Abrikosov and the path to understanding high-Tc superconductivity

An early attempt to try to understand the high superconducting transition temperatures in the cuprate super-conductors was Abrikosov's theory of extended Van Hove singularities. It was based on our early experimental data on the YBa2Cu3O6.9 and YBa2Cu4O8 compounds which showed an extended saddle point singularity in the dispersion of the electronic excitations. This appeared to lead to a Van Hove singularity in the density of states with a divergence stronger than the known logarithmic one observed in conventional materials. The consequent high density of states of the extended singularity was thought to lead to high Tc's in a conventional BCS mechanism. Unfortunately, it was soon realized that the very incoherent nature of the electronic excitations in these materials did not provide the expected high density of states. Here we summarize the many unusual characteristics of the electronic excitations in the cuprates, and what they imply for a possible theoretical description of high-temperature superconductivity.