From granules to bulk superconductors using Richardson-Gaudin equations

Monique Combescot () and Michel Crouzeix
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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

The European Physical Journal B: Condensed Matter and Complex Systems, 2016, vol. 89, issue 7, 1-6

Abstract: 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.

Keywords: Solid; State; and; Materials (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1140/epjb/e2016-70029-3

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