Skip to main content
SpringerLink
Log in

Two-Electron and Two-Hole Cooper Pairs in Superconductivity

  • Original Paper
  • Published:
Journal of Superconductivity and Novel Magnetism Aims and scope Submit manuscript

Abstract

We revisit the generalized Bose-Einstein condensation (GBEC) theory which addresses a ternary boson-fermion gas including two-hole Cooper pairs (2hCPs) as an essential component in superconductivity. Here, we extend the BCS-Bose crossover theory, itself subsumed in BEC, by explicitly including 2hCPs. Shown here are phase diagrams of Tc/TF, where Tc is the critical temperature and TF the Fermi temperature and Δ(0)/EFvsn/nf, where Δ(0) is the energy gap at zero temperature and EF is the Fermi energy of an ideal Fermi gas, with n the total electron number density and nf is that of unbound electrons at zero temperature. These phase diagrams are obtained for two pure phases, one with two-electron Cooper pairs (2eCPs) and the other with 2hCPs, plus a mixed phase with arbitrary proportions of 2e/2hCPs. We find that the extended BCS-Bose crossover predicts Tc/TF as well Δ(0)/EF values for the elemental superconductors (SCs) Al, In, Sn, Pb, Hg, and Nb which compare reasonably well with experimental data.

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

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  1. Schrieffer, R.: Theory of superconductivity, p. 41. Benjamin Inc., New York (1964)

    MATH  Google Scholar 

  2. Keldysh, L.V., Kopaev, Y.V.: Sov. Phys. Sol. St. 6, 2219 (1965)

    Google Scholar 

  3. Popov, V.N.: Sov. Phys. JETP 50, 1034 (1966)

    ADS  Google Scholar 

  4. Labbé, J., et al.: Phys. Rev. Lett. 19, 1039 (1967)

    Article  ADS  Google Scholar 

  5. Eagles, D.M.: Phys. Rev. 186, 456 (1969)

    Article  ADS  Google Scholar 

  6. Leggett, A.J.: J. Phys. (Paris). Colloq. 41, C7–19 (1980)

    Article  Google Scholar 

  7. Carter, R.M., Casas, M., Getino, J.M., de Llano, M., Puente, A., Rubio, H., van der Walt, D.M.: Phys. Rev. B 52, 16149 (1995)

    Article  ADS  Google Scholar 

  8. Bardeen, J., Cooper, L.N., Schrieffer, J.R.: Phys. Rev. 108, 1175 (1957)

    Article  ADS  MathSciNet  Google Scholar 

  9. Nozières, P., Schmitt-Rink, S.: J. Low. Temp. Phys. 59, 195 (1985)

    Article  ADS  Google Scholar 

  10. Quick, R.M., Esebbag, C., de Llano, M.: Phys. Rev. B 47, 11512 (1993)

    Article  ADS  Google Scholar 

  11. Schafroth, M.R.: Phys. Rev. 96, 1442 (1954)

    Article  ADS  Google Scholar 

  12. Schafroth, M.R., Butler, S.T., Blatt, J.M.: Helv. Phys. Acta 30, 93 (1957)

    MathSciNet  Google Scholar 

  13. Schafroth, M.R.: Sol. State Phys. 10, 293 (1960)

    Article  Google Scholar 

  14. Blatt, J.M.: Theory of Superconductivity. Academic, New York (1964)

    MATH  Google Scholar 

  15. Bogoliubov, N.N.: JETP 34, 41 (1958)

    Google Scholar 

  16. Bogoliubov, N.N., Tolmachev, V.V., Shirkov, D.V.: Fortschr. Phys. 6, 605 (1958)

    Article  Google Scholar 

  17. Ranninger, J., Robaszkiewicz, S.: Physica B 135, 468 (1985)

    Article  Google Scholar 

  18. Ranninger, J., et al.: Ann. Phys. Fr. 13, 455 (1988)

    Article  ADS  Google Scholar 

  19. Micnas, R., et al.: Revs. Mod. Phys. 62, 113 (1990)

    Article  ADS  Google Scholar 

  20. Micnas, R., et al.: Phys. Rev. B 66, 104516 (2002)

    Article  ADS  Google Scholar 

  21. Micnas, R., et al.: Struct. Bond 114, 13 (2005)

    Article  Google Scholar 

  22. Friedberg, R., Lee, T.D.: Phys. Rev. B40, 6745 (1989)

    Article  ADS  Google Scholar 

  23. Friedberg, R., et al.: Phys. Rev. B 42, 4122 (1990)

    Article  ADS  Google Scholar 

  24. Friedberg, R., et al.: Phys. Lett. A 152, 417 and 423 (1991)

    Google Scholar 

  25. Friedberg, R., et al.: Phys. Rev. B 45, 10732 (1992)

    Article  ADS  Google Scholar 

  26. Casas, M., Rigo, A., de Llano, M., Rojo, O., Solis, M.A.: Phys. Lett. A 245, 5 (1998)

    Article  ADS  Google Scholar 

  27. Tolmachev, V.V.: Lett. Phys. A 266, 400 (2000)

    Article  Google Scholar 

  28. de Llano, M., Tolmachev, V.V.: Physica A 317, 546 (2003)

