Empirical Relations in Transition Metal Superconductivity

Abstract

The empirical relations among the parameters determining the superconducting transition temperature in transition metals and alloys and for some A-15 compounds are collected. These parameters are the density of states near the Fermi surface, the average phonon frequency, and an average electron-phonon matrix element. The empirical relations suggest a theory for transition metals that is based on the nature of the atomic orbitals, for example the tight binding scheme for the electronic structure. A simple single orbital non-orthogonal tight binding model is used to calculate parameters of importance in superconductivity. The empirical relations follow from such a model. It is argued that a realistic non-orthogonal tight binding model will yield similar results. One of the conclusions of the work is that T_c is higher for materials satisfying the conflicting requirements of large bandwidth, large density of states near the Fermi surface and with the Fermi level lying in a non-bonding part of the band. An application of theory to T_c degradation due to defects or radiation damage further substantiates the conclusions of this work.