Evidence for a new phase of dense hydrogen above 325 gigapascals

A perspective on reducing stabilizing pressure for high-temperature superconductivity in hydrides

The theoretical predictions and experimental syntheses of hydrogen sulfide (H3S) have ignited a surge of research interest in hydride superconductors. Over the past two decades, extensive investigations have been conducted on hydrides with the ultimate goal of achieving room-temperature superconductivity under ambient conditions. In this review, we present a comprehensive summary of the current strategies and progress towards this goal in hydride materials. We conclude their electronic characteristics, hydrogen atom aggregation forms, stability mechanisms, and more. While providing a real-time snapshot of the research landscape, our aim is to offer deeper insights into reducing the stabilizing pressure for high-temperature superconductors in hydrides. This involves defining key long-term theoretical and experimental opportunities and challenges. Although achieving high critical temperatures for hydrogen-based superconductors still requires high pressure, we remain confident in the potential of hydrides as candidates for room-temperature superconductors at ambient pressure.

Remarkable stability of γ - N 2 and its prevalence in the nitrogen phase diagram

Solid nitrogen exhibits a panoply of phenomena ranging from complex molecular crystalline configurations to polymerization and closing band gap at higher densities. Among the elemental molecular solids, nitrogen stands apart for having phases, which can only be stabilized following particular pressure-temperature pathways, indicative of metastability and kinetic barriers. Here, through the combination of Raman spectroscopy and dynamic compression techniques, we find that the appearance of the whole nitrogen phase diagram is determined by the P-T paths taken below 2 GPa. We reveal the existence of the path- and phase-dependent triple point between the β - N 2 , δ loc - N 2 and γ - or ϵ - N 2 . We further show that the β - N 2 towards γ - N 2 path below the triple point, that evades δ ( δ loc )- N 2 , results in the formation of γ - N 2 , which in turn becomes a dominant phase. We then demonstrate, that the β - N 2 through δ ( δ loc )- N 2 above the triple point path leads to the formation of ϵ - N 2 and the "well-established" phase diagram. An additional pathway, which by-passes the rotationally inhibited modifications δ ( δ loc )- N 2 , via rapid compression is found to produce γ - N 2 at higher temperatures. We argue that the pathway and phase sensitive triple point and the compression rate dependent phase formation challenge our understanding of this archetypal dense molecular solid.

A platform for planar dynamic compression of crystalline hydrogen toward the terapascal regime

We describe a method for laser-driven planar compression of crystalline hydrogen that starts with a sample of solid para-hydrogen (even-valued rotational quantum number j) having an entropy of 0.06 kB/molecule at 10 K and 2 atm, with Boltzmann constant kB. Starting with this low-entropy state, the sample is compressed using a small initial shock (<0.2 GPa), followed by a pressure ramp that approaches isentropic loading as the sample is taken to hundreds of GPa. Planar loading allows for quantitative compression measurements; the objective of our low-entropy compression is to keep the sample cold enough to characterize crystalline hydrogen toward the terapascal range.

Ternary superconducting hydrides stabilized via Th and Ce elements at mild pressures

The discovery of covalent H3S and clathrate structure LaH10 with excellent superconducting critical temperatures at high pressures has facilitated a multitude of research on compressed hydrides. However, their superconducting pressures are too high (generally above 150 GPa), thereby hindering their application. In addition, making room-temperature superconductivity close to ambient pressure in hydrogen-based superconductors is challenging. In this work, we calculated the chemically "pre-compressed" Be-H by heavy metals Th and Ce to stabilize the superconducting phase near ambient pressure. An unprecedented ThBeH8 (CeBeH8) with a "fluorite-type" structure was predicted to be thermodynamically stable above 69 GPa (76 GPa), yielding a T c of 113 K (28 K) decompressed to 7 GPa (13 GPa) by solving the anisotropic Migdal-Eliashberg equations. Be-H vibrations play a vital role in electron-phonon coupling and structural stability of these ternary hydrides. Our results will guide further experiments toward synthesizing ternary hydride superconductors at mild pressures.

High-pressure structures of solid hydrogen: Insights from ab initio molecular dynamics simulations

Understanding the structural behavior of solid hydrogen under high pressures is crucial for uncovering its unique properties and potential applications. In this study, starting from the phase I of solid hydrogen-free-rotator hcp structure, we conduct extensive ab initio molecular dynamics calculations to simulate the cooling, heating, and equilibrium processes within a pressure range of 80-260 GPa. Without relying on any structure previously predicted, we identify the high-pressure phase structures of solid hydrogen as P21/c for phase II, P6522 for phase III, and BG1BG2BG3 six-layer structure for phase IV, which are different from those proposed previously using the structure-search method. The reasonability of these structures are validated by Raman spectra and x-ray diffraction patterns by comparison with the experimental results. Our results actually show pronounced changes in the c/a ratio between phases I, III, and IV, which hold no brief for the experimental interpretation of an isostructural hcp transformations for phases I-III-IV.

First-principles study of high-pressure structural phase transition and superconductivity of YBeH8

The theory-led prediction of LaBeH8, which has a high superconducting critical temperature (Tc) above liquid nitrogen under a pressure level below 1 Mbar, has been experimentally confirmed. YBeH8, which has a structural configuration similar to that of LaBeH8, has also been predicted to be a high-temperature superconductor at high pressure. In this study, we focus on the structural phase transition and superconductivity of YBeH8 under pressure by using first-principles calculations. Except for the known face-centered cubic phase of Fm3̄m, we found a monoclinic phase with P1̄ symmetry. Moreover, the P1̄ phase transforms to the Fm3̄m phase at ∼200 GPa with zero-point energy corrections. Interestingly, the P1̄ phase undergoes a complex electronic phase transition from semiconductor to metal and then to superconducting states with a low Tc of 40 K at 200 GPa. The Fm3̄m phase exhibits a high Tc of 201 K at 200 GPa, and its Tc does not change significantly with pressure. When we combine the method using two coupling constants, λopt and λac, with first-principles calculations, λopt is mainly supplied by the Be-H alloy backbone, which accounts for about 85% of total λ and makes the greatest contribution to the high Tc. These insights not only contribute to a deeper understanding of the superconducting behavior of this ternary hydride but may also guide the experimental synthesis of hydrogen-rich compounds.

