Skip to main content
SpringerLink
Log in

A Unified and Asymptotically Exact Theory of Superconductivity from Weak to Strong Coupling in an Electron–Phonon Model

  • Published:
Journal of Low Temperature Physics Aims and scope Submit manuscript

Abstract

Since the discovery of MgB2, fundamental studies of the electronphonon mechanism have received intense interest. In this paper, starting from an electron–phonon model Hamiltonian, the third formalism of quantum statistics, and a diagonalization theorem, a unified and asymptotically exact theory of superconductivity is developed. The results are compared with those of McMillan, Allen and Dynes and experimental data. It is shown that the new results are in very good agreement with the experimental data. The unified theory has no extra assumptions and also supplies an exactly soluble example of the third formalism of quantum statistics. The T c of MgB2 is at a unified T c line, the reason for the vacuum fluctuation mechanism are also discussed.

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. Nagamatsu N. Nakagawa T. Muranaka Y. Zenitani J. Akimitsu (2001) ArticleTitleNature London 63 410

    Google Scholar 

  2. Bud’ko S.L., et al. Phys. Rev. Lett. 86 , 1877 (2001); Hinks DG., et al . Nature (London) 411 , 457 (2001).

  3. R Cubitt S. Lvett (2003) Phys Rev Lett 90 157002 Occurrence Handle1:STN:280:DC%2BD3s3htFOktw%3D%3D Occurrence Handle12732063

    CAS  PubMed  Google Scholar 

  4. e.g. the review paper: Buzea C., Yamashita T., Supercond . Sci. Technol . 14 , R115-R146 (2001).

  5. Fröhlich H. Phys Rev. 79 (1950) 845; Proc. Roy. Soc . A215 , 291 (1952).

  6. J. Bardeen L.N. Cooper JR. Schrieffer (1957) Phys Rev 108 1175 Occurrence Handle10.1103/PhysRev.108.1175 Occurrence Handle1:CAS:528:DyaG1cXjtlGltg%3D%3D

    Article  CAS  Google Scholar 

  7. NN. Bogoliubov (1958) Nuovo Cimento. 7 794

    Google Scholar 

  8. L.P. Gor’kov (1958) Sov Phys JETP 7 505

    Google Scholar 

  9. V. Ambegaokar A. Griffin (1965) Phys Rev. 137 A 1151

    Google Scholar 

  10. GM. Eliashberg (1960) Zh Eksp Teor Fiz . 38 966 Occurrence Handle1:CAS:528:DyaF2cXktFGntLo%3D

    CAS  Google Scholar 

  11. WL. McMillan (1968) Phys Rev 167 331 Occurrence Handle1:CAS:528:DyaF1cXot1altQ%3D%3D

    CAS  Google Scholar 

  12. P.B. Allen RC. Dynes (1975) Phys Rev B. 12 905 Occurrence Handle1:CAS:528:DyaE2MXlsFKmtbs%3D

    CAS  Google Scholar 

  13. HS. Wu JH. Chai C.D Gong GD. Ji JD. Chai (1978) Chin Sci. 1 28

    Google Scholar 

  14. e.g. Schrieffer JR., Theory of Superconductors , W.A.Benjamin, ed. NC ., Publishers, New York, Amsterdam, p. 33 (1964)

  15. e.g. Ginzberg DM., Physical Properties of High Temperature Superconductors , I-IV. World Scientific, Singapore, (1989–1994).

  16. P. Prabhakar Singh (2003) Phys Rev B 67 132511

    Google Scholar 

  17. J. Mitra A.K. Raychaudhuri N. Gayathri (2002) Phys Rev B 65 140406

    Google Scholar 

  18. K. Kotegawa K. Ishida Y. Kitaoka T. Muranaka N. Nakagawa H. Takagiwa J. Akimitsu (2002) Phys Rev B 66 064516

    Google Scholar 

  19. R. Heid B. Renker H. Schober P. Adelmann D. Ernst K.-P. Bohnen (2003) Phys Rev B 67 180510

    Google Scholar 

  20. X.-X. Dai WE. Evenson (2002) Phys Rev E. 65 026118

    Google Scholar 

  21. J. Hubbard (1959) Phys Rev Lett 3 77

    Google Scholar 

  22. D.J. Amit H. Keiter (1973) J Low Temp Phys 11 603

    Google Scholar 

  23. B. Mühschlegel, Lecture Notes University of Pennsylvania (1965) unpublished; Path Integrals and Their Application in Quantum Statistical and Solid State Physics , Ed. by G. J. Papadopoulos and J. T. Devreese ed. Plenum, New York (1978).

  24. S.Q. Wang W.E. Evenson JR. Schrieffer (1969) Phys Rev Lett. 23 92

    Google Scholar 

  25. DR. Hamann (1969) Phys Rev Lett. 23 95

    Google Scholar 

  26. D. Xianxi Ting. Chin-sen (1983) Phys Rev B 28 5243

    Google Scholar 

  27. Xianxi D., J. Phys.: Condens. Matter 3 , 4389 (1991); ibid 4, 1339 (1992).

  28. G. Ma X.-X. Dai (1998) Phys Lett A 242 277 Occurrence Handle1:CAS:528:DyaK1cXisVygt7s%3D Occurrence HandleMR1628300

    CAS  MathSciNet  Google Scholar 

  29. D. Xianxi (1979) Chin Low-Temperature Phys. 1 IssueID4 273–283

    Google Scholar 

  30. NN. Bogoliubov (1959) Lecture on Quantum Statistics, Chinese edition Science Publishing House Beijing

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, Research Group of Quantum Statistics and Methods of Theoretical Physics & Surface Physics Laboratory, Fudan University, Shanghai, 200433, P.R. China

    Lei Sun & Xianxi Dai

  2. Department of Chemistry, New York University, Washington Place, New York, NY, 10003, USA

    Jixin Dai

Authors
  1. Lei Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xianxi Dai
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jixin Dai
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xianxi Dai.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sun, L., Dai, X. & Dai, J. A Unified and Asymptotically Exact Theory of Superconductivity from Weak to Strong Coupling in an Electron–Phonon Model. J Low Temp Phys 139, 419–428 (2005). https://doi.org/10.1007/s10909-004-4731-9

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10909-004-4731-9

Keywords

Search

Navigation