Phase Diagram and High-Temperature Superconductivity of Compressed Selenium Hydrides

Strategies for improving the superconductivity of hydrides under high pressure

The successful prediction and confirmation of unprecedentedly high-temperature superconductivity in compressed hydrogen-rich hydrides signify a remarkable advancement in the continuous quest for attaining room-temperature superconductivity. The recent studies have established a broad scope for developing binary and ternary hydrides and illustrated correlation between specific hydrogen motifs and high-Tcs under high pressures. The analysis of the microscopic mechanism of superconductivity in hydrides suggests that the high electronic density of states at the Fermi level (EF), the large phonon energy scale of the vibration modes and the resulting enhanced electron-phonon coupling are crucial contributors towards the high-Tcphonon-mediated superconductors. The aim of our efforts is to tackle forthcoming challenges associated with elevating theTcand reducing the stabilization pressures of hydrogen-based superconductors, and offer insights for the future discoveries of room-temperature superconductors. Our present Review offers an overview and analysis of the latest advancements in predicting and experimentally synthesizing various crystal structures, while also exploring strategies to enhance the superconductivity and reducing their stabilization pressures of hydrogen-rich hydrides.

Emergent superconductivity in TaO3 at high pressures

Tantalum (Ta) is an interesting transition metal that exhibits superconductivity in its elemental states. Additionally, several Ta chalcogenides (S and Se) have also demonstrated superconducting properties. In this work, we propose the existence of five high-pressure metallic Ta-O compounds (e.g., TaO3, TaO2, TaO, Ta2O, and Ta3O), composed of polyhedra centered on Ta/O atoms. These compounds exhibit distinct characteristics compared to the well-known semiconducting Ta2O5. One particularly interesting finding is that TaO3 shows an estimated superconducting transition temperature (Tc) of 3.87 K at 200 GPa. This superconductivity is primarily driven by the coupling between the low-frequency phonons derived from Ta and the O 2p and Ta 5d electrons. Remarkably, its dynamically stabilized pressure can be as low as 50 GPa, resulting in an enhanced electron-phonon coupling and a higher Tc of up to 9.02 K. When compared to the superconductivity of isomorphic TaX3 (X = O, S, and Se) compounds, the highest Tc in TaO3 is associated with the highest NEF and phonon vibrational frequency. These characteristics arise from the strong electronegativity and small atomic mass of the O atom. Consequently, our findings offer valuable insights into the intrinsic physical mechanisms of high-pressure behaviors in Ta-O compounds.

Superconducting Li10Se electride under pressure

Achieving a compound with interesting multiple coexisting states, such as electride, metallicity, and superconductivity, is of great interest in basic research and practical application. Pressure has become an effective way to realize high-temperature superconductivity in hydrides, whereas most electrides are semiconducting or insulating at high pressure. Here, we have applied swarm-intelligence structural search to identify a hitherto unknown C2/m Li₁₀Se electride that is superconducting at high pressure. More interestingly, Li₁₀Se is estimated to exhibit the highest T_c value of 16 K at 50 GPa, which is the lowest pressure among Li-based chalcogen electrides. This superconducting transition is dominated by Se-related low frequency vibration modes. The increasing electronic occupation of the Se 4d orbital and the decreasing amount of interstitial anion electrons with pressure heighten their coupling with low-frequency phonons, which is responsible for the enhancement of the T_c value. The finding of Li-based chalcogen superconducting electrides provides a reference for the realization of other superconducting electrides at lower pressures.

Study on superconducting Li-Se-H hydrides

The structures, stabilities and superconducting properties of LiSeH_n (n = 4-10) hydrides at 150-300 GPa were studied by the genetic algorithm (GA) and DFT calculation method. Three stable stoichiometries of LiSeH₄, LiSeH₆ and LiSeH₁₀ were uncovered under high pressure. Four other metastable stoichiometries of LiSeH₅, LiSeH₇, LiSeH₈, and LiSeH₉ were also studied. By analyzing the electronic band structure and electronic density of states, C2 LiSeH₄, Pmm2 LiSeH₆ and C2 LiSeH₁₀ were all found to be metal phases above 150 GPa. Electron-phonon coupling calculations showed that C2 LiSeH₄ and Pmm2 LiSeH₆ were promising superconductors. The predicted T_c values of C2 LiSeH₄ and Pmm2 LiSeH₆ were 77 K at 200 GPa and 111 K at 250 GPa, respectively.

