Dale R. Harshman

Digital data for the temperature dependence of electrical resistance, which were extracted and analyzed by Hamlin (arXiv:2210.10766v1) from the pdf file published for "Room temperature superconductivity in a carbonaceous sulfur hydride," show asymmetric serrations in data for 267 GPa in zero magnetic field that comprise smooth and digitized parts. Further analysis shows that the smooth part exhibits a step at the transition of ~16% in magnitude relative to the data. Notably, there is no evidence of asymmetric serrations in extracted data for lower pressures (184-258 GPa) or for 267 GPa in an applied magnetic field (1-9 T). Several questions are raised, the answers to which would help toward resolving these outstanding issues.

Upon thermal annealing at or above room temperature (RT) and at high hydrostatic pressure P ~ 155 GPa, sulfur trihydride H ₃ S exhibits a measured maximum superconducting transition temperature T _C ~ 200 K. Various theoretical frameworks incorporating strong electron–phonon coupling and Coulomb repulsion have reproduced this record-level T _C . Of particular relevance is that experimentally observed H–D isotopic correlations among T _C , P , and annealed order indicate an H–D isotope effect exponent α limited to values ⩽ 0.183, leaving open for consideration unconventional high- T _C superconductivity with electronic-based enhancements. The work presented herein examines Coulombic pairing arising from interactions between neighboring S and H species on separate interlaced sublattices constituting H ₃ S in the Im 3 ¯ m structure. The optimal value of the transition temperature is calculated from T _C0 = k B − 1 Λ e ² / ℓ ζ , with Λ = 0.007465 Å, inter-sublattice S–H separation spacing ζ = a ₀ / 2 , interaction charge linear spacing ℓ = a ₀ (3/ σ ) ^1/2 , average participating charge fraction σ = 3.43 ± 0.10 estimated from calculated H-projected electron states, and lattice parameter a ₀ = 3.0823 Å at P = 155 GPa. The resulting value of T _C0 = 198.5 ± 3.0 K is in excellent agreement with transition temperatures determined from resistivity (196–200 K onsets, 190–197 K midpoints), susceptibility (200 K onset), and critical magnetic fields (203.5 K by extrapolation). Analysis of mid-infrared reflectivity data confirms the expected correlation between boson energy and ζ ⁻¹ . Suppression of T _C below T _C0 , correlating with increasing residual resistance for < RT annealing, is treated in terms of scattering-induced pair breaking. Correspondences between H ₃ S and layered high- T _C superconductor structures are also discussed, and a model considering Compton scattering of virtual photons of energies ⩽ e ² / ζ by inter-sublattice electrons is introduced, illustrating that Λ ∝ ƛ _C , where ƛ _C is the reduced electron Compton wavelength.

A maximum superconductive transition temperature T _C = 203.5 K has recently been reported for a sample of the binary compound tri-hydrogen sulfide (H ₃ S) prepared at high pressure and with room temperature annealing. Measurements of T _C for H ₃ S and its deuterium counterpart D ₃ S have suggested a mass isotope effect exponent α with anomalous enhancements for reduced applied pressures. While widely cited for evidence of phonon-based superconductivity, the measured T _C is shown to exhibit important dependences on the quality and character of the H ₃ S and D ₃ S materials under study; examination of resistance versus temperature data shows that variations in T _C and apparent α are strongly correlated with residual resistance ratio, indicative of sensitivity to metallic order. Correlations also extend to the fractional widths of the superconducting transitions. Using resistance data to quantify and compensate for the evident materials differences between H ₃ S and D ₃ S samples, a value of α = 0.043 ± 0.140 is obtained. Thus, when corrected for the varying levels of disorder, the experimental upper limit (≤0.183) lies well below α derived in phonon-based theories.

Unique among alkali-doped A ₃ C ₆₀ fullerene compounds, the A15 and fcc forms of Cs ₃ C ₆₀ exhibit superconducting states varying under hydrostatic pressure with highest transition temperatures at T C meas = 38.3 and 35.2 K, respectively. Herein it is argued that these two compounds under pressure represent the optimal materials of the A ₃ C ₆₀ family, and that the C ₆₀ -associated superconductivity is mediated through Coulombic interactions with charges on the alkalis. A derivation of the interlayer Coulombic pairing model of high- T _C superconductivity employing non-planar geometry is introduced, generalizing the picture of two interacting layers to an interaction between charge reservoirs located on the C ₆₀ and alkali ions. The optimal transition temperature follows the algebraic expression, T _C0 = (12.474 nm ² K)/ ℓζ , where ℓ relates to the mean spacing between interacting surface charges on the C ₆₀ and ζ is the average radial distance between the C ₆₀ surface and the neighboring Cs ions. Values of T _C0 for the measured cation stoichiometries of Cs _{3− x} C ₆₀ with x ≈ 0 are found to be 38.19 and 36.88 K for the A15 and fcc forms, respectively, with the dichotomy in transition temperature reflecting the larger ζ and structural disorder in the fcc form. In the A15 form, modeled interacting charges and Coulomb potential e ² / ζ are shown to agree quantitatively with findings from nuclear-spin relaxation and mid-infrared optical conductivity. In the fcc form, suppression of T C meas below T _C0 is ascribed to native structural disorder. Phononic effects in conjunction with Coulombic pairing are discussed.