High transition temperature (high-Tc) superconductivity is associated with layered crystal structures. This work considers superconductivity in ultra-thin crystals (of thickness equal to the transverse structural periodicity distance d for one formula unit) of thirty-two cuprate, ruthenate,
rutheno-cuprate, iron pnictide, organic, and transuranic compounds, wherein intrinsic optimal (highest) transition temperatures Tc0 (10 - 150 K) are assumed. Sheet transition temperatures Tcs = {\alpha}Tc0, where {\alpha} < 1, are determined from Kosterlitz-Thouless (KT) theory of phase transitions in two-dimensional superconductors. Calculation of {\alpha} involves superconducting sheet carrier densities NS derived theoretically from crystal structure, ionic valences, and known doping, a two-fluid model for the temperature dependence of the superconducting magnetic penetration depth, and experimental data on KT transitions; {\alpha} is on average 0.83 (varying with standard deviation 0.11). Experiments on several thin crystal structures of thickness dF approaching d are shown to be consistent with calculations of Tc0 from microscopic superconductivity theory and with Tcs from KT theory, where the presence of disorder is also taken into account; careful analyses of these thin film studies indicate a minimum thickness dF \approx d for superconductivity.

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Category: Science