Resonating valence bonds and d wave superconductivity

Özet

The normal state and the superconducting properties of the cuprate superconductors continue to be a one of the most challenging problem in the theory of strongly correlated electron systems. In this talk I will review the results of early and recent mean field treatments of the Hubbard model in its large U limit, the t-J model, that capture many qualitative features of the experimentally observed phase diagram of the cuprates. The low temperature phase is a d wave superconductor, and the order parameter can have an admixture of an s component. At low doping the superconducting transition is controlled by phase fluctuations and a gap in the single particle spectrum opens above-$T_c$. At large doping the superconducting transition temperature is determined by amplitude fluctuations. Some difficulties which faced the early mean field treatment and various attempts to go beyond it will be critically discussed. Some of these issues will be illuminated by presenting some recent progress obtained by carrying out an systematic expansion around the limit of large lattice coordination.