Strong Correlation Theories of High Temperature Superconductors

The theory of high-temperature superconductors is at an interesting state. There are by now a wide range of reliable experimental results that severely restrict the possible explanations of what is going on. It is clear that the normal state properties are quite unusual and that they must be explained by any satisfactory theory of these fascinating new materials. It is known that superconductivity is a consequence of pairing but there is an ongoing debate about that mechanism, and whether established theory of Bardeen, Cooper and Schrieffer is applicable in its original form. The difficulty in obtaining a widely accepted theory is compounded by the fact that the charge-carriers may not be regarded as nearly-free electrons or holes: as will be clear from the ensuing discussion, there are strong correlation effects which are likely to be an integral part of any successful theory. The objective of the present lectures is to give some of the background material that is necessary for an appreciation of the current theoretical debate. Various models of high-temperature superconductors will be introduced and the reasons for believing that strong correlations are important will be described. The start point typically involves "high energy physics,'' which, in the solid-state context, means physics on a scale of a few eV. But in the final analysis, we are interested in explaining low energy properties such as magnetism and superconductivity, which occur on a scale of 10^-3 to 10^-1 eV. Therefore it is desirable to find an effective Hamiltonian from which high-energy processes have been eliminated in order to obtain a (hopefully simpler) description of the low-energy physics. A critical discussion of attempts along these lines will also be given.