Energy of N Cooper Pairs by Analytically Solving the Richardson-Gaudin Equations for Conventional Superconductors

Michel Crouzeix (1) , Monique Combescot (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 INSP - Institut des Nanosciences de Paris

This Letter provides the solution to a yet unsolved basic problem of solid state physics: the ground state energy of an arbitrary number of Cooper pairs interacting via the Bardeen-Cooper-Schrieffer potential. We here break a 50 yr old math problem by analytically solving Richardson-Gaudin equations which give the exact energy of these N pairs via N parameters coupled through N nonlinear equations. Our result fully supports the standard BCS result obtained for a pair number equal to half the number of states feeling the potential. More importantly, it shows that the interaction part of the N-pair energy depends on N as N(N-1) only from N=1 to the dense regime, a result which evidences that Cooper pairs interact via Pauli blocking only.

Domaines: Supraconductivité [cond-mat.supr-con]

Michel Crouzeix, Monique Combescot. Energy of N Cooper Pairs by Analytically Solving the Richardson-Gaudin Equations for Conventional Superconductors. Physical Review Letters, 2011, 107 (26), 4 p. ⟨10.1103/PhysRevLett.107.267001⟩. ⟨hal-00687107⟩