gros, T.M. Rice, H. Shiba, Supercond. 1, 36 (1988)

    Google Scholar 

  45. A.N. Das, J. Konior, D.K. Ray, A.M. Oles, Phys. Rev. B 44, 7680 (1991)

    Article  ADS  Google Scholar 

  46. E. Cappelluti, S. Ciuchi, Phys. Rev. B 66, 165102 (2002)

    Article  ADS  Google Scholar 

  47. D.N. Zubarev, Sov. Phys. Usp. 3, 3 (1960)

    Article  MathSciNet  Google Scholar 

  48. J. Hubbard, Proc. R. Soc. Lond. Ser. A 276, 238 (1963)

    Article  ADS  Google Scholar 

  49. S. Patra, J. Surf. Sci. Technol. 22, 3 (2006)

    Google Scholar 

  50. H. Fehske, H. Roder, G. Wellein, A. Mistriotis, Phys. Rev. B 51, 16581 (1995)

    Article  ADS  Google Scholar 

  51. Y. Takada, A. Chatterjee, Phys. Rev. B 67, 081102(R) (2003)

    Article  ADS  Google Scholar 

  52. A. Chatterjee, Y. Takada, J. Phys. Soc. Jpn 73, 964 (2004)

    Article  ADS  Google Scholar 

  53. T.T. Clay, R.P. Hardikar, Phys. Rev. Lett. 95, 096401 (2005)

    Article  ADS  Google Scholar 

  54. M. Tezuka, R. Arita, H. Aoki, Phys. Rev. Lett. 95, 226401 (2005)

    Article  ADS  Google Scholar 

  55. P.M. Krishna, A. Chatterjee, Physica C 457, 55 (2007)

    Article  ADS  Google Scholar 

  56. R.P. Hardikar, R.T. Clay, Phys. Rev. B 75, 245103 (2007)

    Article  ADS  Google Scholar 

  57. M. Tezuka, R. Arita, H. Aoki, Phys. Rev. B 76, 155114 (2007)

    Article  ADS  Google Scholar 

  58. A. Chatterjee, Adv. Condens. Matter Phys. 2010, 350787 (2010)

    Article  Google Scholar 

  59. S. Ejima, H. Fehske, J. Phys.: Conf. Ser. 200, 012031 (2010)

    ADS  Google Scholar 

  60. A. Payeur, D. Senechal, Phys. Rev. B 83, 033104 (2011)

    Article  ADS  Google Scholar 

  61. Y. Murakami, P. Werner, N. Tsuji, H. Aoki, Phys. Rev. B 88, 125126 (2013)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Physics, University of Hyderabad, Hyderabad, 500046, India

    I. V. Sankar & Ashok Chatterjee

Authors
  1. I. V. Sankar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ashok Chatterjee
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ashok Chatterjee.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sankar, I.V., Chatterjee, A. Self-trapping phase diagram for the strongly correlated extended Holstein-Hubbard model in two-dimensions. Eur. Phys. J. B 87, 154 (2014). https://doi.org/10.1140/epjb/e2014-50146-9

Download citation

  • Received:

  • Revised:

  • Published:

  • DOI: https://doi.org/10.1140/epjb/e2014-50146-9

Keywords

Search

Navigation