On: X-ray diffraction from the electron gas in monatomic metallic hydrogen

Solid hydrogen is expected to become a monatomic metal under sufficiently high compression. With hydrogen having only a single valence electron and no ion core, the nature of x-ray diffraction patterns from the electron gas of monatomic metallic hydrogen is uncertain, and it is unclear whether they may yield enough information for a crystal structure determination. With emphasis on the Cs-IV-type (I41/amd) structure predicted for hydrogen at ∼500 GPa, the electron density distributions, zero-point and thermal atomic motion, and x-ray diffraction intensities are determined from first-principles calculations for several candidate phases of metallic hydrogen. It is shown that the electron distribution is much more structured than might be expected from the commonly employed free-electron-gas picture, and in fact more modulated than what is obtained from the superposition of free-atom charge densities. We demonstrate that an identification of the crystal structure of monatomic metallic hydrogen from x-ray diffraction is fundamentally possible and discuss the possibility of single-crystal diffraction from metallic hydrogen. An atomic scattering factor for the hydrogen atom in monatomic metallic hydrogen is constructed to aid the quantitative analysis of diffraction intensities from future x-ray diffraction experiments.

Superconducting ternary hydrides in Ca-U-H under high pressure

The research on hydrogen-rich ternary compounds attract tremendous attention for it paves new route to room-temperature superconductivity at lower pressures. Here, we study the crystal structures, electronic structures, and superconducting properties of the ternary Ca-U-H system, combining crystal structure predictions withab-initiocalculations under high pressure. We found four dynamically stable structures with hydrogen clathrate cages: CaUH12-Cmmm, CaUH12-Fd-3m, Ca2UH18-P-3m1, and CaU3H32-Pm-3m. Among them, the Ca2UH18-P-3m1 and CaU3H32-Pm-3mare likely to be synthesized below 1 megabar. Thefelectrons in U atoms make dominant contribution to the electronic density of states around the Fermi energy. The electron-phonon interaction calculations reveal that phonon softening in the mid-frequency region can enhance the electron-phonon coupling significantly. TheTcvalue of Ca2UH18-P-3m1 is estimated to be 57.5-65.8 K at 100 GPa. Our studies demonstrate that introducing actinides into alkaline-earth metal hydrides provides possibility in designing novel superconducting ternary hydrides.

Synthesis and characterization of XeAr2 under high pressure

The binary Xe-Ar system has been studied in a series of high pressure diamond anvil cell experiments up to 60 GPa at 300 K. In-situ x-ray powder diffraction and Raman spectroscopy indicate the formation of a van der Waals compound, XeAr2, at above 3.5 GPa. Powder x-ray diffraction analysis demonstrates that XeAr2 adopts a Laves MgZn2-type structure with space group P63/mmc and cell parameters a = 6.595 Å and c = 10.716 Å at 4 GPa. Density functional theory calculations support the structure determination, with agreement between experimental and calculated Raman spectra. Our DFT calculations suggest that XeAr2 would remain stable without a structural transformation or decomposition into elemental Xe and Ar up to at least 80 GPa.

Ultrafast dynamics under high-pressure

High-pressure is a mechanical method to regulate the structure and internal interaction of materials. Therefore, observation of properties' change can be realized in a relatively pure environment. Furthermore, high-pressure affects the delocalization of wavefunction among materials' atoms and thus their dynamics process. Dynamics results are essential data for understanding the physical and chemical characteristics, which is valuable for materials application and development. Ultrafast spectroscopy is a powerful tool to investigate dynamics process and becoming a necessary characterization method for materials investigation. The combination of high-pressure with ultrafast spectroscopy in the nanocosecond∼femtosecond scale enables us to investigate the influence of the enhanced interaction between particles on the physical and chemical properties of materials, such as energy transfer, charge transfer, Auger recombination, etc. Base on this point of view, this review summarizes recent progress in the ultrafast dynamics under high-pressure for various materials, in which new phenomena and new mechanisms are observed. In this review, we describe in detail the principles ofin situhigh pressure ultrafast dynamics probing technology and its field of application. On this basis, the progress of the study of dynamic processes under high-pressure in different material systems is summarized. An outlook onin situhigh-pressure ultrafast dynamics research is also provided.

Magnetic detection under high pressures using designed silicon vacancy centres in silicon carbide

Pressure-induced magnetic phase transitions are attracting interest as a means to detect superconducting behaviour at high pressures in diamond anvil cells, but determining the local magnetic properties of samples is a challenge due to the small volumes of sample chambers. Optically detected magnetic resonance of nitrogen vacancy centres in diamond has recently been used for the in situ detection of pressure-induced phase transitions. However, owing to their four orientation axes and temperature-dependent zero-field splitting, interpreting these optically detected magnetic resonance spectra remains challenging. Here we study the optical and spin properties of implanted silicon vacancy defects in 4H-silicon carbide that exhibit single-axis and temperature-independent zero-field splitting. Using this technique, we observe the magnetic phase transition of Nd2Fe14B at about 7 GPa and map the critical temperature-pressure phase diagram of the superconductor YBa2Cu3O6.6. These results highlight the potential of silicon vacancy-based quantum sensors for in situ magnetic detection at high pressures.

