Analysis of the approximations used in the van Hove-BCS theory

TL;DR

This paper critically examines the approximations in the van Hove-BCS model for high-temperature superconductors, comparing analytical and numerical results to assess their accuracy in predicting thermodynamic properties.

Contribution

It provides a detailed analysis of the validity of asymptotic and approximate expressions within the van Hove-BCS framework, highlighting their limitations and accuracy.

Findings

Asymptotic density of states underestimates critical temperature and gap.

Analytical expressions closely match numerical results for thermodynamic functions.

Approximations are valid within certain temperature ranges for the van Hove model.

Abstract

An analysis of the different approaches used within the van Hove BCS model for the high temperature superconductors has been done. How far the employment of an asymptotic expression for the density of states underestimates the thermodynamic parameters, as for example, the critical temperature, the gap at zero temperature, and the known universal ratios of the BCS model, is discussed. Analytical expressions obtained for some thermodynamic functions are compared with the numerical results for which the exact 2D density of states has been considered. Approximate analytical expressions for the temperature dependence of the reduced gap, the superconducting electronic specific heat, and the critical magnetic field have been obtained and compared with the corresponding numerical results. The validity of the different approximations and of the equations obtained for the thermodynamic functions in the framework of the van Hove model are also analyzed.