Superconducting $I$$\overline{4}$3$m$ CSH$_7$ model applied to resistive transition temperature data for compressed C-S-H at high pressure

This article updates version 1 by restricting consideration to only the resistive data and excluding the questioned 287.7-K datum reported for carbonaceous sulfur hydride in Snider et al., Nature $\textbf{585}$, 373 (2020). The superconducting transitions are considered in terms of the theoretically-discovered compressed $I$$\overline{\textrm{4}}$3$m$ CSH$_7$ structure of Sun et al., Phys. Rev. B $\textbf{101}$, 174102 (2020), which comprises a sublattice similar to $Im$$\overline{\textrm{3}}$$m$ H$_3$S with CH$_4$ intercalates. Positing an electronic genesis of the superconductivity, a model is presented in analogy with earlier work on superconductivity in $Im$$\overline{\textrm{3}}$$m$ H$_3$S, in which pairing is induced via purely electronic Coulomb interactions across the mean distance $\zeta$ between the S and H$_4$ tetrahedra enclosing C. Theoretical superconducting transition temperatures for $I$$\overline{\textrm{4}}$3$m$ CSH$_7$ are derived as $T$$_{\textrm{C0}}$ = (2/3)$^{1/2}$ $\sigma^{1/2}$ $\beta$/$a$$\zeta$, where $\beta$ = 1247.4 $\mathring{\mathrm{A}}$$^2$K is a universal constant, $\sigma$ is the participating charge fraction, and $a$ is the lattice parameter. Analysis suggests persistent bulk superconductivity with a pressure-dependent $\sigma$, increasing from $\sigma$ = 3.5, determined previously for $Im$$\overline{3}$$m$ H$_3$S, to $\sigma$ = 7.5 at high pressure owing to additionally participating C-H bond electrons. With $a$ and $\zeta$ determined by theoretical structure, calculations of $T$$_{\textrm{C0}}$ at the highest pressures, 258 and 271 GPa, are in agreement with resistive transitions to within an overall uncertainty of $\pm$ 3.5 K.