Condensation energy in strongly coupled superconductors

We consider the condensation energy (formula presented) 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 λ∼1, 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 (formula presented) decreases at λ⩾2 and argue that this implies that coherent superconductivity gradually yields to the pseudogap.