Formula for the Critical Temperature of Superconductors Based on the Electronic Density of States and the Effective Mass

A formula for the superconducting transition temperature T(c) is developed by comparing the total condensation energy contained within the coherence volume of a Cooper pair to the number of electronic states at the Fermi surface within the same coherence volume. It is found that T(c) is proportional to the ratio of the condensation energy density and normal state charge carrier density. We find that this relation holds for over 2 orders of magnitude in temperature for numerous well-known superconducting compounds belonging to distinctly different classes.