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, 7, 10],

νσ_{I} = ησ_{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} = k_{B}^{−1} (Λ/ℓ) *e*^{2}/ζ

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; Λ = *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 58 optimal high-T_{C} materials from eleven superconductor families [1-11].

Evidence of the Coulomb potential *e*^{2}/ζ is found in optical reflectance data in the mid-infrared range for Cs_{3}C_{60} [7], and H_{3}S [8], where the electronic contribution is given as,

ℏω = *e*^{2}/ε_{∞}ζ

where ε_{∞} is the high-frequency dielectric constant.

Note: the pairing interaction model, first introduced in 2011 [1] has since been further developed and expanded by Dale R. Harshman and Anthony T. Fiory [2-11].

- 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). - D. R. Harshman and A. T. Fiory, J. Supercond. Nov. Magn.
**33**, 367 (2020). - D. R. Harshman and A. T. Fiory, J. Supercond. Nov. Magn. (2020).
- D. R. Harshman and A. T. Fiory. submitted (2020).