Abstract
A band of holes moving in an antiferromagnetic plane is used to model the weakly non-stoichiometric cuprate superconductors. We note that a singular density of states at the Brillouin-zone boundary, as is obtained from many different starting points, leads to a maximum in the transition temperature as a function of the deviation from stoichiometry. Numerical calculations of this effect, based on (i) the tight-binding bands that follow from Roth's approximate treatment of the Hubbard model for the Cu${\mathrm{O}}_{2}$ planes, and (ii) the attractive pairing between the oxygen holes that can result from considerations of the extended Hubbard model, are presented.
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