The Superconducting Transition Temperatures of CSH Based on InterSublattice S–H4Tetrahedron Electronic Interactions, D. R. Harshman and A. T. Fiory [arXiv]
Significant characteristics of the superconducting transitions reported for carbonaceous sulfur hydride [Snider et al., Nature 585, 373 (2020)] are the exceptionally abrupt onset temperatures and … Continue reading ]]>
The Superconducting Transition Temperatures of CSH Based on InterSublattice S–H_{4}Tetrahedron Electronic Interactions, D. R. Harshman and A. T. Fiory [arXiv]
Significant characteristics of the superconducting transitions reported for carbonaceous sulfur hydride [Snider et al., Nature 585, 373 (2020)] are the exceptionally abrupt onset temperatures and their marked increase toward room temperature at high pressure. Theoretical and experimental studies addressing the superconducting composition and structure have thus far returned mixed results. One possibility, consistent with the experimentally suggested stoichiometry of CSH_{x}, is the theoreticallydiscovered compressed I43m CSH_{7} structure [Sun et al., Phys. Rev. B 101, 174102 (2020)], which comprises a sublattice similar to Im3m 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 Im3m H_{3}S, in which pairing is induced via purely electronic Coulomb interactions across the mean distance ζ between the S and H_{4} tetrahedra enclosing C. Theoretical superconducting transition temperatures for I43m CSH_{7} are derived as T_{C0} = (2/3)^{1/2}σ^{1/2}β/aζ, where β = 1247.4 Å^{2}K is a universal constant, σ is the participating charge fraction, and a is the lattice parameter. Analysis suggests persistent bulk superconductivity with a pressuredependent σ, increasing from σ = 3.5, determined previously for Im3m H_{3}S, to σ = 7.5 at high pressure owing to additionally participating CH bond electrons. With a and ζ determined by theoretical structure, T_{C0} = 283.6 ± 3.5 K is predicted at 267 ± 10 GPa, in excellent agreement (within uncertainty) with the corresponding experimental T_{C} = 287.7 ± 1.2 K. Pressureinduced variations in σ combined with experimental uncertainties in pressure yield overall average (T_{C} − T_{C0}) = (−0.8 ± 3.5).
Dale R. Harshman and Anthony T. Fiory, Journal of Applied Physics 131, 015105 (2022).
]]>Letter/Comment on: Improved predictions for superconductors, D. R. Harshman and A. T. Fiory [arXiv]
An open letter/comment to Physics on M. Rini, Physics 13, s94 (July 27, 2020) and A. Sanna et al., Phys. Rev. Lett. 125, 057001 (2020).
Fig. 1. … Continue reading ]]>
Letter/Comment on: Improved predictions for superconductors, D. R. Harshman and A. T. Fiory [arXiv]
An open letter/comment to Physics on M. Rini, Physics 13, s94 (July 27, 2020) and A. Sanna et al., Phys. Rev. Lett. 125, 057001 (2020).
