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 σ_{I}/*A*_{I} (per formula unit) while the type II reservoir contains the mediating charges (with an areal charge density of σ_{II}/*A*_{II}). 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 [1],

νσ_{I}/*A*_{I} = ησ_{II}/*A*_{II} .

Validation of this equation can be found, *e.g.*, in the charge-compensated cuprate, (Ca_{0.45}La_{0.55})(Ba_{1.3}La_{0.7})Cu_{3}O_{y} (where ν = η = 2 and *A*_{I }= *A*_{II}). Remarkably, the optimal transition temperature T_{C0 }is independent of band structure, determined completely by the interacting charge density and the separation between the two reservoirs according to the algebraic expression [1],

T_{C0} = k_{B}^{−1} *β* (ση/*A*)^{1/2} ζ^{−1} ,

where ζ is the interaction distance (along the transverse axis), σ/*A* (=σ_{I}/*A*_{I}) 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 Å^{2}) is a universal constant; *e*^{–2}*β* 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 T_{C0} are listed under Tabulated results for 50 optimal high-T_{C} materials from seven superconductor families. This pairing interaction model was first introduced in 2011 [1]. and has since been further developed and expanded by Dale R. Harshman and Anthony T. Fiory [2-9].

- D. R. Harshman, A. T. Fiory and J. D. Dow, J. Phys.: Condens. Matter
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**29**, 445702 (2017). - D. R. Harshman and A. T. Fiory, preprint (2019).