Condensation energy in strongly coupled superconductors

We consider the condensation energy E-c of strongly coupled magnetically mediated superconductors within the context of the spin-fermion model. We argue that the actual physics behind the condensation energy is much richer than in BCS theory, and that it is vital to take both the fermionic and bosonic contributions to the condensation energy into account. We argue that at strong coupling lambda>1, the gain in the condensation energy is a result of the feedback on spin excitations, while the fermionic contribution to E-c is positive due to an undressing feedback on the fermions. In addition we argue that the same feedback effect accounts for a gain in the kinetic energy at strong coupling. We also found that the BCS relation E(c)proportional toDelta(2), where Delta is the pairing gap, only holds for lambdaless than or equal to1. At larger lambda, Delta keeps increasing and eventually saturates, while E-c passes through a maximum at lambdasimilar to2 and then exhibits a decrease in the strong-coupling regime.