High-T_C superconductivity in ultrathin crystals: implications for microscopic theory

High-transition temperature (high-T_C) superconductivity is associated with layered crystal structures. This work considers superconductivity in ultrathin crystals (of thickness equal to the transverse structural periodicity distance d for one formula unit) of 32 cuprate, ruthenate, rutheno-cuprate, iron pnictide, organic and transuranic compounds, wherein intrinsic optimal (highest) transition temperatures T_C0 (10−150 K) are assumed. Sheet transition temperatures T_CS = αT_C0, where α < 1, are determined from Kosterlitz–Thouless (KT) theory of phase transitions in two-dimensional superconductors. Calculation of α involves superconducting sheet carrier densities N_S 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; α is on average 0·83 (varying with standard deviation 0·11). Experiments on several thin crystal structures of thickness d_F approaching d are shown to be consistent with the calculations of T_C0 from microscopic superconductivity theory and with T_CS from KT theory, where the presence of disorder is also taken into account; careful analyses of these thin film studies indicate a minimum thickness d_F ≈ d for superconductivity.