High-T _C superconductivity in Cs₃C₆₀ compounds governed by local Cs-C₆₀ Coulomb interactions

Unique among alkali-doped A ₃C₆₀ fullerene compounds, the A15 and fcc forms of Cs₃C₆₀ exhibit superconducting states varying under hydrostatic pressure with highest transition temperatures at [Formula: see text]  =  38.3 and 35.2 K, respectively. Herein it is argued that these two compounds under pressure represent the optimal materials of the A ₃C₆₀ family, and that the C₆₀-associated superconductivity is mediated through Coulombic interactions with charges on the alkalis. A derivation of the interlayer Coulombic pairing model of high-T _C superconductivity employing non-planar geometry is introduced, generalizing the picture of two interacting layers to an interaction between charge reservoirs located on the C₆₀ and alkali ions. The optimal transition temperature follows the algebraic expression, T _C0  =  (12.474 nm² K)/ℓζ, where ℓ relates to the mean spacing between interacting surface charges on the C₆₀ and ζ is the average radial distance between the C₆₀ surface and the neighboring Cs ions. Values of T _C0 for the measured cation stoichiometries of Cs_3-x C₆₀ with x  ≈  0 are found to be 38.19 and 36.88 K for the A15 and fcc forms, respectively, with the dichotomy in transition temperature reflecting the larger ζ and structural disorder in the fcc form. In the A15 form, modeled interacting charges and Coulomb potential e²/ζ are shown to agree quantitatively with findings from nuclear-spin relaxation and mid-infrared optical conductivity. In the fcc form, suppression of [Formula: see text] below T _C0 is ascribed to native structural disorder. Phononic effects in conjunction with Coulombic pairing are discussed.