Universal diamond edge Raman scale to 0.5 terapascal and implications for the metallization of hydrogen

The recent progress in generating static pressures up to terapascal values opens opportunities for studying novel materials with unusual properties, such as metallization of hydrogen and high-temperature superconductivity. However, an evaluation of pressure above ~0.3 terapascal is a challenge. We report a universal high-pressure scale up to ~0.5 terapascal, which is based on the shift of the Raman edge of stressed diamond anvils correlated with the equation of state of Au and does not require an additional pressure sensor. According to the new scale, the pressure values are substantially lower by 20% at ~0.5 terapascal compared to the extrapolation of the existing scales. We compare the available data of H₂ at the highest static pressures. We show that the onset of the proposed metallization of molecular hydrogen reported by different groups is consistent when corrected with the new scale and can be compared with various theoretical predictions.

Generic maximum-valence model for fluid polyamorphism

Recently, a maximal-valence model has been proposed to model a liquid-liquid phase transition induced by polymerization in sulfur. In this paper we present a simple generic model to describe liquid polyamorphism in single-component fluids using a maximum-valence approach for any arbitrary coordination number. The model contains three types of interactions: (i) atoms attract each other by van der Waals forces that generate a liquid-gas transition at low pressures, (ii) atoms may form covalent bonds that induce association, and (iii) additional repulsive forces between atoms with maximal valence and atoms with any valence. This additional repulsion generates liquid-liquid phase separation and the region of the negative heat expansion coefficient (density anomaly) on a P-T phase diagram. We show the existence of liquid-liquid phase transitions for dimerization, polymerization, gelation, and network formation for corresponding coordination numbers z=1,2,...,6 and discuss the limits of this generic model for producing fluid polyamorphism.

Chemically Assisted Precompression of Hydrogen Molecules in Alkaline-Earth Tetrahydrides

Through a series of high pressure diamond anvil experiments, we report the synthesis of alkaline earth (Ca, Sr, Ba) tetrahydrides, and investigate their properties through Raman spectroscopy, X-ray diffraction, and density functional theory calculations. The tetrahydrides incorporate both atomic and quasi-molecular hydrogen, and we find that the frequency of the intramolecular stretching mode of the H2δ- units downshifts from Ca to Sr and to Ba upon compression. The experimental results indicate that the larger the host cation, the longer the H2δ- bond. Analysis of the electron localization function (ELF) demonstrates that the lengthening of the H-H bond is caused by the charge transfer from the metal to H2δ- and by the steric effect of the metal host on the H-H bond. This effect is most prominent for BaH₄, where the precompression of H2δ- units at 50 GPa results in bond lengths comparable to that of pure H₂ above 275 GPa.

Thermodynamic modeling of fluid polyamorphism in hydrogen at extreme conditions

Fluid polyamorphism, the existence of multiple amorphous fluid states in a single-component system, has been observed or predicted in a variety of substances. A remarkable example of this phenomenon is the fluid–fluid phase transition (FFPT) in high-pressure hydrogen between insulating and conducting high-density fluids. This transition is induced by the reversible dimerization/dissociation of the molecular and atomistic states of hydrogen. In this work, we present the first attempt to thermodynamically model the FFPT in hydrogen at extreme conditions. Our predictions for the phase coexistence and the reaction equilibrium of the two alternative forms of fluid hydrogen are based on experimental data and supported by the results of simulations. Remarkably, we find that the law of corresponding states can be utilized to construct a unified equation of state combining the available computational results for different models of hydrogen and the experimental data.

Compression of D_{2} to 460 GPa and Isotopic Effects in the Path to Metal Hydrogen

How are nuclear quantum fluctuations affecting the properties of dense hydrogen approaching metallization? We report here Raman spectroscopy and synchrotron infrared absorption measurements on deuterium up to 460 GPa at 80 K. By comparing to a previous similar study on hydrogen, isotopic effects on the electronic and vibrational properties in phase III are disclosed. Also, evidence of a probable transition to metal deuterium is observed, shifted by about 35 GPa compared to that in hydrogen. Advanced calculations, quantifying a reduction of the band gap caused by nuclear quantum fluctuations, are compared to the present data.

Theoretical methods for structural phase transitions in elemental solids at extreme conditions: statics and dynamics

In recent years, theoretical studies have moved from a traditionally supporting role to a more proactive role in the research of phase transitions at high pressures. In many cases, theoretical prediction leads the experimental exploration. This is largely owing to the rapid progress of computer power and theoretical methods, particularly the structure prediction methods tailored for high-pressure applications. This review introduces commonly used structure searching techniques based on static and dynamic approaches, their applicability in studying phase transitions at high pressure, and new developments made toward predicting complex crystalline phases. Successful landmark studies for each method are discussed, with an emphasis on elemental solids and their behaviors under high pressure. The review concludes with a perspective on outstanding challenges and opportunities in the field.

Stress-induced high-Tc superconductivity in solid molecular hydrogen

Solid molecular hydrogen has been predicted to be metallic and high-temperature superconducting at ultrahigh hydrostatic pressures that push current experimental limits. Meanwhile, little is known about the influence of nonhydrostatic conditions on its electronic properties at extreme pressures where anisotropic stresses are inevitably present and may also be intentionally introduced. Here we show by first-principles calculations that solid molecular hydrogen compressed to multimegabar pressures can sustain large anisotropic compressive or shear stresses that, in turn, cause major crystal symmetry reduction and charge redistribution that accelerate bandgap closure and promote superconductivity relative to pure hydrostatic compression. Our findings highlight a hitherto largely unexplored mechanism for creating superconducting dense hydrogen, with implications for exploring similar phenomena in hydrogen-rich compounds and other molecular crystals.

