Experimental Constraints on the Theory of High- T c Superconductivity

Analysis of the many experiments on high-temperature superconductivity indicate several essential aspects of any theory. The conductivity and other transport properties as a function of disorder, temperature, and frequency point to a non-Fermi liquid-like behavior, whereas photoemission experiments and magnetic properties indicate the presence of a Fermi surface in momentum space. To reconcile this apparent contradiction, a new type of electron liquid, called a Luttinger liquid, has been postulated, and the present article aims to show the need for this postulate. Theory and experiment indicate that the suitable phenomenological electronic structure model of the CuO layers is that of the one-band Hubbard model. It is also argued that experiment clearly indicates that interlayer interactions strongly affect the superconducting transition temperature, T(c), consistent with the fact that no theoretical calculations on two-dimensional Hubbard models have resulted in the prediction of high transition temperatures, and that anyon models are not favored by experiment.