Two-Fluid Models of Superconductivity with Application to Isotope Effects

Abstract

A general form of the two-fluid model of a superconductor, which includes all previous forms, is set up and the underlying assumptions examined in the light of the lattice vibration theory of superconductivity. Thermodynamic relations are derived and their consistency with the observed isotope effects indicated. Specialization to the $\alpha$ model of Casimir and Gorter permits fitting recent precise critical field data and evaluation of the parameter $\alpha$ characterizing different superconductors. Comparison is made with Koppe's form of the two-fluid model, which is shown not to fit all the data, and simplified and limiting forms of his equations are given.