Inference of a "Hot Ice" Layer in Nitrogen-Rich Planets: Demixing the Phase Diagram and Phase Composition for Variable Concentration Helium-Nitrogen Mixtures Based on Isothermal Compression

Van der Waals (vdW) chemistry in simple molecular systems may be important for understanding the structure and properties of the interiors of the outer planets and their satellites, where pressures are high and such components may be abundant. In the current study, Raman spectra and visual observation are employed to investigate the phase separation and composition determination for helium-nitrogen mixtures with helium concentrations from 20 to 95% along the 295 K isothermal compression. Fluid-fluid-solid triple-phase equilibrium and several equilibria of two phases including fluid-fluid and fluid-solid have been observed in different helium-nitrogen mixtures upon loading or unloading pressure. The homogeneous fluid in helium-nitrogen mixtures separates into a helium-rich fluid (F₁) and a nitrogen-rich fluid (F₂) with increasing pressure. The triple-phase point occurs at 295 K and 8.8 GPa for a solid-phase (N₂)₁₁He vdW compound, fluid F₁ with around 50% helium, and fluid F₂ with 95% helium. Helium concentrations of F₁ coexisted with the (N₂)₁₁He vdW compound or δ-N₂ in helium-nitrogen mixtures with different helium concentrations between 40 and 50% and between 20 and 40%, respectively. In addition, the helium concentration of F₂ is the same in helium-nitrogen mixtures with different helium concentrations and decreases upon loading pressure. Pressure-induced nitrogen molecule ordering at 32.6 GPa and a structural phase transition at 110 GPa are observed in (N₂)₁₁He. In addition, at 187 GPa, a pressure-induced transition to an amorphous state is identified.

Compression rate of dynamic diamond anvil cells from room temperature to 10 K

There is an ever increasing interest in studying dynamic-pressure dependent phenomena utilizing dynamic Diamond Anvil Cells (dDACs), devices capable of a highly controlled rate of compression. Here, we characterize and compare the compression rate of dDACs in which the compression is actuated via three different methods: (1) stepper motor (S-dDAC), (2) gas membrane (M-dDAC), and (3) piezoactuator (P-dDAC). The compression rates of these different types of dDAC were determined solely on millisecond time-resolved R1-line fluorescence of a ruby sphere located within the sample chamber. Furthermore, these different dynamic compression-techniques have been described and characterized over a broad temperature and pressure range from 10 to 300 K and 0-50 GPa. At room temperature, piezoactuation (P-dDAC) has a clear advantage in controlled extremely fast compression, having recorded a compression rate of ∼7 TPa/s, which is also found to be primarily influenced by the charging time of the piezostack. At 40-250 K, gas membranes (M-dDAC) have also been found to generate rapid compression of ∼0.5-3 TPa/s and are readily interfaced with moderate cryogenic and ultrahigh vacuum conditions. Approaching more extreme cryogenic conditions (<10 K), a stepper motor driven lever arm (S-dDAC) offers a solution for high-precision moderate compression rates in a regime where P-dDACs and M-dDACs can become difficult to incorporate. The results of this paper demonstrate the applicability of different dynamic compression techniques, and when applied, they can offer us new insights into matter's response to strain, which is highly relevant to physics, geoscience, and chemistry.

Formation and Stability of Dense Methane-Hydrogen Compounds

Through a series of x-ray diffraction, optical spectroscopy diamond anvil cell experiments, combined with density functional theory calculations, we explore the dense CH_{4}-H_{2} system. We find that pressures as low as 4.8 GPa can stabilize CH_{4}(H_{2})_{2} and (CH_{4})_{2}H_{2}, with the latter exhibiting extreme hardening of the intramolecular vibrational mode of H_{2} units within the structure. On further compression, a unique structural composition, (CH_{4})_{3}(H_{2})_{25}, emerges. This novel structure holds a vast amount of molecular hydrogen and represents the first compound to surpass 50 wt % H_{2}. These compounds, stabilized by nuclear quantum effects, persist over a broad pressure regime, exceeding 160 GPa.

Manipulation of the crystalline phase diagram of hydrogen through nanoscale confinement effects in porous carbons

Condensed phases of molecular hydrogen (H₂) are highly desired for clean energy applications ranging from hydrogen storage to nuclear fusion and superconductive energy storage. However, in bulk hydrogen, such dense phases typically only form at exceedingly low temperatures or extremely high (typically hundreds of GPa) pressures. Here, confinement of H₂ within nanoporous materials is shown to significantly manipulate the hydrogen phase diagram leading to preferential stabilization of unusual crystalline H₂ phases. Using pressure and temperature-dependent neutron scattering at pressures between 200-2000 bar (0.02-0.2 GPa) and temperatures between 10-77 K to map out the phase diagram of H₂ when confined inside both meso- and microporous carbons, we conclusively demonstrate the preferential stabilisation of face-centred cubic (FCC) solid ortho-H₂ in microporous carbons, at temperatures five times higher than would be possible in bulk H₂. Through examination of nanoconfined H₂ rotational dynamics, preferential adsorption and spin trapping of ortho-H₂, as well as the loss of rotational energy and severe restriction of rotational degrees of freedom caused by the unique micropore environments, are shown to result in changes to phase behaviour. This work provides a general strategy for further manipulation of the H₂ phase diagram via nanoconfinement effects, and for tuning of anisotropic potential through control of confining material composition and pore size. This approach could potentially provide lower energy routes to the formation and study of more exotic non-equilibrium condensed phases of hydrogen that could be useful for a wide range of energy applications.

