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From granules to bulk superconductors using Richardson-Gaudin equations

Author

Listed:
  • Monique Combescot

    (Institut des NanoSciences de Paris, Université Pierre et Marie Curie, CNRS)

  • Michel Crouzeix

    (Institut de Recherche Mathématiques de Rennes, Université de Rennes 1)

Abstract

We provide a compact expression of the ground-state energy of N-Cooper pairs valid from small to large sample volumes, as checked by numerically solving Richardson-Gaudin equations which give the exact eigenstates of BCS superconductors. This expression contains a contribution linear in the potential amplitude, dominant for small samples, and an exponential contribution dominant when the number of states available for pairing gets larger than a material-dependent threshold independent from sample size. These “available states” are the states feeling the BCS potential, reduced by the Pauli exclusion principle through a “moth-eaten effect” which comes from the composite boson nature of Cooper pairs. This work also presents an elegant derivation of the N-Cooper pair energy obtained recently, which makes use of the roots of the degree-N Hermite polynomial.

Suggested Citation

  • Monique Combescot & Michel Crouzeix, 2016. "From granules to bulk superconductors using Richardson-Gaudin equations," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 89(7), pages 1-6, July.
    • Handle: RePEc:spr:eurphb:v:89:y:2016:i:7:d:10.1140_epjb_e2016-70029-3
    DOI: 10.1140/epjb/e2016-70029-3
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    Keywords

    Solid State and Materials;

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