    Article  ADS  Google Scholar 

  29. de Llano, M., Tolmachev, V.V.: Ukrainian J. Phys. 55, 79 (2010). and refs. therein

    Google Scholar 

  30. Grether, M., de Llano, M., Tolmachev, V.V.: Int. J. Quant. Chem. 112, 3018 (2012)

    Article  Google Scholar 

  31. Bogoliubov, N.N.: N. Cim. 7, 794 (1958)

    Article  ADS  Google Scholar 

  32. Valatin, J.: N. Cim. 7, 843 (1958)

    Article  ADS  Google Scholar 

  33. Mamedov, T.A., de Llano, M.: J. Phys. Soc. Japan 79, 044706 (2010)

    Article  ADS  Google Scholar 

  34. Mamedov, T.A., de Llano, M.: J. Phys. Soc. Japan 80, 074718 (2011)

    Article  ADS  Google Scholar 

  35. Mamedov, T.A., de Llano, M.: Phil. Mag. 93, 2896 (2013)

    Article  ADS  Google Scholar 

  36. Mamedov, T.A., de Llano, M.: Phil. Mag. 94, 4102 (2014)

    Article  ADS  Google Scholar 

  37. Nambu, Y.: Phys. Rev. 117, 648 (1960)

    Article  ADS  MathSciNet  Google Scholar 

  38. de Llano, M., Annett, J.F.: Int J. Mod. Phys. B 21, 3657 (2007)

    Article  ADS  Google Scholar 

  39. Chávez, I., Grether, M., de Llano, M.: J. Supercond. and Novel Mag. 28, 309 (2015)

    Article  Google Scholar 

  40. Adhikari, S.K., de Llano, M., Sevilla, F.J., Solís, M.A., Valencia, J.J.: Physica C 453, 37 (2007)

    Article  ADS  Google Scholar 

  41. Zúñiga, F., Segura, J., de Llano, M.: Helmholtz free-energy lowering in a BCS superconductor for all temperatures below T c, to be published

  42. Chávez, I., García, L.A., Grether, M., de Llano, M.: Int. J. Mod. Phys. B 31, 1745004 (2017)

    Article  ADS  Google Scholar 

  43. Chávez, I., García, L.A., Grether, M., de Llano, M.: Int. J. Mod. Phys. B 31, 1745013 (2017)

    Article  ADS  Google Scholar 

  44. Ashcroft N.W., Mermin, N.D.: Solid State Physics, p 38 and 729. Saunders College Publishing, Philadelphia (1976)

    Google Scholar 

  45. Finnemore, D.K., Stromberg, T.F., Swenson, C.A.: Phys. Rev. 149, 231 (1966)

    Article  ADS  Google Scholar 

  46. Finnemore, D.K., Mapother, D.E., Shaw, R.W.: Phys. Rev. 118, 127 (1960)

    Article  ADS  Google Scholar 

  47. Faber, T.E.: Proc. Roy. Soc. Lond. A 231, 353 (1955)

    Article  ADS  Google Scholar 

  48. Finnemore, D.K., Mapother, D.E.: Phys. Rev. 140, A507 (1965)

    Article  ADS  Google Scholar 

  49. Van der Hoeven, B.J.C., Jr., Keesom, P.H.: Phys. Rev. 137, A103 (1965)

    Article  ADS  Google Scholar 

  50. Townsend, P., Sutton, J.: Phys. Rev. 128, 591 (1962)

    Article  ADS  Google Scholar 

  51. Richards, P., Tinkham, M.: Phys. Rev. 119, 575 (1960)

    Article  ADS  Google Scholar 

  52. Giaver, I., Megerle, K.: Phys. Rev. 122, 1101 (1961)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We thank G.C. Strinati for calling refs. [2, 3] to our attention.

Funding

IC and LAG thank CONACyT (Mexico) for postgraduate grants 291001 and 40376, respectively. MG and MdeLl thank PAPIIT-DGAPA-UNAM (Mexico) for research grants IN116914 and IN102417, respectively. We also thank CONACyT (Mexico) grant CB-2016-I no. 285894.

Author information

Authors and Affiliations

  1. Instituto de Investigaciones en Materiales, Universidad Nacional Autónoma de México, Mexico City, 04510, Mexico

    I. Chávez, L. A. García & M. de Llano

  2. Facultad de Ciencias, Universidad Nacional Autónoma de México, Mexico City, 04510, Mexico

    M. Grether

  3. N.E. Baumann State Technical University, Moscow, Russia

    V. V. Tolmachev

Authors
  1. I. Chávez
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. L. A. García
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. Grether
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. M. de Llano
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. V. V. Tolmachev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to I. Chávez.

Additional information

This paper was presented at ICSM 2018.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chávez, I., García, L.A., Grether, M. et al. Two-Electron and Two-Hole Cooper Pairs in Superconductivity. J Supercond Nov Magn 32, 1633–1638 (2019). https://doi.org/10.1007/s10948-018-4890-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10948-018-4890-6

Keywords

Search

Navigation