Advertisement

Spatial Structure of the Cooper Pair

Abstract

The Cooper pair is generally analyzed in momentum space, but its real-space structure also follows directly from the Bardeen–Cooper–Schrieffer (BCS) theory. It is shown here that this leads to a spherically symmetrical quasi-atomic wavefunction, with an identical “onion-like" layered structure for each of the electrons constituting the Cooper pair, with charge layers ∼0.1 nm and radius ∼100 nm for a classic BCS superconductor. This charge modulation induces a corresponding charge modulation in the background ionic lattice, and the attractive interaction between these two opposite charge modulations produces the binding energy of the Cooper pair. This physically based interaction potential is similar to that in the simple BCS approximation. The implications of this real-space picture for understanding conventional and exotic superconductors are discussed.

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

Access options

Buy single article

Instant unlimited access to the full article PDF.

US$ 39.95

Price includes VAT for USA

Subscribe to journal

Immediate online access to all issues from 2019. Subscription will auto renew annually.

US$ 199

This is the net price. Taxes to be calculated in checkout.

References

  1. 1.

    L. N. Cooper, Bound electron pairs in a degenerate fermi gas. Phys. Rev. 104, 1189 (1956).

  2. 2.

    J. Bardeen, L. N. Cooper, and J. R. Schrieffer, Theory of superconductivity. Phys. Rev. 108, 1175 (1957).

  3. 3.

    V. F. Weisskopf, The formation of superconducting pairs and the nature of superconducting currents. Contemp. Phys. 22, 375 (1981).

  4. 4.

    J. R. Waldram, Superconductivity of Metals and Cuprates, pp. 160–161 (Institute of Physics, Bristol, 1996

  5. 5.

    I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series and Products (Academic Press, New York, 1980).

  6. 6.

    M. Tinkham, Introduction to Superconductivity, 1st Ed. (McGraw-Hill, New York, 1975) p. 119.

  7. 7.

    C. C. Tsuei and J. R. Kirtley, Pairing symmetry in cuprate superconductors. Rev. Mod. Phys. 72, 969 (2000).

  8. 8.

    A. P. MacKenzie and Y. Maeno, The superconductivity of Sr2RuO4 and the physics of spin triplet pairing. Rev. Mod. Phys. 75, 657 (2003).

  9. 9.

    J. R. Waldram, Superconductivity of Metals and Cuprates (Institute of Physics, Bristol, 1996) p. 191.

Download references

Author information

Correspondence to Alan M. Kadin.

Additional information

PACS Numbers: 74.20.Fg; 74.20.-z; 74.20.Rp; 74.20.Mn.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Kadin, A.M. Spatial Structure of the Cooper Pair. J Supercond Nov Magn 20, 285–292 (2007) doi:10.1007/s10948-006-0198-z

Download citation

Keywords

  • superconducting energy gap
  • electron-phonon interaction
  • coherence length
  • polarizable lattice
  • High-Tc superconductor
  • D-wave symmetry