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

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.