Phonon-mediated superconductivity in two-dimensional hydrogenated phosphorus carbide: HPC3

In recent years, three-dimensional (3D) high-temperature superconductors at ultrahigh pressure have been reported, typical examples are the polyhydrides H₃S, LaH₁₀, YH₉, etc. To find high-temperature two-dimensional (2D) superconductors at atmospheric pressure is another research hotspot. Here, we investigated the possible superconductivity in a hydrogenated monolayer phosphorus carbide based on first-principles calculations. The results reveal that monolayer PC₃ transforms from a semiconductor to a metal after hydrogenation. Interestingly, the C-π-bonding band contributes most to the states at the Fermi level. Based on the electron-phonon coupling mechanism, it is found that the electron-phonon coupling constant of HPC₃ is 0.95, which mainly originates from the coupling of C-π electrons with the in-plane vibration modes of C and H. The calculated critical temperature T_c is 31.0 K, which is higher than those in most 2D superconductors. By further applying a biaxial tensile strain of 3%, the T_c can be boosted to 57.3 K, exceeding the McMillan limit. Thus, hydrogenation and strain are effective ways for increasing the superconducting T_c of 2D materials.

Prediction of a Supersolid Phase in High-Pressure Deuterium

Supersolid is a mysterious and puzzling state of matter whose possible existence has stirred a vigorous debate among physicists for over 60 years. Its elusive nature stems from the coexistence of two seemingly contradicting properties, long-range order and superfluidity. We report computational evidence of a supersolid phase of deuterium under high pressure (p>800  GPa) and low temperature (T<1.0  K). In our simulations, that are based on bosonic path integral molecular dynamics, we observe a highly concerted exchange of atoms while the system preserves its crystalline order. The exchange processes are favored by the soft core interactions between deuterium atoms that form a densely packed metallic solid. At the zero temperature limit, Bose-Einstein condensation is observed as the permutation probability of N deuterium atoms approaches 1/N with a finite superfluid fraction. Our study provides concrete evidence for the existence of a supersolid phase in high-pressure deuterium and could provide insights on the future investigation of supersolid phases in real materials.

Design Principles for High-Temperature Superconductors with a Hydrogen-Based Alloy Backbone at Moderate Pressure

Hydrogen-based superconductors provide a route to the long-sought goal of room-temperature superconductivity, but the high pressures required to metallize these materials limit their immediate application. For example, carbonaceous sulfur hydride, the first room-temperature superconductor made in a laboratory, can reach a critical temperature (T_{c}) of 288 K only at the extreme pressure of 267 GPa. The next recognized challenge is the realization of room-temperature superconductivity at significantly lower pressures. Here, we propose a strategy for the rational design of high-temperature superconductors at low pressures by alloying small-radius elements and hydrogen to form ternary H-based superconductors with alloy backbones. We identify a "fluorite-type" backbone in compositions of the form AXH_{8}, which exhibit high-temperature superconductivity at moderate pressures compared with other reported hydrogen-based superconductors. The Fm3[over ¯]m phase of LaBeH_{8}, with a fluorite-type H-Be alloy backbone, is predicted to be thermodynamically stable above 98 GPa, and dynamically stable down to 20 GPa with a high T_{c}∼185  K. This is substantially lower than the synthesis pressure required by the geometrically similar clathrate hydride LaH_{10} (170 GPa). Our approach paves the way for finding high-T_{c} ternary H-based superconductors at conditions close to ambient pressures.

Isotope Quantum Effects in the Metallization Transition in Liquid Hydrogen

Quantum effects in condensed matter normally only occur at low temperatures. Here we show a large quantum effect in high-pressure liquid hydrogen at thousands of Kelvins. We show that the metallization transition in hydrogen is subject to a very large isotope effect, occurring hundreds of degrees lower than the equivalent transition in deuterium. We examined this using path integral molecular dynamics simulations which identify a liquid-liquid transition involving atomization, metallization, and changes in viscosity, specific heat, and compressibility. The difference between H_{2} and D_{2} is a quantum mechanical effect that can be associated with the larger zero-point energy in H_{2} weakening the covalent bond. Our results mean that experimental results on deuterium must be corrected before they are relevant to understanding hydrogen at planetary conditions.

Hydrogen Clathrate Structures in Uranium Hydrides at High Pressures

Room-temperature superconductivity has always been an area of intensive research. Recent findings of clathrate metal hydrides structures have opened up the doors for achieving room-temperature superconductivity in these materials. Here, we report first-principles calculations for stable H-rich clathrate structures of uranium hydrides at high pressures. The clathrate uranium hydrides contain H cages with stoichiometries of H24, H29, and H32, in which H atoms are bonded covalently to other H atoms, and U atoms occupy the centers of the cages. Especially, a UH10 clathrate structure containing H32 cages is predicted to have an estimated T c higher than 77 K at high pressures.

Evidence for supercritical behaviour of high-pressure liquid hydrogen

Hydrogen, the simplest and most abundant element in the Universe, develops a remarkably complex behaviour upon compression¹. Since Wigner predicted the dissociation and metallization of solid hydrogen at megabar pressures almost a century ago², several efforts have been made to explain the many unusual properties of dense hydrogen, including a rich and poorly understood solid polymorphism^1,3-5, an anomalous melting line⁶ and the possible transition to a superconducting state⁷. Experiments at such extreme conditions are challenging and often lead to hard-to-interpret and controversial observations, whereas theoretical investigations are constrained by the huge computational cost of sufficiently accurate quantum mechanical calculations. Here we present a theoretical study of the phase diagram of dense hydrogen that uses machine learning to 'learn' potential-energy surfaces and interatomic forces from reference calculations and then predict them at low computational cost, overcoming length- and timescale limitations. We reproduce both the re-entrant melting behaviour and the polymorphism of the solid phase. Simulations using our machine-learning-based potentials provide evidence for a continuous molecular-to-atomic transition in the liquid, with no first-order transition observed above the melting line. This suggests a smooth transition between insulating and metallic layers in giant gas planets, and reconciles existing discrepancies between experiments as a manifestation of supercritical behaviour.

