Influence of screening on the superconductive transition temperature

Abstract

We extend the Morel-Anderson model, originally developed to account for the superconductive transition temperature, ${T}_{c},$ of the elements, so that it accounts for the complete phase line for ${T}_{c}$ of disordered systems over the full range of metallic behavior, from the pure metal to the extinction of the metallic state at the metal-insulator transition. The cornerstone of this model is the calculation of the BCS interaction potential, V, and the single-particle density of states, N, using the Landau theory for interacting fermions evaluated with a screened Coulomb interaction potential. Thus, an interpolation is established between Fermi liquid behavior and the critical regime where disorder and Coulomb interactions define the metal-insulator transition. Experimental values for ${T}_{c},$ N, and V were compared with these predictions and the agreement was excellent. Furthermore, since the model is expressed entirely in terms of parameters that may be calculated or measured, it has predictive powers that may prove useful in the search for $\mathrm{h}\mathrm{i}\mathrm{g}\mathrm{h}\ensuremath{-}{T}_{c}$ materials.