Abstract
There have been recent suggestions that high-${\mathit{T}}_{\mathit{c}}$ superconductivity can be understood in terms of conventional BCS theory if there is a logarithmic Van Hove singularity in the electron density of states near the Fermi energy as suggested by band theory. We consider the effects of broadening of the singularity on theories of this type. The broadening may be caused by inhomogeneities arising from doping or structural defects, electron inelastic scattering, and three-dimensional dispersion.
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