d-wave Superconductivity in the Cuprates

The high temperature superconductors have very interesting electronic properties. For instance, there is strong experimental evidence that the superconducting gap function has the unconventional d-wave symmetry. Experiments also suggest that the antiferromagnetic spin fluctuations and Coulomb correlations play an important role in producing the unusual electronic properties of these materials. Numerical calculations on simple models have been particularly helpful in understanding how d-wave pairing might arise in these materials and how the proximity to the metal-insulator transition modifies the electronic excitations. In this talk we will discuss, in simple terms, the experimental results on the electronic properties of these materials and what we have learned from numerical calculations of simple models. We will also discuss the search for other high temperature superconductors and the newly discovered superconducting cuprate ladder compounds.