Quantitative Rotational to Librational Transition in Dense H2 and D2

Raman spectroscopy demonstrates that the rotational spectrum of solid hydrogen, and its isotope deuterium, undergoes profound transformations upon compression while still remaining in phase I. We show that these changes are associated with a loss of quantum character in the rotational modes and that the angular momentum J gradually ceases to be a good quantum rotational number. Through isotopic comparisons of the rotational Raman contributions, we reveal that hydrogen and deuterium evolve from a quantum rotor to a harmonic oscillator. We find that the mechanics behind this transformation can be well-described by a quantum-mechanical single inhibited rotor, accurately reproducing the striking spectroscopic changes observed in phase I.

New possible candidate structure for phase IV of solid hydrogen

It has been proved in experiments that there are at least five phases of solid hydrogen at high pressure, however, only the structure of phase I has been absolutely determined. We revisited the phase space of solid hydrogen in the pressure range of 200-500 GPa using the particle swarm optimization technique combined with first-principles simulations. A novel orthorhombic structure named Ama2 is proposed as a possible candidate structure for phase IV. The Ama2 structure is a 'mixed structure' with two different types of layers and is distinctly different from the previously reported Pc structure. Enthalpies and Gibbs free energies show that Ama2 and Pc are competitive in the pressure region of phase IV. Nevertheless, the Raman and infrared vibron frequencies of Ama2 calculated by using density functional perturbation theory based on first-principles lattice dynamics show a better agreement with the experimental measurements than those of the Pc structure. And the pressure dependence of these low-frequency Raman vibrons of Ama2 obtained from the first-principles molecular dynamics simulation shows a steeper slope, which resolves the long-standing issue of large discrepancies between the calculated Raman frequencies and the experimental ν ₁ [P. Loubeyre, F. Occelli and P. Dumas, Phys. Rev. B: Condens. Matter Mater. Phys., 2013, 87, 134101 and C. S. Zha, R. E. Cohen, H. K. Mao and R. J. Hemley, Proc. Natl. Acad. Sci. U.S.A., 2014, 111, 4792]. Structural and vibrational analyses show that the hydrogen molecules in the weakly bonded molecular layer of Ama2 form distorted hexagonal patterns, and their vibration can be used to explain the experimental ν ₁ vibron. It is found that the weakly bonded layer is almost the same as the layers in the C2/c structure. This confirms the experimental conclusion [P. Loubeyre, F. Occelli and P. Dumas, Phys. Rev. B: Condens. Matter Mater. Phys., 2013, 87, 134101] that the ordering of hydrogen molecules in the weakly bonded molecular layers of the 'mixed structure' for phase IV is similar to that in the layers of the C2/c structure.

Temperature effect on the phase stability of hydrogenC2/cphase from first-principles molecular dynamics calculations

The structural stability of hydrogenC2/cphase from 0 K to 300 K is investigated by combining the first-principles molecular dynamics (MD) simulations and density functional perturbation theory. Without considering the temperature effect, theC2/cphase is stable from 150 GPa to 250 GPa based on the harmonic phonon dispersion relations. The hydrogen molecules at the solid lattice sites are sensitive to temperature. The structural stability to instability transition of theC2/cphase upon temperature is successfully captured by the radial distribution function and probability distribution of atomic displacements from first-principles MD simulations, confirmed by the phonon power spectrum analysis in the phase space. The existence of phonon quasiparticle for different normal modes is observed directly. The phonon power spectrum of specific normal modes corresponding to the Raman and infrared (IR) activations are depicted at different temperatures and pressures. The changes of frequency with temperature are in agreement with experimental results, supporting theC2/cas the hydrogen phase III. For the first time, the anharmonic phonon dispersion curves and density of states are predicted based on the phonon quasi-particle approach. Therefore, the temperature dependence of lattice vibrations can be observed directly, providing a more complete physical picture of phonon frequency distribution with respect to the Raman and IR spectra. It is found that the high-frequency regions adopt significant frequency shifts compared to the harmonic case.

Counterintuitive effects of isotopic doping on the phase diagram of H2-HD-D2 molecular alloy

Molecular hydrogen forms the archetypical quantum solid. Its quantum nature is revealed by behavior which is classically impossible and by very strong isotope effects. Isotope effects between [Formula: see text], [Formula: see text], and HD molecules come from mass difference and the different quantum exchange effects: fermionic [Formula: see text] molecules have antisymmetric wavefunctions, while bosonic [Formula: see text] molecules have symmetric wavefunctions, and HD molecules have no exchange symmetry. To investigate how the phase diagram depends on quantum-nuclear effects, we use high-pressure and low-temperature in situ Raman spectroscopy to map out the phase diagrams of [Formula: see text]-HD-[Formula: see text] with various isotope concentrations over a wide pressure-temperature (P-T) range. We find that mixtures of [Formula: see text], HD, and [Formula: see text] behave as an isotopic molecular alloy (ideal solution) and exhibit symmetry-breaking phase transitions between phases I and II and phase III. Surprisingly, all transitions occur at higher pressures for the alloys than either pure [Formula: see text] or [Formula: see text] This runs counter to any quantum effects based on isotope mass but can be explained by quantum trapping of high-kinetic energy states by the exchange interaction.

