Theory of the Specific Heat of Superconductors Based on an Energy-Gap Model

A two-fluid model of a superconductor is proposed, based on an approximation in which one-electron states within a range of the order of $k{T}_c$ from the Fermi level are forbidden. It is assumed that the corresponding energy gap decreases with temperature and vanishes at the transition temperature; such an assumption is necessary in order to have a second-order transition. Assumptions are also made concerning the behavior of the electrons in a superconductor, and general formulas are developed involving two parameters which describe the approximate shape of the gap. Detailed calculations are presented for two different sets of values of these parameters, and our results for the electronic specific heat predict the general exponential dependence on temperature which agrees with recent experimental data for Sn and V.