Non Fermi-Liquid States and Pairing of a general Model of Copper-Oxide   Metals
  A model of copper-oxygen bonding and anti-bonding bands with the most general two-body interactions allowable by symmetry is considered. The model has a continuous transition as a function of hole-density x and temperature T to a phase in which a current circulates in each unit cell. This phase preserves the translational symmetry of the lattice while breaking time-reversal invariance and the four-fold rotational symmetry. The product of time-reversal and four-fold rotation is preserved. The circulating current phase terminates at a critical point at $x=x_c, T=0$. In the quantum-critical region about this point the logarithm of the frequency of the current fluctuations scales with their momentum. The microscopic basis for the marginal Fermi-liquid phenemenology and the observed long wavelength transport anomalies near $x=x_c$ are derived from such fluctuations. The symmetry of the current fluctuations is such that the associated magnetic field fluctuations are absent at oxygen sites and have the correct form to explain the anomalous copper nuclear relaxation rate. Cross-overs to the Fermi-liquid phase on either side of $x_c$ and the role of disorder are briefly considered. The current fluctuations promote superconductive instability with a propensity towards ``D-wave" symmetry or ``extended S-wave"symmetry depending on details of the band-structure. 
C. M. Varma