Focus on Hydride and High-Pressure Superconductors

The primary mechanism governing the emergence of near-room-temperature superconductivity (NRTS) in superhydrides is widely accepted to be the electron–phonon interaction. If so, the temperature-dependent resistance, R(T), in these materials should obey the Bloch–Grüneisen (BG) equation, where the power-law exponent, p, should be equal to the exact integer value of p= 5. However, there is a well-established theoretical result showing that the pure electron–magnon interaction should be manifested by p= 3, and p= 2 is the value for pure electron–electron interaction. Here we aimed to reveal the type of charge carrier interaction in the layered transition metal dichalcogenides PdTe₂, high-entropy alloy (ScZrNb)_0.65[RhPd]_0.35 and highly-compressed elemental boron and superhydrides H₃S, LaH_x, PrH₉ and BaH₁₂ by fitting the temperature-dependent resistance of these materials to the BG equation, where the power-law exponent, p, is a free-fitting parameter. The results showed that the high-entropy alloy (ScZrNb)_0.65[RhPd]_0.35 exhibited pure electron–phonon mediated superconductivity with p = 4.9 ± 0.4. Unexpectedly, we revealed that all studied superhydrides exhibit 1.8 < p < 3.2. This implies that it is unlikely that the electron–phonon interaction is the primary mechanism for the Cooper pairs formation in highly-compressed superhydrides, and alternative pairing mechanisms, for instance, the electron–magnon, the electron–polaron, the electron–electron and other pairing mechanisms should be considered as the origin for the emergence of NRTS in these compounds.

Critical temperature, T_c, and transition width, ΔT_c, are two primary parameters of the superconducting transition. The latter parameter reflects the superconducting state disturbance originating from the thermodynamic fluctuations, atomic disorder, applied magnetic field, the presence of secondary crystalline phases, applied pressure, etc. Recently, Hirsch and Marsiglio (2021 Phys. Rev. B 103 134505, doi: 10.1103/PhysRevB.103.134505) performed an analysis of the transition width in several near-room-temperature superconductors and reported that the reduced transition width, ΔT_c/T_c, in these materials does not follow the conventional trend of transition width broadening in applied magnetic field observed in low- and high-T_c superconductors. Here, we present a thorough mathematical analysis of the magnetoresistive data, R(T, B), for the high-entropy alloy (ScZrNb)_0.65[RhPd]_0.35 and hydrogen-rich superconductors of Im-3m-H₃S, C2/m-LaH₁₀ and P6₃/mmc-CeH₉. We found that the reduced transition width, ΔT_c/T_c, in these materials follows a conventional broadening trend in applied magnetic field.

Among the metal hydrides, Th₄H₁₅ is the first reported superconductor with a relatively high T_c ≈ 8 K at ambient pressure. Here we report on the synthesis and characterization of a low-T_c superconducting modification of Th₄H₁₅, which is obtained via hydrogenating Th metal at 5 GPa and 800 °C by using the ammonia borane as the hydrogen source. Measurements of resistivity, magnetic susceptibility, and specific heat confirm that the obtained Th₄H₁₅ sample shows a bulk superconducting transition at T_c ≈ 6 K, which is about 2 K lower than that reported previously. Various characteristic superconducting parameters have been extracted for this compound and unusual lattice dynamics were evidenced from the specific-heat analysis.

Recently, Snider et al (2020 Nature 586 373) reported on the observation of superconductivity in highly compressed carbonaceous sulfur hydride, H_x(S,C)_y. The highest critical temperature in H_x(S,C)_y exceeds the previous record of T_c = 280 K by 5 K, as reported by Somayazulu et al (2019 Phys. Rev. Lett. 122 027001) for highly compressed LaH₁₀. In this paper, we analyze experimental temperature-dependent magnetoresistance data, R(T,B), reported by Snider et al. The analysis shows that H_x(S,C)_y compound exhibited T_c = 190 K (P = 210 GPa), has the electron–phonon coupling constant λ_e−ph = 2.0 and the ratio of critical temperature, T_c, to the Fermi temperature, T_F, in the range of 0.011 ⩽ T_c/T_F ⩽ 0.018. These deduced values are very close to the ones reported for H₃S at P = 155–165 GPa (Drozdov et al 2015 Nature 525 73). This means that in all considered scenarios the carbonaceous sulfur hydride 190 K superconductor falls into the unconventional superconductor band in the Uemura plot, where all other highly compressed super-hydride/deuterides are located. It should be noted that our analysis shows that all raw R(T,B) data sets for H_x(S,C)_y samples, for which Snider et al (2020 Nature 586 373) reported T_c > 200 K, cannot be characterized as reliable data sources. Thus, independent experimental confirmation/disproof for high-T_c values in the carbonaceous sulfur hydride are required.

