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

Abstract

Upon thermal annealing at or above room temperature (RT) and high pressure $P$ $\sim$ 155 GPa, H${}_3$S exhibits superconductivity at $T_C$ $\sim$ 200 K. Various theoretical frameworks with strong electron-phonon coupling and Coulomb repulsion have reproduced this record-level $T_C$. Of particular relevance is that observed H-D isotopic correlations among $T_C$, $P$, and annealed order indicate limitations on the H-D isotope effect, leaving open for consideration unconventional high-$T_C$ 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 $T$${}_{C0}$ = $k$${}_B$${}^{-1}$$\Lambda$$e$${}^2$/$\ell$$\zeta$, with $\Lambda$ = 0.007465 $\mathring{A}$, inter-sublattice S-H separation spacing $\zeta$ = $a$${}_0$/$\sqrt{2}$, interaction charge linear spacing $\ell$ = $a$${}_0$(3/$\sigma$)${}^{1/2}$, average participating charge fraction $\sigma$ = 3.43 $\pm$ 0.10 estimated from theory, and lattice parameter $a$${}_0$ = 3.0823 Å. The result $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 $T_C$ with increasing residual resistance for $<$ RT annealing is treated by scattering-induced pair breaking. Correspondence with layered high-$T_C$ superconductor structures are discussed. A model considering Compton scattering of virtual photons of energies $\le$ $e$${}^2$/$\zeta$ by inter-sublattice electrons is introduced, illustrating $\Lambda$ is proportional to the reduced electron Compton wavelength.

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