BCS-Universal Ratios within the Van Hove Scenario

TL;DR

This paper demonstrates that within a specific van Hove scenario, BCS theory can produce universal ratios independent of material parameters, aligning with conventional superconductivity and aiding in characterizing high-Tc superconductors.

Contribution

It introduces a model that maintains the universal ratios of BCS theory within the van Hove scenario, bridging conventional and high-Tc superconductor descriptions.

Findings

Universal ratios are independent of parameters in the proposed model.

The model aligns with features of high-Tc oxides.

Mathematical approach ensures ratios are consistent with conventional superconductivity.

Abstract

The central result of BCS theory are the Universal Ratios which do not depend on physical parameters of the superconductor under study. Several attempts have been made to introduce the van Hove Scenario within BCS theory but in none of them the Universal Ratios of conventional superconductivity appear to be a number independent of parameters. This fact prevents the precise definition of a deviation from the BCS value for a particular superconductor. This concept is at the basis of several applications of BCS theory in characterizing conventional superconductors. We define a system that constitutes a weak coupling limit that retains the essential features of the high-Tc oxides and which does not differ in any essential way from other models widely used in generalizations of BCS theory to high-Tc superconductors. The difference is that we found a natural way of dealing with the mathematics of the problem so as to get Universal Ratios in the same sense as in conventional superconductivity.