Compressed superhydrides: the road to room temperature superconductivity

Room-temperature superconductivity has been a long-held dream and an area of intensive research. The discovery of H₃S and LaH₁₀under high pressure, with superconducting critical temperatures (T_c) above 200 K, sparked a race to find room temperature superconductors in compressed superhydrides. In recent groundbreaking work, room-temperature superconductivity of 288 K was achieved in carbonaceous sulfur hydride at 267 GPa. Here, we describe the important attempts of hydrides in the process of achieving room temperature superconductivity in decades, summarize the main characteristics of high-temperature hydrogen-based superconductors, such as hydrogen structural motifs, bonding features, electronic structure as well as electron-phonon coupling etc. This work aims to provide an up-to-date summary of several type hydrogen-based superconductors based on the hydrogen structural motifs, including covalent superhydrides, clathrate superhydrides, layered superhydrides, and hydrides containing isolated H atom, H₂and H₃molecular units.

Materials by design at high pressures

Pressure, a fundamental thermodynamic variable, can generate two essential effects on materials. First, pressure can create new high-pressure phases via modification of the potential energy surface. Second, pressure can produce new compounds with unconventional stoichiometries via modification of the compositional landscape. These new phases or compounds often exhibit exotic physical and chemical properties that are inaccessible at ambient pressure. Recent studies have established a broad scope for developing materials with specific desired properties under high pressure. Crystal structure prediction methods and first-principles calculations can be used to design materials and thus guide subsequent synthesis plans prior to any experimental work. A key example is the recent theory-initiated discovery of the record-breaking high-temperature superhydride superconductors H3S and LaH10 with critical temperatures of 200 K and 260 K, respectively. This work summarizes and discusses recent progress in the theory-oriented discovery of new materials under high pressure, including hydrogen-rich superconductors, high-energy-density materials, inorganic electrides, and noble gas compounds. The discovery of the considered compounds involved substantial theoretical contributions. We address future challenges facing the design of materials at high pressure and provide perspectives on research directions with significant potential for future discoveries.

Strong correlation between electronic bonding network and critical temperature in hydrogen-based superconductors

By analyzing structural and electronic properties of more than a hundred predicted hydrogen-based superconductors, we determine that the capacity of creating an electronic bonding network between localized units is key to enhance the critical temperature in hydrogen-based superconductors. We define a magnitude named as the networking value, which correlates with the predicted critical temperature better than any other descriptor analyzed thus far. By classifying the studied compounds according to their bonding nature, we observe that such correlation is bonding-type independent, showing a broad scope and generality. Furthermore, combining the networking value with the hydrogen fraction in the system and the hydrogen contribution to the density of states at the Fermi level, we can predict the critical temperature of hydrogen-based compounds with an accuracy of about 60 K. Such correlation is useful to screen new superconducting compounds and offers a deeper understating of the chemical and physical properties of hydrogen-based superconductors, while setting clear paths for chemically engineering their critical temperatures.

Ba with Unusual Oxidation States in Ba Chalcogenides under Pressure

The preparation of compounds with novel atomic oxidation states and emergent properties is of fundamental interest in chemistry. As s-block elements, alkali-earth metals invariably show a +2 formal oxidation state at normal conditions, and among them, barium (Ba) presents the strongest chemical reactivity. Herein, we propose that novel valence states of Ba can be achieved in pressure-induced chalcogenides, where it also shows a feature of 5d-elements. First-principles swarm-intelligence structural search calculations identify three novel stoichiometric compounds: BaCh₄ (Ch = O, S) containing Ba²⁺, Ba₃Ch₂ (Ch = S, Se, Te) with Ba⁺ and Ba²⁺, and Ba₂Ch (Ch = Se, Te) with Ba⁺ cations. The pressure-induced drop of the Ba 5d level relative to Ba 6s is responsible for this unusual oxidation state. These compounds display captivating structural characters, such as Ba-centered polyhedra and chain-shaped Ch units. More interestingly still, the interaction between two Ba⁺ ions ensures their structural stability.