D. R. Harshman and A. T. Fiory, An open letter to Physics, arXiv:2102.10459 [condmat.suprcon] (2021).
]]>Superconductivity in Hydrogen Clathrates Mediated by Coulomb Interactions between Hydrogen and CentralAtom Electrons, D. R. Harshman and A. T. Fiory [arXiv]
The uniquely characteristic macrostructures of binary hydrogenclathrate compounds MHn formed at high pressure, a cage of hydrogens surrounding a centralatom host, is theoretically predicted in … Continue reading ]]>
Superconductivity in Hydrogen Clathrates Mediated by Coulomb Interactions between Hydrogen and CentralAtom Electrons, D. R. Harshman and A. T. Fiory [arXiv]
The uniquely characteristic macrostructures of binary hydrogenclathrate compounds MH_{n} formed at high pressure, a cage of hydrogens surrounding a centralatom host, is theoretically predicted in various studies to include structurally stable phononmediated superconductors. High superconductive transition temperatures T_{C} have thus far been measured for syntheses with M = La, Y, and Th. In compressed LaH_{10}, independent studies report T_{C} of 250 K and over 260 K, a maximum in T_{C} with pressure P, and normalstate resistance scaling with temperature (suggesting unconventional pairing). According to reported band structure calculations of Fm3mphase LaH_{10}, the La is anionic, with the chemical valence electrons appearing evenly split between La and H_{10}. Thus, compressed LaH_{10} contains the combination of structure, charge separation, and optimal balanced allocation of valence electrons for supporting unconventional highT_{C} superconductivity mediated by Coulomb interactions between electronic charges associated with La and H_{10}. A general expression for the optimal superconducting transition temperature for MH_{n} clathrates is derived as T_{C0} = k_{B}^{1}Λ[(n + v)/2A]^{1/2}e^{2}/ζ, where Λ 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 Hpolyhedron cage, and ζ is the mean distance between the M site and the centroids of the polyhedron faces. Applied to Fm3m LaH_{10}, T_{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, and HD isotope effect in T_{C} of Fm3m LaH_{10} and Im3m H_{3}S are discussed, along with a generalized prospective for Coulombmediated superconductivity in MH_{n}.
Dale R. Harshman and Anthony T. Fiory, Journal of Superconductivity and Novel Magnetism 33, 2945 (2020).
]]>HighTC Superconductivity Originating from Interlayer Coulomb Coupling in GateCharged Twisted Bilayer Graphene Moiré Superlattices, D. R. Harshman and A. T. Fiory [arXiv]
Unconventional superconductivity in bilayer graphene has been reported for twist angles θ near the first magic angle and charged electrostatically with holes near half filling … Continue reading ]]>
HighT_{C} Superconductivity Originating from Interlayer Coulomb Coupling in GateCharged Twisted Bilayer Graphene Moiré Superlattices, D. R. Harshman and A. T. Fiory [arXiv]
Unconventional superconductivity in bilayer graphene has been reported for twist angles θ near the first magic angle and charged electrostatically with holes near half filling of the lower flat bands. A maximum superconducting transition temperature T_{C} ≈ 1.7 K was reported for a device with θ = 1.05° at ambient pressure and a maximum T_{C} ≈ 3.1 K for a device with θ = 1.27° under 1.33 GPa hydrostatic pressure. A highT_{C} model for the superconductivity is proposed herein, where pairing is mediated by Coulomb coupling between charges in the two graphene sheets. The expression derived for the optimal transition temperature, T_{C0} = k_{B}^{−1}Λ(n_{opt} − n_{0}/2)^{1/2}e^{2}/ζ, is a function of mean bilayer separation distance ζ, measured gated charge areal densities n_{opt} and n_{0} corresponding to maximum T_{C} and superconductivity onset, respectively, and the length constant Λ = 0.00747(2) Å. Based on existing experimental carrier densities and theoretical estimates for ζ, T_{C0} = 1.94(4) K is calculated for the θ = 1.05° ambientpressure device and T_{C0} = 3.02(3) K for the θ = 1.27° pressurized device. Experimental meanfield transition temperatures T_{C}^{mf} = 1.83(5) K and T_{C}^{mf} = 2.86(5) K are determined by fitting superconducting fluctuation theory to resistance transition data for the ambientpressure and pressurized devices, respectively; the theoretical results for T_{C0} are in remarkable agreement with these experimental values. Corresponding BerezinskiiKosterlitzThouless temperatures T_{BKT} of 0.96(3) K and 2.2(2) K are also determined and interpreted.
Dale R. Harshman and Anthony T. Fiory, Journal of Superconductivity and Novel Magnetism 33, 367 (2020).
