UNDERSTANDING HIGH-TEMPERATURE SUPERCONDUCTIVITY - A PROGRESS REPORT

I review recent theoretical calculations and experimental measurements which demonstrate that the planar excitations in the normal state of the superconducting cuprates are best described as a nearly antiferromagnetic Fermi liquid. Its anomalous transport, optical and quasiparticle properties arise from the magnetic interaction between the quasiparticles which gives rise to a high T(c) transition to a superconducting state with dx2-y2 symmetry now observed in nuclear magnetic resonance, penetration depth, SQUID and other tunneling experiments, Raman and neutron scattering, photoemission, and numerous other experiments. I discuss the influences of imperfections on both T(c) and the low-temperature properties, review experiments on dirty d-wave superconductors, and suggest a possible ''intrinsic imperfection'' hierarchy of cuprate superconductors.