Hydrogen Pentagraphenelike Structure Stabilized by Hafnium: A High-Temperature Conventional Superconductor

The recent discovery of H_{3}S and LaH_{10} superconductors with record high superconducting transition temperatures T_{c} at high pressure has fueled the search for room-temperature superconductivity in the compressed superhydrides. Here we introduce a new class of high T_{c} hydrides with a novel structure and unusual properties. We predict the existence of an unprecedented hexagonal HfH_{10}, with remarkably high value of T_{c} (around 213-234 K) at 250 GPa. As concerns the novel structure, the H ions in HfH_{10} are arranged in clusters to form a planar "pentagraphenelike" sublattice. The layered arrangement of these planar units is entirely different from the covalent sixfold cubic structure in H_{3}S and clathratelike structure in LaH_{10}. The Hf atom acts as a precompressor and electron donor to the hydrogen sublattice. This pentagraphenelike H_{10} structure is also found in ZrH_{10}, ScH_{10}, and LuH_{10} at high pressure, each material showing a high T_{c} ranging from 134 to 220 K. Our study of dense superhydrides with pentagraphenelike layered structures opens the door to the exploration of a new class of high T_{c} superconductors.

Distinguishing the Structures of High-Pressure Hydrides with Nuclear Magnetic Resonance Spectroscopy

The structural characterization of high-pressure hydrides has encountered many difficulties mainly due to the weak X-ray scattering of hydrogen. Herein, we investigate the prospect of detecting the H₃S and LaH₁₀ structures with nuclear magnetic resonance (NMR) spectroscopy. Our calculations demonstrate that the different candidate structures of H₃S (or LaH₁₀) exhibit significant differences in the electric field gradient (EFG) tensor of the ³³S (or ¹³⁹La) sites, indicating that the NMR spectroscopy can well capture the structural differences, even the small changes in the atomic position, and hence can be used to effectively probe the structures and the phase transitions of H₃S and LaH₁₀. Our results clarify the relationship between the structures and the EFG tensor parameters and provide a potential means to detect the structures of high-pressure hydrides.

Intense Reactivity in Sulfur-Hydrogen Mixtures at High Pressure under X-ray Irradiation

Superconductivity near room temperature in the sulfur-hydrogen system arises from a sequence of reactions at high pressures, with X-ray diffraction experiments playing a central role in understanding these chemical-structural transformations and the corresponding S:H stoichiometry. Here we document X-ray irradiation acting as both a probe and as a driver of chemical reaction in this dense hydride system. We observe a reaction between molecular hydrogen (H₂) and elemental sulfur (S₈) under high pressure, induced directly by X-ray illumination, at photon energies of 12 keV using a free electron laser. The rapid synthesis of hydrogen sulfide (H₂S) at 0.3 GPa was confirmed by optical observations, spectroscopic measurements, and microstructural changes detected by X-ray diffraction. These results document X-ray induced chemical synthesis of superconductor-forming dense hydrides, revealing an alternative production strategy and confirming the disruptive nature of X-ray exposure in studies on high-pressure hydrogen chalcogenides, from water to high-temperature superconductors.

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.

Route to a Superconducting Phase above Room Temperature in Electron-Doped Hydride Compounds under High Pressure

The recent theory-orientated discovery of record high-temperature superconductivity (T_{c}∼250  K) in sodalitelike clathrate LaH_{10} is an important advance toward room-temperature superconductors. Here, we identify an alternative clathrate structure in ternary Li_{2}MgH_{16} with a remarkably high estimated T_{c} of ∼473  K at 250 GPa, which may allow us to obtain room-temperature or even higher-temperature superconductivity. The ternary compound mimics a Li- or electron-doped binary hydride of MgH_{16}. The parent hydride contains H_{2} molecules and is not a good superconductor. The extra electrons introduced break up the H_{2} molecules, increasing the amount of atomic hydrogen compared with the parent hydride, which is necessary for stabilizing the clathrate structure or other high-T_{c} structures. Our results provide a viable strategy for tuning the superconductivity of hydrogen-rich hydrides by donating electrons to hydrides via metal doping. Our approach may pave the way for finding high-T_{c} superconductors in a variety of ternary or quaternary hydrides.

Synthesis and stability of hydrogen selenide compounds at high pressure

The observation of high-temperature superconductivity in hydride sulfide (H₂S) at high pressures has generated considerable interest in compressed hydrogen-rich compounds. High-pressure hydrogen selenide (H₂Se) has also been predicted to be superconducting at high temperatures; however, its behaviour and stability upon compression remains unknown. In this study, we synthesize H₂Se in situ from elemental Se and molecular H₂ at pressures of 0.4 GPa and temperatures of 473 K. On compression at 300 K, we observe the high-pressure solid phase sequence (I-I'-IV) of H₂Se through Raman spectroscopy and x-ray diffraction measurements, before dissociation into its constituent elements. Through the compression of H₂Se in H₂ media, we also observe the formation of a host-guest structure, (H₂Se)₂H₂, which is stable at the same conditions as H₂Se, with respect to decomposition. These measurements show that the behaviour of H₂Se is remarkably similar to that of H₂S and provides further understanding of the hydrogen chalcogenides under pressure.

