Spin Gaps in High Temperature Superconductors

The phenomenology and theory of spin gap effects in high temperature superconductors is summarized. It is argued that the spin gap behavior can only be explained by a model of charge 0 spin 1/2 fermions which become paired into singlets and that there are both theoretical and experimental reasons for believing that the pairing is greatly enhanced in the bilayer structure of the $YBa_2Cu_3O_{6+x}$ system. This article will appear in the Proceedings of the Stanford Conference on Spectroscopies in Novel Superconductors. To obtain postscript files containing the figures send mail to [email protected]: 9 pages, revtex. To obtain figures contact [email protected]

Superconducting Order Parameter Symmetry in Multi-layer Cuprates

We discuss the allowed order parameter symmetries in multi-layer cuprates and their physical consequences using highly non-specific forms of the inter- and intra-plane interactions. Within this framework, the bi-layer case is discussed in detail with particular attention paid to the role of small orthorhombic distortions as would derive from the chains in YBCO or superlattice effects in BSCCO. In the orthorhombic bi-layer case the (s,-s) state is of special interest, since for a wide range of parameters this state exhibits pi phase shifts in corner Josephson junction experiments. In addition, its transition temperature is found to be insensitive to non-magnetic inter-plane disorder, as would be present at the rare earth site in YBCO, for example. Of particular interest, also, are the role of van Hove singularities which are seen to stabilize states with d_{x^2 - y^2}-like symmetry, (as well as nodeless s-states) and to elongate the gap functions along the four van Hove points, thereby leading to a substantial region of gaplessness. We find that d_{x^2 - y^2}-like states are general solutions for repulsive interactions; they possess the fewest number of nodes and therefore the highest transition temperatures. In this way, they should not be specifically associated with a spin fluctuation driven pairing mechanism.Comment: REVTeX documentstyle, 34 pages, 10 figures include