Explanation of the Phase Diagram of High-Temperature Superconductors in   Terms of the Model of Negative-U Centers Superconductivity
  It is demonstrated qualitatively how a unified explanation of the wide variety of different regions in a typical phase diagram of HTSC can be given in terms of the model of negative-U centers superconductivity. Both the existence of four regions (pseudogap, superconducting, non Fermi-liquid and Fermi-liquid), in the phase diagram and all the transitions between these regions were explained by assuming that negative-U centers exist in HTSC and qualitatively taking into account their thermodynamic and direct quantum-mechanical interaction with ordinary electrons from the valence band. It is found that the principal parameter determining the properties of HTSC in the model of negative-U centers is the relative concentration of electrons belonging to negative-U centers. The negative-U centers naturally determine both the superconducting properties of HTSC systems and the entire phase diagram in the normal state. 
K.D. Tsendin, B.P. Popov, D.V. Denisov