High transition temperature superconductivity originates from the Coulombic interaction between two adjacent charge reservoirs; the type I reservoir hosts the superconducting condenstate with areal charge density σI/AI (per formula unit) while the type II reservoir contains the mediating charges (with an areal charge density of σII/AII). Given ν type I and η type II interacting component layers (interfaces), the optimal superconducting state is achieved when the two reservoirs are in equilibrium defined by ,
νσI/AI = ησII/AII .
Validation of this equation can be found, e.g., in the charge-compensated cuprate, (Ca0.45La0.55)(Ba1.3La0.7)Cu3Oy (where ν = η = 2 and AI = AII). Remarkably, the optimal transition temperature TC0 is independent of band structure, determined completely by the interacting charge density and the separation between the two reservoirs according to the algebraic expression ,
TC0 = kB−1 β (ση/A)1/2 ζ−1 ,
where ζ is the interaction distance (along the transverse axis), σ/A (=σI/AI) is the optimal areal charge density per type I layer per formula unit for participating charges, η is the number of mediating layers (e.g., the number of cuprate planes), and β (= 0.1075 ± 0.0003 eV Å2) is a universal constant; e–2β is approximately twice the reduced electron Compton wavelength. Rules for determining σ are discussed here (see also, notes), and the relevant experimental parameters and the calculated values of TC0 are listed under Tabulated results for 50 optimal high-TC materials from seven superconductor families. This pairing interaction model was first introduced in 2011 . and has since been further developed and expanded by Dale R. Harshman and Anthony T. Fiory [2-9].
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