A diamond anvil cell (DAC) has become an effective tool for investigating physical phenomena that occur at extremely high pressure, such as high-transition temperature superconductivity. Electrical transport measurements, which are used to characterize one of the most important properties of superconducting materials, are difficult to perform using conventional DACs. The available sample space in conventional DACs is very small and there is an added risk of electrode deformation under extreme operating conditions. To overcome these limitations, we herein report the fabrication of a boron-doped diamond microelectrode and undoped diamond insulation on a beveled culet surface of a diamond anvil. Using the newly developed DAC, we have performed in-situ electrical transport measurements on sulfur hydride H₂S, which is a well-known precursor of the pressure-induced, high-transition temperature superconducting sulfur hydride, H₃S. These measurements conducted under high pressures up to 192 GPa, indicated the presence of a multi-step superconducting transition, which we have attributed to elemental sulfur and possibly HS₂.

Electron–phonon interaction is of central importance for the electrical and heat transport properties of metals, and is directly responsible for charge-density-waves or (conventional) superconducting instabilities. The direct observation of phonon dispersion anomalies across electronic phase transitions can provide insightful information regarding the mechanisms underlying their formation. Here, we review the current status of phonon dispersion studies in superconductors under hydrostatic and uniaxial pressure. Advances in the instrumentation of high resolution inelastic x-ray scattering beamlines and pressure generating devices allow these measurements to be performed routinely at synchrotron beamlines worldwide.

The experimental discovery of near-room-temperature (NRT) superconductivity in highlycompressed H₃S, LaH₁₀ and YH₆ has restored fundamental interest in the electron–phonon pairing mechanism in superconductors. One of the prerequisites of phonon-mediated NRT superconductivity in highly compressed hydrides is strong electron–phonon interactions, which can be quantified by dimensionless ratios of the Bardeen–Cooper–Schrieffer (BCS) theory vs $\left( {{k_B}{T_c}} \right)/\left( {\hbar {\omega _{ln}}} \right)$ variable, where T_c is the critical temperature and ${\omega _{ln}}$ is the logarithmic phonon frequency (Mitrovic et al 1984 Phys. Rev. B 29 184). However, all known strong-coupling correction functions for the BCS ratios are applicable for $\left( {{k_B}{T_c}} \right)/\left( {\hbar {\omega _{ln}}} \right)$ < 0.20, which is not a high enough $\left( {{k_B}{T_c}} \right)/\left( {\hbar {\omega _{ln}}} \right)$ range for NRT superconductors, because the latter exhibit variable values of 0.13 < $\left( {{k_B}{T_c}} \right)/\left( {\hbar {\omega _{ln}}} \right)$ < 0.32. In this paper, we reanalyze the full experimental dataset (including data for highly compressed H₃S) and find that the strong-coupling correction functions for the gap-to-critical-temperature ratio and for the specific-heat-jump ratio are double-valued nearly linear functions of $\left( {{k_B}{T_c}} \right)/\left( {\hbar {\omega _{ln}}} \right)$.

Since the milestone experimental discovery by Drozdov et al( 2015 Nature 525 73–6) who reported the observation of near-room-temperature (NRT) superconductivity in highly-compressed sulphur hydride, the quest for room-temperature superconductivity is primarily focused on highly-compressed materials. Extreme conditions and space confinement inside a diamond anvil cell (DAC) dramatically limits the number of experimental techniques which can be applied to study highly-compressed superconductors. For this reason, the development of new approaches to characterize materials at extreme conditions is one of the central topics in the field of NRT superconductivity. In this paper, we describe an approach to categorize highly-compressed superconductors, including NRT superconductors, as unconventional superconductors. The primary idea for the classification is based on the empirical finding of Uemura (1997 Physica C 282–7 197) who showed that all unconventional superconductors have the ratio of the superconducting transition temperature, T_c, to the Fermi temperature, T_F, within a range of 0.01 ≤ T_c/T_F ≤ 0.05. To deduce the Fermi temperature in highly-compressed superconductors, we utilize temperature dependence of the upper critical field and the resistance data (which both can be more or less routinely measured for highly-compressed superconductors) and reported results by first principles calculations for these materials. We demonstrate the application of the approach for highly-compressed oxygen, sulphur, lithium, and recently discovered yttrium superhydride polymorphs, YH_n( n = 4,6,7,9) (Troyan et al( 2019 arXiv:1908.01534) and Kong et al( 2019 arXiv:1909.10482)). We also show the application of the approach for the newly discovered uncompressed Nd_2-xSr_xNiO₂ nickelate superconductor.

