HIGH-T(C) SUPERCONDUCTORS - DISORDERED METALS WITH PAIRING VIA POLARIZABILITY FROM LOCALIZED STATES NEAR THE MOBILITY EDGE

The electronic structure of the high-T(c) superconductors is that of a disordered metal with the Fermi energy (E(F)) relatively close to the mobility edge (E(c)); E(F) is similar to 0.1-0.2 eV from E(c), lying in the extended-state region in the O 2p band. In such a metal, the polarizability of the localized states near E(c) can lead to an indirect attractive interaction between electrons (or holes) in extended states near E(F). Although the direct and exchange terms cancel in second-order perturbation theory, we argue that because of the response of the many-electron wave function to the ''core hole'' in the intermediate state, exchange processes are turned off near threshold at E(F) in analogy with the x-ray-absorption-edge problem. Thus, V(indirect) = -2f(L)(delta/E(F))(U(L))2\E(F)-E(c)\-1, where U(L) is the screened Coulomb interaction between electrons in extended states near E(F) and electrons in localized states near E(c), f(L) is the fraction of the total number of states in the band which is localized, and delta is an energy interval near E(F) (delta < E(F)) in which the exchange scattering is suppressed. Using V(indirect) as the basis for pairing in BCS theory, one obtains 2DELTA0 = 2\E(F)-E(c)\exp{-2/N(E(F))V(indirect}, where N(E(F)) is the density of states at E(F). Since 2\E(F)-E(c)\is similar to 0.2-0.4 eV, the transition temperature can in principle be quite high. Moreover, as \E(F)-E(c)\ is increased from zero by doping beyond the metal-insulator transition, the gap (and T(c)) would initially increase, and then decrease when the exponential factor begins to dominate, in qualitative agreement with the phase diagram of the high-temperature superconducting cuprates and with the overdoping phenomenon. The interaction between electrons near E(F) will cause scattering and the dissipation of momentum, thereby making a contribution to the normal-state resistivity, which is linear in temperature, in agreement with experiment. We show that T(c) can be estimated directly from the magnitude of the linear term in the Drude scattering rate, with results that are also in agreement with experiment.