Insulator-metal transition in high-T$_c$ superconductors as result of   percolation over -U centers
  The mechanism of -U center formation in high-$T_{c}$ superconductors (HTS) with doping is considered. It is shown that the transition of HTS from insulator to metal passes through the particular dopant concentration range where the local transfer of singlet electron pairs from oxygen ions to pairs of neighboring cations (-U centers) are allowed while the single-electron transitions are still forbidden. We believe it is this concentration range that corresponds to the region of high-Tc superconductivity and the interelectron attraction results from the interaction of electron pairs with -U centers. Additional hole carriers are generated as the result of singlet electron pair transitions from oxygen ions to -U-centers. The orbitals of the arising singlet hole pairs are localized in the nearest vicinity of -U center. In such a system the hole conductivity starts up at the dopant concentration exceeding the classical 2D-percolation threshold for singlet hole pair orbitals. In the framework of the proposed model the phase diagram Ln-214 HTS compounds is constructed. The remarkable accord between calculated and experimental phase diagrams may be considered as the confirmation of the supposed model. The main features of hole carriers in HTS normal state are found to be the nondegenerate distribution and the dominant contribution of electron-electron scattering to the hole carrier relaxation processes. Various experimentally observed anomalies of HTS properties are shown to be the consequences of the above-mentioned features. The conclusion is made that HTS compounds are the special class of solids where the unusual mechanism of superconductivity different from BCS is realized. 
K. V. Mitsen and O. M. Ivanenko