Spectroscopic evidence of a new energy scale for superconductivity in H3S

Are hydrides under high-pressure-high-temperature superconductors?

Contrary to the current consensus, I argue that the existing evidence for high-temperature superconductivity in hydrides under high pressure is not compelling. I suggest that the focus of the field should urgently shift to establish unequivocally experimentally whether or not superconductivity in pressurized hydrides exists, instead of continuing to search for new materials that might show elusive signals of unproven superconductivity at ever higher temperatures. The implications of a negative finding for the theoretical understanding of superconductivity are discussed.

Future Study of Dense Superconducting Hydrides at High Pressure

The discovery of a record high superconducting transition temperature (Tc) of 288 K in a pressurized hydride inspires new hope to realize ambient-condition superconductivity. Here, we give a perspective on the theoretical and experimental studies of hydride superconductivity. Predictions based on the BCS-Eliashberg-Midgal theory with the aid of density functional theory have been playing a leading role in the research and guiding the experimental realizations. To date, about twenty hydrides experiments have been reported to exhibit high-Tc superconductivity and their Tc agree well with the predicted values. However, there are still some controversies existing between the predictions and experiments, such as no significant transition temperature broadening observed in the magnetic field, the experimental electron-phonon coupling beyond the Eliashberg-Midgal limit, and the energy dependence of density of states around the Fermi level. To investigate these controversies and the origin of the highest Tc in hydrides, key experiments are required to determine the structure, bonding, and vibrational properties associated with H atoms in these hydrides.

Cooper-pair distribution function [Formula: see text] for superconducting [Formula: see text] and [Formula: see text]

Cooper-pair distribution function, [Formula: see text], is a recent theoretical proposal that reveals information about the superconductor state through the determination of the spectral regions where Cooper pairs are formed. This is built from the well-established Eliashberg spectral function and phonon density of states, calculated by first-principles. From this function is possible to obtain the [Formula: see text] parameter, which is proportional to the total number of Cooper pairs formed at a critical temperature [Formula: see text]. Herein, we reported [Formula: see text] function of the compressed [Formula: see text] and [Formula: see text] high-[Formula: see text] conventional superconductors, including the effect of stable sulfur isotopes in [Formula: see text]. [Formula: see text] suggests that the vibration energy range of 10-70 meV is where the Cooper pairs are possible for these superconductors, pointing out the possible importance of the low-energy region on the electron-phonon superconductivity. This has been confirmed by the fact that a simple variation in the low-frequency region induced for the substitution of S atoms in [Formula: see text] by its stable isotopes can lead to important changes in [Formula: see text]. The results also show proportionality between [Formula: see text] parameter and experimental or theoretical [Formula: see text] values.

Synthesis of Yttrium Superhydride Superconductor with a Transition Temperature up to 262 K by Catalytic Hydrogenation at High Pressures

The recent observation of room-temperature superconductivity will undoubtedly lead to a surge in the discovery of new, dense, hydrogen-rich materials. The rare earth metal superhydrides are predicted to have very high-T_{c} superconductivity that is tunable with changes in stoichiometry or doping. Here we report the synthesis of an yttrium superhydride that exhibits superconductivity at a critical temperature of 262 K at 182±8  GPa. A palladium thin film assists the synthesis by protecting the sputtered yttrium from oxidation and promoting subsequent hydrogenation. Phonon-mediated superconductivity is established by the observation of zero resistance, an isotope effect and the reduction of T_{c} under an external magnetic field. The upper critical magnetic field is 103 T at zero temperature.

The higher superconducting transition temperatureTcand the functional derivative ofTcwithα2F(ω) for electron-phonon superconductors

This work presents an analysis of the functional derivative of the superconducting transition temperatureT_cwith respect to the electron-phonon coupling functionα²F(ω) [δT_c/δα²F(ω)] andα²F(ω) spectrum of H₃S (Im3̄m), in the pressure range where the high-T_cwas measured (155-225 GPa). The calculations are done in the framework of the Migdal-Eliashberg theory. We find for this electron-phonon superconductor, a correlation between the maximums ofδT_c/δα²F(ω) andα²F(ω) with its higherT_c. We corroborate this behavior in other electron-phonon superconductors by analyzing data available in the literature, which suggests its validity in this type of superconductors. The correlation observed could be considered as a theoretical tool that in an electron-phonon superconductor, allows describing qualitatively the proximity to its highestT_c, and determining the optimal physical conditions (pressure, alloying or doping concentration) that lead to the superconductor reaching its highestT_cpossible.

Topological phase transition in superconductors with mirror symmetry

We provide analytical and numerical evidence that the attractive two-dimensional Kitaev model on a lattice with mirror symmetry demonstrates an unusual 'intrinsic' phase at half filling. This phase emerges in the phase diagram at the boundary separating two topological superconductors with opposite Chern numbers and exists due to the condensation of non-zero momentum Cooper pairs. Unlike Fulde-Ferrell-Larkin-Ovchinnikov superconductivity, the Cooper pairs momenta are lying along two lines in the Brillouin zone meaning simultaneous condensation of a continuum of Cooper pairs.

