Condensation energy in strongly coupled superconductors

We consider the condensation energy E-c in superconductors where the pairing is electronic in origin and is mediated by a collective bosonic mode. We use magnetically mediated superconductivity as an example, and show that for spin-fermion couplings lambdasimilar to1, the physics is qualitatively different from the BCS theory as the condensation energy results predominantly from the feedback on spin excitations. The same feedback effect accounts for the gain of the the kinetic energy at strong couplings due to an undressing feedback on the fermions. We show that E-c decreases at lambdagreater than or equal to2 and argue that this implies that coherent superconductivity gradually yields to the pseudogap.