Difference between Normal and Superconducting States of a Metal

Abstract

Three general theorems of statistical mechanics are used to calculate the differences, between the normal and superconducting states of a metal in (i) the mean kinetic energy of the electrons, (ii) the mean kinetic energy of the lattice, and (iii) the mean potential energy of the entire system. The word "mean" implies thermal average at a given temperature and pressure. The formal properties of these differences are established and a numerical calculation is carried out in the case of tin. The most important results of this investigation are that (a) all three differences are of the same order of magnitude (∼${10}^{-3\mathrm{}}$ cal/mole for a typical superconductor) at all temperatures, (b) they all vanish at the transition temperature, (c) the mean kinetic energy of the electrons is greater in the superconducting state than in the normal state and depends strongly on the isotopic mass, (d) the mean kinetic energy of the lattice is less in the superconducting state than in the normal state and depends equally strongly on the electron mass, and (e) the mean potential energy of the entire system is also less in the superconducting state than in the normal state. In the final section these results are discussed from a physical point of view.