A chemical perspective on high pressure crystal structures and properties

The general availability of third generation synchrotron sources has ushered in a new era of high pressure research. The crystal structure of materials under compression can now be determined by X-ray diffraction using powder samples and, more recently, from multi-nano single crystal diffraction. Concurrently, these experimental advancements are accompanied by a rapid increase in computational capacity and capability, enabling the application of sophisticated quantum calculations to explore a variety of material properties. One of the early surprises is the finding that simple metallic elements do not conform to the general expectation of adopting 3D close-pack structures at high pressure. Instead, many novel open structures have been identified with no known analogues at ambient pressure. The occurrence of these structural types appears to be random with no rules governing their formation. The adoption of an open structure at high pressure suggested the presence of directional bonds. Therefore, a localized atomic hybrid orbital description of the chemical bonding may be appropriate. Here, the theoretical foundation and experimental evidence supporting this approach to the elucidation of the high pressure crystal structures of group I and II elements and polyhydrides are reviewed. It is desirable and advantageous to extend and apply established chemical principles to the study of the chemistry and chemical bonding of materials at high pressure.

Computational Design of Novel Hydrogen-Rich YS-H Compounds

The recent successful findings of H3S and LaH10 compressed above 150 GPa with a record high T c (above 200 K) have shifted the focus on hydrogen-rich materials for high superconductivity at high pressure. Moreover, some studies also report that transition-metal ternary hydrides could be synthesized at a relatively low pressure (∼10 GPa). Therefore, it is highly desirable to investigate the crystal structures of ternary hydrides compounds at high pressure since they have been long considered as promising superconductors and hydrogen-storage materials with a high T c, and can be possibly synthesized at low pressure as well. In this work, combining state-of-the-art crystal structure prediction and first-principles calculations, we have performed extensive simulations on the crystal structures of YSH n (n = 1-10) compounds from ambient pressure to 200 GPa. We uncovered three thermodynamically stable compounds with stoichiometries of YSH, YSH2, and YSH5, which became energetically stable at ambient pressure, 143, and 87 GPa, respectively. Remarkably, it is found that YSH contains monoatomic H atoms, while YSH2 and YSH5 contain a mixture of atomlike and molecular hydrogen units. Upon compression, YSH, YSH2, and YSH5 undergo a transition from a semiconductor to a metallic phase at pressures of 168, 143, and 232 GPa, respectively. Unfortunately, electron-phonon coupling calculations reveal that these compounds possess a weak superconductivity with a relatively low T c (below 1 K), which mainly stem from the low value of density of states occupation at the Fermi level (E F). These results highlight that the crystal structures play a critical role in determining the high-temperature superconductivity.

High-pressure integrated synchrotron infrared spectroscopy system at the Shanghai Synchrotron Radiation Facility

We describe a new integrated optical spectroscopy facility for high-pressure research in materials research and mineral science located at the beamline BL01B of the Shanghai Synchrotron Radiation Facility. The system combines infrared synchrotron Fourier-Transform spectroscopy with broadband laser visible/near infrared and conventional laser Raman spectroscopy in one instrument. The system utilizes a custom-built microscope optics designed for a variety of diamond anvil cell experiments, which include low-temperature and ultrahigh pressure studies. We demonstrate the capabilities of the facility for studies of a variety of high-pressure phenomena such as phase and electronic transitions and chemical transformations.

Superconducting phase diagram of H3S under high magnetic fields

The discovery of superconductivity at 260 K in hydrogen-rich compounds like LaH₁₀ re-invigorated the quest for room temperature superconductivity. Here, we report the temperature dependence of the upper critical fields μ₀H_c2(T) of superconducting H₃S under a record-high combination of applied pressures up to 160 GPa and fields up to 65 T. We find that H_c2(T) displays a linear dependence on temperature over an extended range as found in multigap or in strongly-coupled superconductors, thus deviating from conventional Werthamer, Helfand, and Hohenberg (WHH) formalism. The best fit of H_c2(T) to the WHH formalism yields negligible values for the Maki parameter α and the spin-orbit scattering constant λ_SO. However, H_c2(T) is well-described by a model based on strong coupling superconductivity with a coupling constant λ ~ 2. We conclude that H₃S behaves as a strong-coupled orbital-limited superconductor over the entire range of temperatures and fields used for our measurements.

Orbital Symmetry and Orbital Excitations in High-Tc Superconductors

We discuss a few possibilities of high- T c superconductivity with more than one orbital symmetry contributing to the pairing. First, we show that the high energies of orbital excitations in various cuprates suggest a simplified model with a single orbital of x 2 − y 2 symmetry doped by holes. Next, several routes towards involving both e g orbital symmetries for doped holes are discussed: (i) some give superconductivity in a CuO 2 monolayer on Bi2212 superconductors, Sr 2 CuO 4 − δ , Ba 2 CuO 4 − δ , while (ii) others as nickelate heterostructures or Eu 2 − x Sr x NiO 4 , could in principle realize it as well. At low electron filling of Ru ions, spin-orbital entangled states of t 2 g symmetry contribute in Sr 2 RuO 4 . Finally, electrons with both t 2 g and e g orbital symmetries contribute to the superconducting properties and nematicity of Fe-based superconductors, pnictides or FeSe. Some of them provide examples of orbital-selective Cooper pairing.