Complex Hydrogen Substructure in Semimetallic RuH4

When compressed in a matrix of solid hydrogen, many metals form compounds with increasingly high hydrogen contents. At high density, hydrogenic sublattices can emerge, which may act as low-dimensional analogues of atomic hydrogen. We show that at high pressures and temperatures, ruthenium forms polyhydride species that exhibit intriguing hydrogen substructures with counterintuitive electronic properties. Ru₃H₈ is synthesized from RuH in H₂ at 50 GPa and at temperatures in excess of 1000 K, adopting a cubic structure with short H-H distances. When synthesis pressures are increased above 85 GPa, we observe RuH₄ which crystallizes in a remarkable structure containing corner-sharing H₆ octahedra. Calculations indicate this phase is semimetallic at 100 GPa.

Distinguishing the Structure of High-Pressure Hydrogen with Dielectric Constants

Identifying the structures of high-pressure hydrogen has been one of the central goals in high-pressure physics; however, it still presents a fundamental challenge because of the lack of an effective measure for distinguishing the structures. Herein, we address this issue by focusing on the potential candidates of phases II and III of high-pressure hydrogen. We find that the anisotropic dielectric constants of the different hydrogen solids and their responses to pressure behave differently depending on the atomic structures, corresponding to the different polarization responses of the structures to the external electric field. These findings are robust regardless of the quantum and thermal motion of hydrogen solids. Therefore, the anisotropic dielectric property can serve as a potential measure for probing the structures of high-pressure hydrogen as well as other high-pressure materials.

Thermophysical Measurements in Liquid Alloys and Phase Diagram Studies

Towards the construction of pressure-dependent phase diagrams of binary alloy systems, both thermophysical measurements and thermodynamic modeling are employed. High-accuracy measurements of sound velocity, density, and electrical resistivity were performed for selected metallic elements from columns III to V and their alloys in the liquid phase. Sound velocity measurements were made using ultrasonic techniques, density measurements using the gamma radiation attenuation method, and electrical resistivity measurements were performed using the four probe method. Sound velocity and density data, measured at ambient pressure, were incorporated into a thermodynamic model to calculate the pressure dependence of binary phase diagrams. Electrical resistivity measurements were performed on binary systems to study phase separation and identify phase transitions in the liquid state.

Synthesis of clathrate cerium superhydride CeH9 at 80-100 GPa with atomic hydrogen sublattice

Hydrogen-rich superhydrides are believed to be very promising high-T_c superconductors. Recent experiments discovered superhydrides at very high pressures, e.g. FeH₅ at 130 GPa and LaH₁₀ at 170 GPa. With the motivation of discovering new hydrogen-rich high-T_c superconductors at lowest possible pressure, here we report the prediction and experimental synthesis of cerium superhydride CeH₉ at 80–100 GPa in the laser-heated diamond anvil cell coupled with synchrotron X-ray diffraction. Ab initio calculations were carried out to evaluate the detailed chemistry of the Ce-H system and to understand the structure, stability and superconductivity of CeH₉. CeH₉ crystallizes in a P6₃/mmc clathrate structure with a very dense 3-dimensional atomic hydrogen sublattice at 100 GPa. These findings shed a significant light on the search for superhydrides in close similarity with atomic hydrogen within a feasible pressure range. Discovery of superhydride CeH₉ provides a practical platform to further investigate and understand conventional superconductivity in hydrogen rich superhydrides.

Hydrogen-rich superhydrides are promising high-temperature superconductors which have been observed only at pressures above 170 GPa. Here the authors show that CeH₉ can be synthesized at 80-100 GPa with laser heating, and is characterized by a clathrate structure with a dense 3-dimensional atomic hydrogen sublattice.

Ultrahigh-pressure isostructural electronic transitions in hydrogen

High-pressure transitions are thought to modify hydrogen molecules to a molecular metallic solid and finally to an atomic metal¹, which is predicted to have exotic physical properties and the topology of a two-component (electron and proton) superconducting superfluid condensate^2,3. Therefore, understanding such transitions remains an important objective in condensed matter physics^4,5. However, measurements of the crystal structure of solid hydrogen, which provides crucial information about the metallization of hydrogen under compression, are lacking for most high-pressure phases, owing to the considerable technical challenges involved in X-ray and neutron diffraction measurements under extreme conditions. Here we present a single-crystal X-ray diffraction study of solid hydrogen at pressures of up to 254 gigapascals that reveals the crystallographic nature of the transitions from phase I to phases III and IV. Under compression, hydrogen molecules remain in the hexagonal close-packed (hcp) crystal lattice structure, accompanied by a monotonic increase in anisotropy. In addition, the pressure-dependent decrease of the unit cell volume exhibits a slope change when entering phase IV, suggesting a second-order isostructural phase transition. Our results indicate that the precursor to the exotic two-component atomic hydrogen may consist of electronic transitions caused by a highly distorted hcp Brillouin zone and molecular-symmetry breaking.

Polyhydride CeH9 with an atomic-like hydrogen clathrate structure

Compression of hydrogen-rich hydrides has been proposed as an alternative way to attain the atomic metallic hydrogen state or high-temperature superconductors. However, it remains a challenge to get access to these states by synthesizing novel polyhydrides with unusually high hydrogen-to-metal ratios. Here we synthesize a series of cerium (Ce) polyhydrides by a direct reaction of Ce and H2 at high pressures. We discover that cerium polyhydride CeH9, formed above 100 GPa, presents a three-dimensional hydrogen network composed of clathrate H29 cages. The electron localization function together with band structure calculations elucidate the weak electron localization between H-H atoms and confirm its metallic character. By means of Ce atom doping, metallic hydrogen structure can be realized via the existence of CeH9. Particularly, Ce atoms play a positive role to stabilize the sublattice of hydrogen cages similar to the recently discovered near-room-temperature lanthanum hydride superconductors.