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.

On the critical temperature discontinuity at the theoretical bcc-fcc phase transition in compressed selenium and tellurium superconductors

Recent hydrides-driven advent in the high-pressure phonon-mediated superconductivity motivates research on chemical elements which compound with hydrogen. It is desired that such elements should allow chemical pre-compression of hydrogen to assure the induction of the superconducting phase with the high transition temperature (T _C). Herein, we present detailed theoretical insight into the properties of the superconducting state induced under pressure (p) in two of such component elements, namely selenium (Se) and tellurium (Te) at [Formula: see text] GPa and [Formula: see text] GPa, respectively. The assumed external pressure conditions allow us to conduct our analysis just above previously theoretically predicted bcc-fcc structural phase transition of Se and Te, and identify the possible associated discontinuity effect of the critical temperature. In particular, our numerical analysis is conducted within Migdal-Eliashberg formalism, due to the confirmed electron-phonon pairing mechanism and relatively high electron-phonon coupling constant in the materials of interest. We predict that T _C values in Se and Te equal 8.13 K and 5.96 K, respectively, and mark the highest critical temperature values for these elements within the postulated fcc phase. Additionally, we supplement these results by the estimated maximum values of the superconducting energy band gap and the effective mass of electrons. We predict that all these parameters can be used as a guidelines for experimental observation of the critical temperature discontinuity and the corresponding bcc-fcc phase transition in Se and Te superconductors. Moreover, we show that the thermodynamics of superconducting phase in both elements may exhibit deviations from the conventional estimates of the Bardeen-Cooper-Schrieffer theory, and suggest existence of the strong-coupling and retardation effects. Finally, we note that our results can be also instructive for future screening of chemical elements for applications in superconducting hydrides.

Hydrogen Clathrate Structures in Rare Earth Hydrides at High Pressures: Possible Route to Room-Temperature Superconductivity

Room-temperature superconductivity has been a long-held dream and an area of intensive research. Recent experimental findings of superconductivity at 200 K in highly compressed hydrogen (H) sulfides have demonstrated the potential for achieving room-temperature superconductivity in compressed H-rich materials. We report first-principles structure searches for stable H-rich clathrate structures in rare earth hydrides at high pressures. The peculiarity of these structures lies in the emergence of unusual H cages with stoichiometries H_{24}, H_{29}, and H_{32}, in which H atoms are weakly covalently bonded to one another, with rare earth atoms occupying the centers of the cages. We have found that high-temperature superconductivity is closely associated with H clathrate structures, with large H-derived electronic densities of states at the Fermi level and strong electron-phonon coupling related to the stretching and rocking motions of H atoms within the cages. Strikingly, a yttrium (Y) H_{32} clathrate structure of stoichiometry YH_{10} is predicted to be a potential room-temperature superconductor with an estimated T_{c} of up to 303 K at 400 GPa, as derived by direct solution of the Eliashberg equation.

Structural evolution of FeH4 under high pressure

Here, we systematically investigated global energetically stable structures of FeH₄ in the pressure range of 80–400 GPa using a first-principles structural search.

Quantitative analysis of nonadiabatic effects in dense H3S and PH3 superconductors

The comparison study of high pressure superconducting state of recently synthesized H₃S and PH₃ compounds are conducted within the framework of the strong-coupling theory. By generalization of the standard Eliashberg equations to include the lowest-order vertex correction, we have investigated the influence of the nonadiabatic effects on the Coulomb pseudopotential, electron effective mass, energy gap function and on the 2Δ(0)/T_C ratio. We found that, for a fixed value of critical temperature (178 K for H₃S and 81 K for PH₃), the nonadiabatic corrections reduce the Coulomb pseudopotential for H₃S from 0.204 to 0.185 and for PH₃ from 0.088 to 0.083, however, the electron effective mass and ratio 2Δ(0)/T_C remain unaffected. Independently of the assumed method of analysis, the thermodynamic parameters of superconducting H₃S and PH₃ strongly deviate from the prediction of BCS theory due to the strong-coupling and retardation effects.