]]>Compressed H3S: intersublattice Coulomb coupling in a highTC superconductor, D. R. Harshman and A. T. Fiory [arXiv]
Upon thermal annealing at or above room temperature (RT) and at high hydrostatic pressure P ~ 155 GPa, sulfur trihydride H3S exhibits a measured maximum superconducting transition temperature TC … Continue reading ]]>
Compressed H_{3}S: intersublattice Coulomb coupling in a highT_{C} superconductor, D. R. Harshman and A. T. Fiory [arXiv]
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 electronphonon coupling and Coulomb repulsion have reproduced this recordlevel T_{C}. Of particular relevance is that experimentally observed HD isotopic correlations among T_{C}, P, and annealed order indicate an HD isotope effect exponent α limited to values ≤ 0.183, leaving open for consideration unconventional highT_{C} superconductivity with electronicbased 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 Im3m structure. The optimal value of the transition temperature is calculated from T_{C0} = k_{B}^{–1}Λe^{2}/ℓζ, with Λ= 0.007465 Å, intersublattice SH 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 Hprojected 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 midinfrared 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 scatteringinduced pair breaking. Correspondences between H_{3}S and layered highT_{C} superconductor structures are also discussed, and a model considering Compton scattering of virtual photons of energies ≤ e^{2}/ζ by intersublattice electrons is introduced, illustrating that Λ ∝ ƛ_{C}, where ƛ_{C} is the reduced electron Compton wavelength.
Illustration of Im3m unit cell of compressed H_{3}S with color contrast distinguishing the two simple cubic sublattices; basis H_{3}S is shown with S larger than H. Lattice parameter a_{0} is cube edge; intersublattice SH distance ζ is onehalf cube face diagonal. 

Variation of measured T_{C} of H_{3}S with applied pressure P for ≥ RT (room temperature) anneal, green circles with center dot, and < RT anneal, blue circles (from [1, 5, 6]). Gray symbols are various theoretical calculations denoted as (D) [2], (E) [4], (P) [8], (A) [10], (K) [11], (G) [13], (F) [14], (S) [16], (К) [17], and (J) [18]; structure indicated where available. Red square symbol (H) corresponds to T_{C0} from this work. 
Dale R. Harshman and Anthony T. Fiory, Journal of Physics: Condensed Matter 29, 445702 (2017).
]]>On the Isotope Effect in Compressed Superconducting H3S and D3S, D. R. Harshman and A. T. Fiory [arXiv]
A maximum superconductive transition temperature TC = 203.5 K has recently been reported for a sample of the binary compound trihydrogen sulfide (H3S) prepared at high pressure … Continue reading ]]>
On the Isotope Effect in Compressed Superconducting H_{3}S and D_{3}S, D. R. Harshman and A. T. Fiory [arXiv]
A maximum superconductive transition temperature T_{C} = 203.5 K has recently been reported for a sample of the binary compound trihydrogen 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 phononbased 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 vs. 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 phononbased theories.
Transition temperatures T_{C} for H_{3}S (green circles) and D_{3}S (blue circles) vs. applied pressure P with corresponding dashed lines fitted to joined linear trends using equation (1) of the article with parameters in table 1 of the article (left scale). Residual resistance ratios RRR are shown for H_{3}S (red triangles) and D_{3}S (red diamonds) vs. P (right scale). Data are for samples annealed at or above room temperature (see REfs. [1,2] of the article). 

Residual resistance ratio RRR vs. fractional transition width ΔT_{C}/T_{C} for samples of H_{3}S (green triangles) and D_{3}S (blue diamonds). A linearly fitted dashed line is drawn to indicate the trend.  Transition temperature T_{C} vs. residual resistance ratio RRR for H_{3}S (green triangles) and D_{3}S (blue diamonds). The eight symbols with dot fill correspond to data for P ≳ P_{m} with trend shown by the fitted dashed line. 
Dale R. Harshman and Anthony T. Fiory, Supercond. Sci. and Technol. 30, 045011 (2017).
]]>HighTC Superconductivity in Cs3C60 Compounds Governed by Local CsC60 Coulomb Interactions, D. R. Harshman and A. T. Fiory [arXiv]
Unique among alkalidoped A3C60 fullerene compounds, the A15 and fcc forms of Cs3C60 exhibit superconducting states varying under hydrostatic pressure with highest transition temperatures at TCmeas = 38.3 … Continue reading ]]>
HighT_{C} Superconductivity in Cs_{3}C_{60} Compounds Governed by Local CsC_{60} Coulomb Interactions, D. R. Harshman and A. T. Fiory [arXiv]
Unique among alkalidoped 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 highT_{C} superconductivity employing nonplanar 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 nuclearspin relaxation and midinfrared 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.
