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}). Owing to the energies involved, 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 [2-8].

- D. R. Harshman, A. T. Fiory and J. D. Dow, J. Phys.: Condens. Matter
**23**, 295701 (2011);**23**349501 (2011). - D. R. Harshman and A. T. Fiory, J. Phys.: Condens. Matter
**24**, 135701 (2012). - D. R. Harshman and A. T. Fiory, Phys. Rev. B
**86**, 144533 (2012). - D. R. Harshman and A. T. Fiory, J. Phys. Chem. Solids
**85**, 106 (2015). - D. R. Harshman and A. T. Fiory, Phys. Rev. B
**90**, 186501 (2014). - D. R. Harshman and A. T. Fiory, J. Supercond. Nov. Magn.
**28**, 2967 (2015). - D. R. Harshman and A. T. Fiory, J. Phys.: Condens. Matter
**29**, 145602 (2017). - D. R. Harshman and A. T. Fiory, J. Phys.: Condens. Matter
**29**, 445702 (2017).