From one to N Cooper pairs, step by step

W. V. Pogosov (1) , Monique Combescot (1)

1 INSP - Institut des Nanosciences de Paris

We extend the one-pair Cooper configuration towards Bardeen-Cooper-Schrieffer (BCS) model of superconductivity by adding one-by-one electron pairs to an energy layer, where a small attraction acts. To do it, we solve Richardson's equations analytically in the dilute limit of pairs on the one-Cooper pair scale. We find, through only keeping the first order term in this expansion, that the N correlated pair energy reads as the energy of N isolated pairs within a N(N - 1) correction induced by the Pauli exclusion principle which tends to decrease the average pair binding energy when the pair number increases. Quite remarkably, extension of this first-order result to the dense regime gives the BCS condensation energy exactly. This leads us to suggest a different understanding of the BCS condensation energy with a pair number equal to the number of pairs feeling the potential and an average pair binding energy reduced by Pauli blocking to half the single Cooper pair energy - instead of the more standard but far larger superconducting gap. (C) 2011 Elsevier B.V. All rights reserved.

Mots clés: Cooper pair; Richardson equations; BCS theory; Superconducting gap

Domaines: Matière Condensée [cond-mat]

W. V. Pogosov, Monique Combescot. From one to N Cooper pairs, step by step. Physica C: Superconductivity and its Applications, 2011, 471 (19-20), pp.566-576. ⟨10.1016/j.physc.2011.07.007⟩. ⟨hal-01229213⟩