Compressed H$_3$S: inter-sublattice Coulomb coupling in a high-$\textit{T}$$_C$ superconductor

Abstract

Upon thermal annealing at or above room temperature (RT) and high pressure $\it P$ $\sim$ 155 GPa, H$_3$S exhibits superconductivity at $\it T_C$ $\sim$ 200 K. Various theoretical frameworks with strong electron-phonon coupling and Coulomb repulsion have reproduced this record-level $\it T_C$. Of particular relevance is that observed H-D isotopic correlations among $\it T_C$, $\it P$, and annealed order indicate limitations on the H-D isotope effect, leaving open for consideration unconventional high-$\it T_C$ superconductivity with electronic-based enhancements. The present work examines Coulombic pairing arising from interactions between neighboring S and H species on separate interlaced sublattices constituting H$_3$S in the Im$\overline{3}$m structure. The optimal transition temperature is calculated from $\it{T}$$_{C0}$ = $\it{k}$$_B$$^{-1}$$\Lambda$$\it{e}$$^2$/$\ell$$\zeta$, with $\Lambda$ = 0.007465 $\AA$, inter-sublattice S-H separation spacing $\zeta$ = $\it{a}$$_0$/$\sqrt{2}$, interaction charge linear spacing $\ell$ = $\it{a}$$_0$(3/$\sigma$)$^{1/2}$, average participating charge fraction $\sigma$ = 3.43 $\pm$ 0.10 estimated from theory, and lattice parameter $\it{a}$$_0$ = 3.0823 \AA. The result $\it{T}$$_{C0}$ = 198.5 $\pm$ 3.0 K is in excellent agreement with transition temperatures determined from resistivity and susceptibility data. Analysis of mid-infrared reflectivity confirms correlation between boson energy and $\zeta$$^{-1}$. Suppression of $\it T_C$ with increasing residual resistance for $<$ RT annealing is treated by scattering-induced pair breaking. Correspondence with layered high-$\it T_C$ superconductor structures are discussed. A model considering Compton scattering of virtual photons of energies $\leq$ $\it e$$^2$/$\zeta$ by inter-sublattice electrons is introduced, illustrating $\Lambda$ is proportional to the reduced electron Compton wavelength.