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Ever since BCS theory was first formulated it was recognized that a largeelectronic density of states at the Fermi level was beneficial to enhancing$T_c$. The A15 compounds and the high temperature cuprate materials both havehad an enormous amount of effort devoted to studying the possibility that suchpeaks play an important role in the high critical temperatures existing inthese compounds. Here we provide a systematic study of the effect of thesepeaks on the superconducting transition temperature for a variety oftight-binding models of simple structures, both in two and three dimensions. Inthree dimensions large enhancements in $T_c$ can occur, due to van Hovesingularities that result in divergences in the density of states. Furthermore,even in more realistic structures, where the van Hove singularity disappears,large enhancements in $T_c$ continue due to the presence of `robust' peaks inthe densities of states. Such a peak, recently identified in the bcc structureof H$_3$S, is likely the result of such a van Hove singularity. In certainregimes, anomalies in the isotope coefficient are also expected.

physical review. b./physical review. b

A systematic study of the superconducting critical temperature in two  and three dimensional tight-binding models: a possible scenario for  superconducting H$_3$S ?