Condensation energy in phonon and spin mediated superconductors - strong coupling approach

We consider the condensation energy, $E_c$ of strongly coupled, magnetically-mediated superconductors within the context of the spin fermion model. We argue that although experimentally obtained values of $E_c$ are of the same order of magnitude as would be expected from BCS theory in optimally and overdoped cuprates, this agreement is coincidental. The actual physics behind the condensation energy is much richer. In particular, we argue that it is vital to take both the fermionic and bosonic contributions to the condensation energy into account when considering such materials, and that it is only the sum of the two contributions $E_c$ which has physical meaning. Both the experimental and our theoretically calculated condensation energies exhibit a {\it decrease} with further underdoping past optimal doping, e.g. in the mid to strong coupling regime. Below optimal doping, the physics is qualitatively different from BCS theory as the gain in the condesation energy is a reult of the feedback on spin excitations, while the fermionic contribution to $E_c$ is positive due to an "undressing" feedback on the fermions. We argue that the same feedback effect accounts for a gain in the kinetic energy at strong coupling.