High-$T$$_\textrm{C}$ Superconductivity in Hydrogen Clathrates Mediated by Coulomb Interactions between Hydrogen and Central-Atom Electrons

The uniquely characteristic macrostructures of binary hydrogen-clathrate compounds $M$H$_\textrm{n}$ formed at high pressure, a cage of hydrogens surrounding a central-atom host, is theoretically predicted in various studies to include structurally stable phonon-mediated superconductors. High superconductive transition temperatures $T$$_\textrm{C}$ have thus far been measured for syntheses with $M$ = La, Y, and Th. In compressed LaH$_\textrm{10}$, independent studies report $T$$_\textrm{C}$ of 250 K and over 260 K, a maximum in $T$$_\textrm{C}$ with pressure $P$, and normal-state resistance scaling with temperature (suggesting unconventional pairing). According to reported band structure calculations of $Fm$$\bar{3}$$m$-phase LaH$_\textrm{10}$, the La is anionic, with the chemical valence electrons appearing evenly split between La and H$_\textrm{10}$. Thus, compressed LaH$_\textrm{10}$ contains the combination of structure, charge separation, and optimal balanced allocation of valence electrons for supporting unconventional high-$T$$_\textrm{C}$ superconductivity mediated by Coulomb interactions between electronic charges associated with La and H$_\textrm{10}$. A general expression for the optimal superconducting transition temperature for $M$H$_\textrm{n}$ clathrates is derived as $T$$_\textrm{C0}$ = $k$$_\textrm{B}$$^{-1}$$\Lambda$[(n + $v$)/2$A$]$^{1/2}$$e$$^{2}$/$\zeta$, where $\Lambda$ is a universal constant, (n + $v$) is the chemical valence sum per formula unit, taking unity for H and $v$ for atom $M$, $A$ is the surface area of the H-polyhedron cage, and $\zeta$ is the mean distance between the $M$ site and the centroids of the polyhedron faces. Applied to $Fm$$\bar{3}$$m$ LaH$_\textrm{10}$, $T$$_\textrm{C0}$ values of 249.8(1.3) K and 260.7(2.0) K are found for the two experiments. Associated attributes of charge allocation, structure, effective Coulomb potential, . . .