Canonical perturbation theory and the two-band model for high-Tcsuperconductors

Abstract

We analyze in more detail a model which describes spins localized on the Cu sites and carriers of oxygen character which has been proposed for high-temperature superconducting oxides by, among others, Emery and Hirsch. This model is discussed in a more general framework of the electronic structure of transition-metal compounds as has emerged from detailed electron-spectroscopy studies. We argue that the Emery model corresponds with the charge-transfer semiconductor in this electronic picture. Using canonical perturbation theory we analyze systematically the near-ground-state physics when holes are introduced into such a system. We derive explicit expressions for the carrier-spin, spin-spin, and carrier-carrier interactions which turn out to depend in a nontrivial way on the electronic parameters, thereby creating a link between the high-energy data and the macroscopic physics in these systems. We find that the dominant interactions are the Kondo-like spin-carrier interactions which give rise to the well-known magnetic semiconductor physics characterized by ferromagnetic correlations (spin polarons, double exchange). Using some simple finite models we discuss then the pairing mechanisms as proposed by Emery and Hirsch. We show that both of them are based on fourth-order attractive interactions. These are, however, overruled by the second-order processes which favor the opposite behavior and suppress the pairing. Our conclusion is that the charge degrees of freedom are essential in the real high-temperature superconductors and we supply further evidence in favor of their mixed-valence behavior.