High-temperature superconductivity in cuprates and organics : where do we stand ? (3)

Here I expand on what we've learned about Hubbard's model for cuprates and for layered superconductors, mainly using approaches based on generalizations of dynamic mean-field theory. I start with the normal state and the pseudogap, demonstrating that there can be a first-order transition at low temperature between a pseudogap phase and a normal metal. Gradual changes in high-temperature behavior can be linked to this first-order transition and the associated Widom line. In the second part, I turn to superconductivity. I discuss what's special about strongly correlated superconductivity by contrasting it with BCS theory. I discuss c-axis superconducting stiffness and scanning tunneling spectroscopy. I conclude with a discussion of the mechanism, the role of retardation and open questions.