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Historical Notes on Feshbach and Shape Resonances

FEB 01, 2005

DOI: 10.1063/1.4796861

D. M. Eagles

Daniel Kleppner’s Reference Frame piece implies incorrectly that the crossover between Bardeen-Cooper-Schrieffer and Bose–Einstein condensation theory was first studied by Anthony Leggett in 1980. Actually, my early work on this topic was published 11 years before then. 1

In the mid-1980s, I and colleagues in Australia also found the first example 2 of a system that lay on the Bose-gas side of the BCS–Bose gas transition, in a ceramic sample of 3% zirconium-doped strontium titanate (SrTiO3), although with a pairing temperature much lower than that predicted for the 1969 model used for this material. In three dimensions there is a threshold in the coupling strength for the existence of Bose-gas superconductivity at very low carrier concentrations, and for strengths slightly above the threshold, the pair-binding energy is proportional to the square of the difference of the coupling from the threshold value. Thus, for example, a calculated coupling error that gives a value 5% above threshold instead of 1% above would make a factor of 25 error in the pair-binding energy.

A later attempt 3 to reach the Bose-gas regime in macrocrystalline samples of Zr-doped SrTiO3 with similar carrier concentrations to those in the ceramic sample mentioned indicated that some nonuniform state prevented the Bose-gas regime being reached. However, there is still much interesting physics awaiting study in this material.

References

  1. 1. D. M. Eagles, Phys. Rev. 186, 456 (1969) https://doi.org/10.1103/PhysRev.186.456 .

  2. 2. R. J. Tainsh, C. Andrikidis, Solid State Commun. 60, 517 (1986) https://doi.org/10.1016/0038-1098(86)90729-5
    D. M. Eagles, Solid State Commun. 60, 521 (1986) https://doi.org/10.1016/0038-1098(86)90730-1 .

  3. 3. C. Andrikidis, R. J. Tainsh, D. M. Eagles, Physica B 165, 1517 (1990) https://doi.org/10.1016/S0921-4526(09)80344-X .

More about the Authors

D. M. Eagles. (d.eagles@ic.ac.uk) Romford, England .

This Content Appeared In
pt-cover_2005_02.jpeg

Volume 58, Number 2

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