Is there a lowest upper bound for superconductive transition temperatures?

Abstract

The values of superconductive transition temperatures Tc in conventional crystalline metallic superconductors are widely scattered, depend on the details of the Fermi surface (especially the density of states N(EF)), and are typically below 1 K. By far the highest Tc 's (~100 K) are found in the cuprates, and there Tc is apparently insensitive to the geometry of the Fermi surface, while it depends strongly on dopant density and configuration. For the cuprates there is a smooth master curve Tcmax(<R>) for the highest Tc's as a function of the average number <R> of Pauling resonating bonds/atom in the parent (undoped) insulator. The existence of such an <R>-dependent optimized Tc is suggested by analogies with the microscopic theory of optimized molecular glass networks (such as window glass), but it remains to derive a rigorous quantum theory of the origin of Tcmax(<R>).