• To provide conclusive evidence that over-doped cuprates are not classic Fermi liquids, and to resolve the question of whether there is a quantum critical point at zero temperature in the superconducting domain.

  • To explore the differences between the electron- and hole-doped materials and whether the distinctions between them in d-wave pairing behavior hold in the superconducting state.

The effect of magnetic fields perpendicular to Cu-O planes is also of great interest. Vortex arrays that form in a superconducting domain govern the magnetic and transport properties (see Appendix H). The quasi particles that appear near the nodes of the d-wave gap may make an essential contribution to the dynamic properties of these vortices. Measurements of optical conductivity in magnetic fields under different doping conditions will be critical to uncovering these quasi-particle effects. At the same time parallel (to the CuO planes) field studies could break new ground in cuprates. Indeed, one expects that in very thin films, the Zeeman energy will be sufficient to split low-lying “spin-up” and “spin-down” quasi particles. Thus, a portion of the Fermi surface near the nodes of the energy gap will become normal, even at 0 K, and this effect will be detectable because of the corresponding reduction in ρs(0). This state indeed would be a novel superconducting one.

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