Theoretical prospects for high-temperature superconductors

Progress in the quest to understand the electronic basis for high-temperature superconductors is reviewed with emphasis on theories that make contact with experimental realities in copper oxides. Key anomalies, such as the unconventional strong damping of the electrons (or holes), are examined at a level suitable for non-specialists. Correlations of superconducting temperatures T-c with the damping are drawn, in contrast to the insensitivity of T-c to the electron density of states. Infrared conductivity, the Hall effect, spin susceptibility, Raman spectra, NMR relaxation, the Knight shift and the microwave surface resistance of cuprates are considered, together with possible theoretical explanations. The nested Fermi liquid theory is compared to typical experimental data on cuprates. Mechanisms for high-temperature superconductivity are discused in the context of growing evidence for an energy gap with d-wave symmetry in the high-T-c materials, whose magnitude is much larger than conventional theories predict. Relevant spin fluctuation concepts for d-wave pairing are reviewed. Other oxides are related to more traditional theories, including the BCS model of electron-phonon coupling and polarons. Novel states, such as holons and spinons, spin bags and anyons are discussed and guides to calculations for t-J models and Monte Carlo simulations are presented. Future challenges for field theory, as well as experimental probes at high pressure, are suggested.