What is the "mechanism" of superconductivity in the cuprates?

Thomas Maier gave a nice talk at the conference. He considered this question [or at least what is the mechanism of superconductivity in the Hubbard model?] via a Bethe-Salpeter equation (some of the results are described in this PRB and this PRB).

where Gamma^pp is the irreducible particle-particle vertex and chi_0 is

Their calculations are for a cluster DMFT treatment of the doped Hubbard model. They find that the irreducible particle-particle vertex peaks at a wavevector of (pi,pi) as does the spin susceptibility chi(K-K'). Indeed they find that this vertex is to a good approximation related to the spin susceptibility via an RPA type relation.

where U(T) is a temperature dependent renormalised Hubbard U.

But why does the superconductivity go away as one approaches the Mott insulator? After all, the spin fluctuations are increasing! This is because chi_0 ~ GG [Thomas had a name for this that I did not catch] is decreasing because of the suppresion of quasi-particle weight as the Mott insulator is approached.

I would be interested to see this approach applied to an extended Hubbard model on the square lattice at one quarter filling, near the charge ordering transition [see this PRL and PRB for the context]. Two questions the approach could answer are

• Is there superconductivity? If so, is it d_xy symmetry?
• Is it mediated by spin or charge fluctuations?

The latter question is relevant because there is spin ordering associated with the charge ordering and when the charge order melts so will the spin order, potentially leading to significant spin  fluctuations.