From granules to bulk superconductors using Richardson-Gaudin equations

Monique Combescot (1) , Michel Crouzeix (2)

1 INSP-E1 - Nanostructures et systèmes quantiques
2 IRMAR - Institut de Recherche Mathématique de Rennes

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.

Mots clés: solid state and materials

Domaines: Analyse numérique [math.NA]; Mécanique des matériaux [physics.class-ph]

Monique Combescot, Michel Crouzeix. From granules to bulk superconductors using Richardson-Gaudin equations. The European Physical Journal B: Condensed Matter and Complex Systems, 2016, 89 (7), 6 p. ⟨10.1140/epjb/e2016-70029-3⟩. ⟨hal-01377509⟩