Journal of Superconductivity and Novel Magnetism

, Volume 28, Issue 2, pp 309–313 | Cite as

Is BCS Related with BEC?

Original Paper


We present the complete phase diagram implied by the generalized Bose-Einstein condensation (GBEC) formalism that in essence is a ternary boson-fermion (BF) model with three constituents: two bosonic [two-electron Cooper pairs (2e-CPs) and two-hole Cooper pairs (2h-CPs)] along with unpaired electrons whose number naturally vanishes in the limit of infinite e-e coupling. There arise three coupled transcendental equations to be solved self-consistently: two gap-like equations (one for each kind of CPs) and a third which guarantees charge conservation via the number equation for the total electron number density of the system. The unknown variables are the chemical potential as well as the number density of zero-momentum 2e-CPs and 2h-CPs, each depending on coupling as well as absolute temperature. The GBEC subsumes as special cases all statistical theories of superconductors including BCS and BEC. It also subsumes the BCS-Bose “crossover” theory which in turn relates BCS with BEC. The GBEC formalism yields a substantial increase in critical temperature compared with BCS theory even with only electron-phonon dynamics.


Generalized Bose-Einstein Condensation High-Tc superconductors BCS theory Cooper pairs 



IC thanks CONACyT-Mexico for the postgraduate grant 260978 and MG and MdeLl thank PAPIIT-UNAM-Mexico for grants IN116914 and IN100314, respectively.


  1. 1.
    Bardeen, J., Cooper, L.N., Schrieffer, J.R.: Phys. Rev. 108, 1175 (1957)CrossRefADSMATHMathSciNetGoogle Scholar
  2. 2.
    Tolmachev, V.V.: Phys. Lett. A 266, 400 (2000)CrossRefADSGoogle Scholar
  3. 3.
    de Llano, M., Tolmachev, V.V.: Phys. A 317, 546 (2003)CrossRefMATHGoogle Scholar
  4. 4.
    Adhikari, S.K., de Llano, M., Sevilla, F.J., Solís, M.A., Valencia, J.J.: Phys. C 453, 37 (2007)CrossRefADSGoogle Scholar
  5. 5.
    de Llano, M., Tolmachev, V.V.: Ukr. J. Phys. 55, 79 (2010)Google Scholar
  6. 6.
    Grether, M., de Llano, M., Tolmachev, V.V.: Int. J. Quant. Chem. 112, 3018 (2012)CrossRefGoogle Scholar
  7. 7.
    Eagles, D.M.: Phys. Rev. 186, 456 (1969)CrossRefADSGoogle Scholar
  8. 8.
    Ranninger, J., Micnas, R., Robaszkiewicz, S.: Ann. Phys. (Paris) 13, 455 (1988)ADSGoogle Scholar
  9. 9.
    Friedberg, R., Lee, T.D.: Phys. Rev. B 40, 6745 (1989), R. Friedberg, T.D. Lee, and H.C. Ren, Phys. Lett. A 152, 417 & 423 (1991)Google Scholar
  10. 10.
    Casas, M., Davidson, N.J., de Llano, M., Mamedov, T.A, Puente, A., Quick, R.M., Rigo, A., Solís, M.A.: Phys. A 295, 146 (2001)CrossRefGoogle Scholar
  11. 11.
    Casas, M., de Llano, M., Puente, A., Rigo, A., Solís, M.A.: Solid State Comm. 123, 101 (2002)CrossRefADSGoogle Scholar
  12. 12.
    Einstein, A.: Sitzber. Kgl. Preuss. Akad. Wiss 1, 3 (1925)Google Scholar
  13. 13.
    Bose, S.N., für, Z.: Phys. 26, 178 (1924)CrossRefMATHGoogle Scholar
  14. 14.
    Grether, M., de Llano, M., Ramírez, S., Rojo, O.: Int. J. Mod. Phys. B 22, 4367 (2008)CrossRefADSGoogle Scholar
  15. 15.
    Kulić, M.L.: Phys. Reports 338, 1-264 (2003); AIP Conf. Proc. 715, 75 (2004); V.Z. Kresin and S.A. Wolf, Revs Mod. Phys. 81, 481, (2009)Google Scholar
  16. 16.
    Sutton, A.P.: Electronic Structure of Materials. Clarendon, Oxford (1993)Google Scholar
  17. 17.
    de Llano, M, Sevilla, F.J., Tapia, S. Int. J. Mod. Phys. B 20, 2931 (2006)CrossRefADSMATHGoogle Scholar
  18. 18.
    Bogoliubov, N.N.: N. Cim. 7, 794 (1958)CrossRefGoogle Scholar
  19. 19.
    Mamedov, T.A., de Llano, M. J.: Phys. Soc. Japan 79, 044706 (2010); 80, 074718 (2011); Phil. Mag. 93, 2896 (2013) & to be published in 2014Google Scholar
  20. 20.
    Valatin, J.: N. Cim. 7, 843 (1958)CrossRefMathSciNetGoogle Scholar
  21. 21.
    Uemura, Y.J.: Phys. B 374-375, 1 (2006)CrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Instituto de Investigaciones en MaterialesUniversidad Nacional Autónoma de MéxicoMéxico, D.F.Mexico
  2. 2.Facultad de CienciasUniversidad Nacional Autónoma de MéxicoMéxico, D.F.Mexico

Personalised recommendations