Hydrogen-rich compounds show high-$T_{\mathrm{c}}$ superconductivity related to dense hydrogen under extremely high pressure (above 100 GPa). A recent investigation to search for high-$T_{\mathrm{c}}$ superconductive hydrides has advanced a synthesis technique using infrared laser heating of a hydrogen source material under conditions of extremely high pressure and temperature. In order to find a suitable synthesis route for high-$T_{\mathrm{c}}$ superconductive hydrides, the selection of a hydrogen source material has to be considered. In this study, the synthesis of hydrogen-rich lanthanum hydrides (LaH_x) was performed using aluminium trihydride (AlH₃) as the hydrogen source. Simple lanthanum on AlH₃ was pressurized at 150 GPa and heated by infrared laser irradiation. After the laser heating, superconductivity at $T_{\mathrm{c}}$ ∼ 70 K was observed at 170 GPa. This indicates that LaH_x (x $<$ 10) was synthesized using AlH₃ as the hydrogen source under conditions of extremely high pressure.

We explored the superconductivity in a oxygen-hydrogen binary system, H_hO_1 − h, under highpressure using an evolutionary algorithm-based materials informatics approach. We searched for metallic and superconducting phases in pressures up to 300 GPa using a crystal structure prediction technique based on a genetic algorithm and first-principles calculations, and found that hydrogen superoxide (HO₂) with an orthorhombic Pnnm, which emerges as a metastable compound in pressure above 180 GPa, is the only compound showing the superconductivity. The superconducting critical temperature $T_{\rm c}$ is 9.78 K at 200 GPa, which is higher than that of pure solid oxygen, 2.87 K, due to the effect of the hydrogenation. We confirmed that the $T_{\rm c}$ value shows a good agreement with potential superconducting critical temperature $T_{\rm c}^{\,\rm pot}$ estimated by the superconductivity predictor, which we have previously developed by a genetic programming using 497 first-principles datasets of other binary hydrides. Moreover, supposing that all the H_hO_1 − h compounds are superconductors at pressures in 150–200 GPa, we investigated the potential superconductivity of the H_hO_1 − h system using the predictor and obtained that $T_{\rm c}^{\,\rm pot}$ shows 10 K for h = 0.033 3 and increases to 100 K with the increase of h to 0.966 7.

Any theory of electron-phonon mediated superconductivity requires knowledge of the full phonon spectrum ${\alpha ^2}\left( \omega \right) \cdot F\left( \omega \right)$ in order to calculate superconducting transition temperature, T_c. However, there is currently no experimental technique for measuring ${\alpha ^2}\left( \omega \right) \cdot F\left( \omega \right)$ in highly-compressed near-room-temperature (NRT) superconductors. In this paper, we propose to advance McMillan's approach (1968 Phys Rev 167 331), which utilises the Debye temperature ${T_\theta }$ (an integrated parameter for the full phonon spectrum), deduced via the fit of experimentally measured temperature-dependent resistance data R(T) to the Bloch-Grüneisen equation for highly-compressed black phosphorous, boron, GeAs, SiH₄, H_xS, D_xS, LaH_x, and LaD_y. By utilizing the relations between T_c, T_θ, and the electron-phonon coupling strength constant λ_e-ph (which can be computed from first-principles calculations), it is possible to affirm/disprove the electron-phonon coupling mechanism in given superconductors. We show that computed λ_e-ph for highly-compressed black phosphorous, boron, GeAs, SiH₄, and for one sample of LaH₁₀ are in a good agreement with λ_e-ph values deduced from experimental data. A remarkable constancy of ${T_\theta } = 1531 \pm 70\,{\rm K}$ for H₃S at different ageing stages is also found. We also show that if the phonon spectra of two isotopic counterparts share an identical shape (or, in the case of highly-compressed superconductors, the same material at different pressures), then within electron-phonon phenomenology, these materials should obey the relation of T_θ,₁/T_θ,2 = T_c,1/T_c,2 = ω_ln,1/ω_ln,2 (where subscripts 1 and 2 designate two isotopic counterparts). We further report that H₃S-D₃S pair ratios of T_c,H3S/T_c,D3S = ω_ln,H3S/ω_ln,D3S = 1.27 are largely different from deduced T_θ,H3S/T_θ,D3S = 1.65. This implies that NRT superconductivity in H₃S-D₃S systems originates from more than one mechanism, where the electron-phonon coupling lifts T_c in H₃S vs D₃S, but the primary origin for the NRT background of T_c ∼ 150 K in both H₃S and D₃S remains to be discovered.