BCS-universal ratios within the Van Hove scenario

Abstract

Within conventional superconductivity, BCS theory represents a well defined weakcoupling limit. The central result are the Universal Ratios which do not depend on physical parameters of the particular 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. This formulation could play an analogous role as the original BCS theory played in conventional superconductivity. A central result of this theory are the Universal Ratios (UR). These relate thermodynamic quantities among themselves in a universal way, i. e. they are equal to the same number for every possible superconductor.When compared to experiment, BCS turns out not to be an exact theory of CS. Deviations from it are frequent in all but some of the weak coupling CSr as Al, In, and Sn.Since it is a precisely established limit, the deviations from it do have a well defined physical meaning. This theory is useful as a point of reference and as a tool to study different, more complicated physical situations in a transparent and easy way from which trends can be established. It is important to recall that, in the spirit of the theoretical treatment of CS, the deviations from BCS theory characterize the particular superconductor, not the theory. The validity of BCS theory itself is based on its approximate description of the most important experimental trends and on its characterization as a well-defined weak coupling limit. This is a very important point for this letter. The precise many-body theory of the electron-phonon (e-ph) CS is described through the so called Eliashberg gap Equations [2]

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Simple analytical model of the effect of high pressure on the critical temperature and other thermodynamic properties of superconductors

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