THE INSTABILITY OF A 2D ELECTRON-GAS NEAR THE CRITICAL DENSITY FOR A WIGNER POLARON CRYSTAL GIVING THE QUANTUM STATE OF CUPRATE SUPERCONDUCTORS

Experimental evidence that the metallic phase in the Bi2212 high T(c) cuprate superconductors results from an instability of a 2D-electron gas with density lower or larger than the critical density pc for the formation of a generalized Wigner polaronic crystal is reported. The critical density pc is obtained from rho(c) = 1/S(p) where S(p) is the measured area of condensed polarons. We have found that the 2D-electron gas at charge densities rho not-equal rho(c) in the range rho(c)/2<rho<rho(c) and rho(c)<rho<2rho(c) shows a phase separation between 1) a polaron gas with local density rho = rho(c) condensed in a generalized Wiper charge density wave (CDW) at T<T* and 2) a Fermi liquid with local density rho(i) not-equal rho(c). The polaron pair filling factor nu = 2rhoS(p) is shown to be the good variable to describe the phase diagram of the 2D-electron gas in the CuO2 plane as function of doping in several families of cuprate superconductors. At integer values of nu we find the insulating phases of a 2D-polaron gas: the generalized Wigner CDW at nu = 1, and the generalized Wigner crystal at nu = 2. At non integer values 1<nu<2 (2<nu<4) we find the low (high) density metallic phase resulting from the instability toward the phase separation. The maximum of the critical temperature T(c1max) (T(c2max)) is found for the value of the ratio [delta(t)]/[delta(l)] near 1 (near 2), where [delta(i)] is the average hole doping for the Fermi liquid and [delta(l)] for the polaron gas. The sharp drop of the isotope exponent from approximately 0.5 for nu<2 to approximately 0.1 for nu>2 supports the model for the pairing mechanism.