Measured optimal transition temperature T_{C}^{meas} versus (ℓζ)^{–1} for A15 Cs_{2.85(1)}C_{60} and fcc Cs_{2.901(6)}C_{60} (legend upper left), compared to other highT_{C} superconductors: cuprates; iron pnictides and chalcogenides; intercalated group4metal nitridechlorides; and RuO and ETbased compounds (legend lower right). The line represents the theoretical T_{C0}. 

Maximum measured transition temperature T_{C}^{max} plotted against Rb content x in Rb_{x}Cs_{3–x}C_{60} for x = 0 and x = 0.35, 0.5, 0.75 and 1), denoted by circle symbols. Triangles denote corresponding measured V_{per C60}. Dashed curves are guides to the eye. After Refs. [8] and [13] of paper. 
Dale R. Harshman and Anthony T. Fiory, J. Phys.: Condens. Matter 29, 145602 (2017).
]]>Optimal HighTC Superconductivity in Cs3C60, D. R. Harshman and A. T. Fiory
The highest superconducting transition temperatures in the (A1xBx)3C60 superconducting family are seen in the A15 and FCC structural phases of Cs3C60 (optimized under hydrostatic pressure), exhibiting measured values for nearstoichiometric samples of TC0meas. = 37.8 … Continue reading ]]>
Optimal HighT_{C} Superconductivity in Cs_{3}C_{60}, D. R. Harshman and A. T. Fiory
The highest superconducting transition temperatures in the (A_{1x}B_{x})_{3}C_{60} superconducting family are seen in the A15 and FCC structural phases of Cs_{3}C_{60} (optimized under hydrostatic pressure), exhibiting measured values for nearstoichiometric samples of T_{C0}^{meas.} = 37.8 K and 35.7 K, respectively. It is argued these two Csintercalated C_{60} compounds represent the optimal materials of their respective structures, with superconductivity originating from Coulombic e–h interactions between the C_{60} molecules, which host the ntype superconductivity, and mediating holes associated with the Cs cations. A variation of the interlayer Coulombic pairing model [Harshman and Fiory, J. Supercond. Nov. Magn. 28, 2967 (2015), and references therein] is introduced in which T_{C0}^{calc.} ∝ 1/ℓζ where ℓ relates to the mean spacing between interacting charges on surfaces of the C_{60} molecules, and ζ is the average radial distance between the surface of the C_{60} molecules and the neighboring Cs cations. For stoichiometric Cs_{3}C_{60}, T_{C0}^{calc.} = 38.08 K and 35.67 K for the A15 and FCC macrostructures, respectively; the dichotomy is attributable to differences in ζ.
Dale R. Harshman and Anthony T. Fiory, APS Meeting (abstract: MAR162015004113), Baltimore, Maryland, 1418 March 2016 (slides).
]]>Modeling Intercalated Group4Metal Nitride Halide Superconductivity with Interlayer Coulomb Coupling, D. R. Harshman and A. T. Fiory [arXiv]
Behavior consistent with Coulombmediated highTC superconductivity is shown to be present in the intercalated group4metal nitride halides Ax(S)yMNX, where the MNX host (M = Ti, Zr, Hf; … Continue reading ]]>
Modeling Intercalated Group4Metal Nitride Halide Superconductivity with Interlayer Coulomb Coupling, D. R. Harshman and A. T. Fiory [arXiv]
Behavior consistent with Coulombmediated highT_{C} superconductivity is shown to be present in the intercalated group4metal nitride halides A_{x}(S)_{y}MNX, where the MNX host (M = Ti, Zr, Hf; X = Cl, Br) is partially intercalated with cations A_{x} and optionally molecular species (S)_{y} in the van der Waals gap between the halide X layers, expanding the basalplane spacing d. The optimal transition temperature is modeled by T_{C0} ∝ ζ^{–1}(σ/A)^{1/2}, where the participating fractional charge per area per formula unit σ/A and the distance ζ, given by the transverse A_{x}–X separation (ζ < d), govern the interlayer Coulomb coupling. From experiment results for βform compounds based on Zr and Hf, in which concentrations x of A_{x} are varied, it is shown that σ = γ[v(x_{opt} − x_{0})], where x_{opt} is the optimal doping, x_{0} is the onset of superconducting behavior, v is the A_{x} charge state, and γ = 1/8 is a factor determined by the model. Observations of T_{C} < T_{C0} in the comparatively more disordered αA_{x}(S)_{y}TiNX compounds are modeled as pairbreaking by remote Coulomb scattering from the A_{x} cations, which attenuates exponentially with increasing ζ. The T_{C0} values calculated for nine A_{x}(S)_{y}MNCl compounds, shown to be optimal, agree with the measured T_{C} to within experimental error. The model for T_{C0} is also found to be consistent with the absence of highT_{C} characteristics for A_{x}MNX compounds in which a spatially separated intercalation layer is not formed.