Structure and superconductivity of hydrides at high pressures

Hydrogen atoms can provide high phonon frequencies and strong electron–phonon coupling in hydrogen-rich materials, which are believed to be potential high-temperature superconductors at lower pressure than metallic hydrogen. Especially, recently both of theoretical and experimental reports on sulfur hydrides under pressure exhibiting superconductivity at temperatures as high as 200 K have further stimulated an intense search for room-temperature superconductors in hydrides. This review focuses on crystal structures, stabilities, pressure-induced transformations, metallization, and superconductivity of hydrogen-rich materials at high pressures.

Superconductivity of novel tin hydrides (Sn(n)H(m)) under pressure

With the motivation of discovering high-temperature superconductors, evolutionary algorithm USPEX is employed to search for all stable compounds in the Sn-H system. In addition to the traditional SnH4, new hydrides SnH8, SnH12 and SnH14 are found to be thermodynamically stable at high pressure. Dynamical stability and superconductivity of tin hydrides are systematically investigated. I4m2-SnH8, C2/m-SnH12 and C2/m-SnH14 exhibit higher superconducting transition temperatures of 81, 93 and 97 K compared to the traditional compound SnH4 with Tc of 52 K at 200 GPa. An interesting bent H3-group in I4m2-SnH8 and novel linear H in C2/m-SnH12 are observed. All the new tin hydrides remain metallic over their predicted range of stability. The intermediate-frequency wagging and bending vibrations have more contribution to electron-phonon coupling parameter than high-frequency stretching vibrations of H2 and H3.

Tellurium Hydrides at High Pressures: High-Temperature Superconductors

Observation of high-temperature superconductivity in compressed sulfur hydrides has generated an irresistible wave of searches for new hydrogen-containing superconductors. We herein report the prediction of high-T_{c} superconductivity in tellurium hydrides stabilized at megabar pressures identified by first-principles calculations in combination with a swarm structure search. Although tellurium is isoelectronic to sulfur or selenium, its heavier atomic mass and weaker electronegativity makes tellurium hydrides fundamentally distinct from sulfur or selenium hydrides in stoichiometries, structures, and chemical bondings. We identify three metallic stoichiometries of H_{4}Te, H_{5}Te_{2}, and HTe_{3}, which are not predicted or known stable structures for sulfur or selenium hydrides. The two hydrogen-rich H_{4}Te and H_{5}Te_{2} phases are primarily ionic and contain exotic quasimolecular H_{2} and linear H_{3} units, respectively. Their high-T_{c} (e.g., 104 K for H_{4}Te at 170 GPa) superconductivity originates from the strong electron-phonon couplings associated with intermediate-frequency H-derived wagging and bending modes, a superconducting mechanism which differs substantially with those in sulfur or selenium hydrides where the high-frequency H-stretching vibrations make considerable contributions.

Decomposition Products of Phosphine Under Pressure: PH2 Stable and Superconducting?

Evolutionary algorithms (EAs) coupled with density functional theory (DFT) calculations have been used to predict the most stable hydrides of phosphorus (PHn, n = 1-6) at 100, 150, and 200 GPa. At these pressures phosphine is unstable with respect to decomposition into the elemental phases, as well as PH2 and H2. Three metallic PH2 phases were found to be dynamically stable and superconducting between 100 and 200 GPa. One of these contains five formula units in the primitive cell and has C2/m symmetry (5FU-C2/m). It comprises 1D periodic PH3-PH-PH2-PH-PH3 oligomers. Two structurally related phases consisting of phosphorus atoms that are octahedrally coordinated by four phosphorus atoms in the equatorial positions and two hydrogen atoms in the axial positions (I4/mmm and 2FU-C2/m) were the most stable phases between ∼160-200 GPa. Their superconducting critical temperatures (Tc) were computed as 70 and 76 K, respectively, via the Allen-Dynes modified McMillan formula and using a value of 0.1 for the Coulomb pseudopotential, μ*. Our results suggest that the superconductivity recently observed by Drozdov, Eremets, and Troyan when phosphine was subject to pressures of 207 GPa in a diamond anvil cell may result from these, and other, decomposition products of phosphine.

Prediction of stoichiometric PoHn compounds: crystal structures and properties

The calculated formation enthalpies of PoH_n (n = 1–6) with respect to Po and H at different pressures.