Viewpoint: the road to room-temperature conventional superconductivity

It is a honor to write a contribution on this memorial for Sandro Massidda. For both of us, at different stages in our lives, Sandro was first and foremost a friend. We both admired his humble, playful and profound approach to life and physics. In this contribution we describe the route which permitted to meet a long-standing challenge in solid state physics, i.e. room temperature superconductivity. In less than 20 years the critical temperature of conventional superconductors, which in the last century had been widely believed to be limited to 25 K, was raised from 40 K in MgB₂ to 265 K in LaH₁₀. This discovery was enabled by the development and application of computational methods for superconductors, a field in which Sandro Massidda played a major role.

Post-tilleyite, a dense calcium silicate-carbonate phase

Calcium carbonate is a relevant constituent of the Earth's crust that is transferred into the deep Earth through the subduction process. Its chemical interaction with calcium-rich silicates at high temperatures give rise to the formation of mixed silicate-carbonate minerals, but the structural behavior of these phases under compression is not known. Here we report the existence of a dense polymorph of Ca5(Si2O7)(CO3)2 tilleyite above 8 GPa. We have structurally characterized the two phases at high pressures and temperatures, determined their equations of state and analyzed the evolution of the polyhedral units under compression. This has been possible thanks to the agreement between our powder and single-crystal XRD experiments, Raman spectroscopy measurements and ab-initio simulations. The presence of multiple cation sites, with variable volume and coordination number (6-9) and different polyhedral compressibilities, together with the observation of significant amounts of alumina in compositions of some natural tilleyite assemblages, suggests that post-tilleyite structure has the potential to accommodate cations with different sizes and valencies.

Unveiling a Novel, Cation-Rich Compound in a High-Pressure Pb-Te Binary System

Because of the common oxidation states of group IV elements (+2 or +4) and group VI elements (-2), 1:1 and 1:2 are two typical stoichiometries found in the IV-VI compounds. Particularly, in the Pb-Te binary system, the 1:1 stoichiometric PbTe is believed to be the only stable compound. Herein, using evolutionary algorithms, density functional theory, a laser-heated diamond anvil cell, and synchrotron X-ray diffraction experiments, we discovered a novel Pb-Te compound with an unexpected stoichiometry of 3:2 above 20 GPa. This tetragonal Pb3Te2 is the one of the very few cation-rich compounds that has ever been discovered in the entire IV-VI binary system. Further analyses based on electron density distribution, electron localization function, and Bader charge have shown that this newly discovered compound has a mixed character of chemical bonding with a decreased ionicity. By further calculating the electron-phonon interaction, Pb3Te2 is predicted to exhibit a superconducting transition at low temperatures. The discovery of Pb3Te2 paves the way for further explorations of other novel cation-rich IV-VI group compounds.

Nuclear Magnetic Resonance Spectroscopy as a Dynamical Structural Probe of Hydrogen under High Pressure

An unambiguous crystallographic structure solution for the observed phases II-VI of high pressure hydrogen does not exist due to the failure of standard structural probes at extreme pressure. In this work we propose that nuclear magnetic resonance spectroscopy provides a complementary structural probe for high pressure hydrogen. We show that the best structural models available for phases II, III, and IV of high pressure hydrogen exhibit markedly distinct nuclear magnetic resonance spectra which could therefore be used to discriminate amongst them. As an example, we demonstrate how nuclear magnetic resonance spectroscopy could be used to establish whether phase III exhibits polymorphism. Our calculations also reveal a strong renormalization of the nuclear magnetic resonance response in hydrogen arising from quantum fluctuations, as well as a strong isotope effect. As the experimental techniques develop, nuclear magnetic resonance spectroscopy can be expected to become a useful complementary structural probe in high pressure experiments.

Band gap closure, incommensurability and molecular dissociation of dense chlorine

Diatomic elemental solids are highly compressible due to the weak interactions between molecules. However, as the density increases the intra- and intermolecular distances become comparable, leading to a range of phenomena, such as structural transformation, molecular dissociation, amorphization, and metallisation. Here we report, following the crystallization of chlorine at 1.15(30) GPa into an ordered orthorhombic structure (oC8), the existence of a mixed-molecular structure (mC8, 130(10)-241(10) GPa) and the concomitant observation of a continuous band gap closure, indicative of a transformation into a metallic molecular form around 200(10) GPa. The onset of dissociation of chlorine is identified by the observation of the incommensurate structure (i-oF4) above 200(10) GPa, before finally adopting a monatomic form (oI2) above 256(10) GPa.

Direct Reaction between Copper and Nitrogen at High Pressures and Temperatures

Transition-metal nitrides have applications in a range of technological fields. Recent experiments have shown that new nitrogen-bearing compounds can be accessed through a combination of high temperatures and pressures, revealing a richer chemistry than was previously assumed. Here, we show that at pressures above 50 GPa and temperatures greater than 1500 K  elemental copper reacts with nitrogen, forming copper diazenide (CuN₂). Through a combination of synchrotron X-ray diffraction and first-principles calculations we have explored the stability and electronic structure of CuN₂. We find that the novel compound remains stable down to 25 GPa before decomposing to its constituent elements. Electronic structure calculations show that CuN₂ is metallic and exhibits partially filled N₂ antibonding orbitals, leading to an ambiguous electronic structure between Cu⁺/Cu²⁺. This leads to weak Cu-N bonds and the lowest bulk modulus observed for any transition-metal nitride.