Abstract
A model to study the electronic properties of high-${\mathit{T}}_{\mathit{c}}$ superconductors is presented. It is based on a Hamiltonian that includes the interatomic and intra-atomic electronic repulsion at the various Cu and O sites of ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{6+\mathit{x}}$. We analyze in detail the effects of the oxygen concentration and the disorder in the basal plane. Most of the observed properties are well reproduced. Among them is the metal-non metal transition as a function of oxygen concentration and of the total charge transferred by the cationic elements. Under the assumption that the transition temperature is proportional to the number of holes in the ${\mathrm{CuO}}_{2}$ planes, we reproduce the concentration dependence of ${\mathit{T}}_{\mathit{c}}$.
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