Coexistence of pressure-induced structural phases in bulk black phosphorus: a combined x-ray diffraction and Raman study up to 18 GPa

We report a study of the structural phase transitions induced by pressure in bulk black phosphorus by using both synchrotron x-ray diffraction for pressures up to 12.2 GPa and Raman spectroscopy up to 18.2 GPa. Very recently black phosphorus attracted large attention because of the unique properties of few-layers samples (phosphorene), but some basic questions are still open in the case of the bulk system. As concerning the presence of a Raman spectrum above 10 GPa, which should not be observed in an elemental simple cubic system, we propose a new explanation by attributing a key role to the non-hydrostatic conditions occurring in Raman experiments. Finally, a combined analysis of Raman and XRD data allowed us to obtain quantitative information on presence and extent of coexistences between different structural phases from ~5 up to ~15 GPa. This information can have an important role in theoretical studies on pressure-induced structural and electronic phase transitions in black phosphorus.

Detecting Superconductivity in the High Pressure Hydrides and Metallic Hydrogen from Optical Properties

We present a new technique for measuring the critical temperature T_{c} in the high pressure, high T_{c} electron-phonon-driven superconducting hydrides. This technique does not require connecting leads to the sample. In the region of the absorption spectrum above the sum of the optical gap and maximum phonon energy, the reflectance mirrors the temperature variation of the superconducting order parameter. For an appropriately chosen value of fixed photon energy, the temperature dependence of the reflectance varies much more rapidly below T=T_{c} than above. It increases with increasing temperature in the superconducting state while it decreases in the normal state. Examining the temperature dependence of the reflectance at a fixed photon energy, there is a cusp at T=T_{c} which provides a measurement of the critical temperature. We discuss these issues within the context of the recently reported atomic metallic phase of hydrogen, but our proposed technique should prove useful for other hydrides with large coupling to high energy phonons.

Strong Electron-Phonon and Band Structure Effects in the Optical Properties of High Pressure Metallic Hydrogen

The recent claim of having produced metallic hydrogen in the laboratory relies on measurements of optical spectra. Here, we present first-principles calculations of the reflectivity of hydrogen between 400 and 600 GPa in the I4_{1}/amd crystal structure, the one predicted at these pressures, based on both time-dependent density functional and Eliashberg theories, thus, covering the optical properties from the infrared to the ultraviolet regimes. Our results show that atomic hydrogen displays an interband plasmon at around 6 eV that abruptly suppresses the reflectivity, while the large superconducting gap energy yields a sharp decrease of the reflectivity in the infrared region approximately at 120 meV. The experimentally estimated electronic scattering rates in the 0.7-3 eV range are in agreement with our theoretical estimations, which show that the huge electron-phonon interaction of the system dominates the electronic scattering in this energy range. The remarkable features in the optical spectra predicted here encourage extending the optical measurements to the infrared and ultraviolet regions as our results suggest optical measurements can potentially identify high-pressure phases of hydrogen.

Superconducting Hydrogen Sulfide

The recent discovery of superconductivity above 200 K in hydrogen sulfide under high pressure marks a milestone in superconductor research. Not only does its critical temperature T_c exceed the previous record in cuprates by more than 50 K, the superconductivity in hydrogen sulfide also exhibits convincing evidence that it is of conventional phonon-mediated type. Moreover, this is the first time that a previously unknown high-T_c superconductor is predicted by theory and afterwards verified by experiment. In this Minireview, we survey the progress made in the last three years in understanding this novel material, and discuss unsolved problems and possible developments to encourage future investigations.

Strong electron–phonon interaction retarding phonon transport in superconducting hydrogen sulfide at high pressures

Ultrahigh pressure greatly shortens interatomic distances and induces strong electron–phonon coupling that significantly reduces the phonon transport of superconducting H₃S.

Strain-induced modulations of electronic structure and electron–phonon coupling in dense H3S

External stress is an effective tool to modulate the Fermi surface topology, logarithmic average frequency, and electron–phonon coupling parameter of dense H₃S and thus has a sensitive and considerable effect to the superconducting critical temperature.

Compressed H3S: inter-sublattice Coulomb coupling in a high-T C superconductor

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 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 H₃S in the Im[Formula: see text]m structure. The optimal value of the transition temperature is calculated from T _C0  =  [Formula: see text]Λe ²/[Formula: see text] ζ, with Λ  =  0.007465 Å, inter-sublattice S-H separation spacing ζ  =  a ₀/[Formula: see text], interaction charge linear spacing [Formula: see text] =  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 H₃S 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.