High-temperature superconductivity in the Van Hove scenario

Abstract

The influence of a logarithmic Van Hove singularity in the electronic density of states is studied in the framework of the BCS theory. We use a simplified model, neglecting effects such as interlayer coupling and pair breaking. Through analytic and numerical analyses it is found that although the model can give rise to high temperatures, there are other properties, such as the isotope effect and specific-heat jump at the transition temperature, which cannot be explained properly with this model, as recent experimental data in the high-${\mathit{T}}_{\mathit{c}}$ oxides show.