Dale R. Harshman and Anthony T. Fiory, J. Supercond. Nov. Mater. 28, 2967 (2015).
Superconducting Interaction Charge in ThalliumBased HighTC Cuprates: Roles of cation oxidation state and electronegativity, D. R. Harshman and A. T. Fiory [arXiv]
Superconductivity in the Tlbased cuprates encompasses a notably broad range of measured optimal transition temperatures TC0, ranging from lowest in the chargedepleted Tl1201 compounds … Continue reading ]]>
Superconducting Interaction Charge in ThalliumBased HighT_{C} Cuprates: Roles of cation oxidation state and electronegativity, D. R. Harshman and A. T. Fiory [arXiv]
Superconductivity in the Tlbased cuprates encompasses a notably broad range of measured optimal transition temperatures T_{C0}, ranging from lowest in the chargedepleted Tl1201 compounds (Tl_{1–x}(Ba/Sr)_{1+y}La_{1–y}CuO_{5–δ}), such as Tl_{0.7}LaSrCuO_{5} (37 K) and TlBa_{1.2}La_{0.8}CuO_{5} (45.4 K), to highest in the Tl1223 compound TlBa_{2}Ca_{2}Cu_{3}O_{9±δ} (133.5 K). Seven Tlbased cuprates are considered and compared using the model of superconductive pairing via electronic interactions between two physically separated charge reservoirs, where T_{C0} ∝ (ση/A)^{1/2 }ζ^{–1} is determined by the superconducting interaction charge fraction σ the number η of CuO_{2} layers, and the basalplane area A, each per formula unit, and the transverse distance ζ between interacting layers. Herein it is demonstrated that σ follows from the elemental electronegativity and the oxidation state of Tl, and other structurally analogous cations. The comparatively lower elemental electronegativity of Tl, in conjunction with its oxidation state, explains the higher σ and T_{C0} values in the Tlbased compounds relative to their Bibased cuprate homologues. A derivation of σ is introduced for the optimal Tl_{2}Ba_{2}Ca_{η–1}Cu_{η}O_{2η+2} (for η = 1, 2, 3) compounds, which exhibit a Tl oxidation state at or near +3, obtaining the fundamental value σ_{0} = 0.228 previously established for YBa_{2}Cu_{3}O_{6.92}. Also reported is the marked enhancement in σ associated with Tl^{+1} and analogous innerlayer cations relative to highervalence cations. For a model proposition of σ = σ_{0}, the fractional Tl^{+1} content of the mixedvalence compound, TlBa_{2}Ca_{2}Cu_{3}O_{9±δ}, is predicted to be 1/3 at optimization, in agreement with existing data. Charge depletion is illustrated for the two Tl1201 compounds, where σ < σ_{0} values are determined according to substitution of Ba^{+2} or Sr^{+2} by La^{+3}, and/or Tl depletion. Additionally, statistical analysis of calculated and experimental transition temperatures of 48 optimal superconductors shows an absence of bias in determining σ, A, and ζ.
Dale R. Harshman and Anthony T. Fiory, J. Phys. Chem. Solids 85, 106 (2015).