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

Abstract

The uniquely characteristic macrostructures of binary hydrogen-clathrate compounds $M$H${}_{\text{n}}$ 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$${}_{\text{C}}$ have thus far been measured for syntheses with $M$ = La, Y, and Th. In compressed LaH${}_{\text{10}}$, independent studies report $T$${}_{\text{C}}$ of 250 K and over 260 K, a maximum in $T$${}_{\text{C}}$ with pressure $P$, and normal-state resistance scaling with temperature (suggesting unconventional pairing). According to reported band structure calculations of $Fm$$\bar{3}$$m$-phase LaH${}_{\text{10}}$, the La is anionic, with the chemical valence electrons appearing evenly split between La and H${}_{\text{10}}$. Thus, compressed LaH${}_{\text{10}}$ contains the combination of structure, charge separation, and optimal balanced allocation of valence electrons for supporting unconventional high-$T$${}_{\text{C}}$ superconductivity mediated by Coulomb interactions between electronic charges associated with La and H${}_{\text{10}}$. A general expression for the optimal superconducting transition temperature for $M$H${}_{\text{n}}$ clathrates is derived as $T$${}_{\text{C0}}$ = $k$${}_{\text{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${}_{\text{10}}$, $T$${}_{\text{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, . . .

arXiv comment25 pages, 9 figures, 3 tables

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