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Gap Anisotropy and Tc Enhancement: General Theory, and Calculations for Nb, using Fermi Surface Harmonics

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Superconductivity in d- and f-Band Metals

Abstract

A general theory is given of the anisotropy of the energy gap and the resulting transition temperature (Tc) enhancement of pure superconductors. The frequency dependence of the gap Δ (k,ω) is approximated by the two square well form of McMillan, but otherwise an exact algebraic solution of the strong-coupling Eliashberg equations is given, valid for arbitrarily large anisotropy. In the limit of weak anisotropy a simple perturbative formula is also derived. The method of solution relies on the use of expansion functions called Fermi surface harmonics (FSH’s) which are velocity polynomials orthonormalized on the Fermi surface. Methods for explicit construction of these functions are described. As an application of these techniques the mass enhancement and gap anisotropy are calculated for Nb, in an approximation which includes all electronic anisotropy but neglects the contribution to the anisotropy which arises from phonons. The rms gap anisotropy in this model is 6% which is not inconsistent with most of the current experimental data. The resulting Tc enhancement is predicted to be 0.7% or .06°K.

Research supported by ERDA under contract with Union Carbide Corp.

Supported in part by NSF Grant No. DMR 73-07578A01

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Authors and Affiliations

  1. Oak Ridge National Laboratory, Oak Ridge, Tennessee, 37830, USA

    W. H. Butler

  2. State University of New York, Stony Brook, New York, 11794, USA

    P. B. Allen

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  1. W. H. Butler
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  2. P. B. Allen
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Editor information

Editors and Affiliations

  1. University of Rochester, Rochester, New York, USA

    D. H. Douglass

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© 1976 Plenum Press, New York

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Butler, W.H., Allen, P.B. (1976). Gap Anisotropy and Tc Enhancement: General Theory, and Calculations for Nb, using Fermi Surface Harmonics. In: Douglass, D.H. (eds) Superconductivity in d- and f-Band Metals. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-8795-8_6

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  • DOI: https://doi.org/10.1007/978-1-4615-8795-8_6

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4615-8797-2

  • Online ISBN: 978-1-4615-8795-8

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