On the arXiv, Andre-Marie Tremblay has posted a nice tutorial review Strongly correlated superconductivity. It is based on some summer school lectures and will be particularly valueable to students. I think it is particularly clearly and nicely highlights some key concepts.
For example, the figure below highlights a fundamental difference between a Mott-Hubbard insulator and a band insulator [or semiconductor].
There is also two clear messages that should not be missed. A minority of people might disagree.
1. For both the cuprates and large classes of organic charge transfer salts the relevant effective Hamiltonians are "simple" one-band Hubbard models. They can capture the essential details of the phase diagrams, particularly the competition between superconductivity, Mott insulator, and antiferromagnetisim.
2. Cluster Dynamical Mean-Field Theory (CDMFT) captures the essential physics of these Hubbard models.
I agree completely.
Tremblay does mention some numerical studies that doubt that there is superconductivity in the Hubbard model on the anisotropic triangular lattice at half filling. My response to that criticism is here.
Thank you. I should have included your response to doubts concerning superconductivity in the one-band Hubbard model. I had missed that post. I agree with your point of view. You can also see http://xxx.lanl.gov/abs/1302.3473 concerning experiment in cuprates vs the one-band Hubbard model.
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