Superconductivity in hydrogen dominant materials: silane

Ductile copper hydride Eliashberg superconductors with Tc in the liquid-nitrogen temperature range and band topology at ambient pressure

The engineering demands for superconductors require not only a high transition temperature (Tc) but also eco-friendliness, mechanical workability, and abundance. Currently, superconductors exhibiting both mechanical ductility and Tc above the liquid-nitrogen temperature are still lacking. Considering that copper is one of the most important conductive materials for power transmission, we investigate the synthetic routes, band topology, electron-phonon coupling (EPC) and anharmonic superconductivity of copper hydrides using first-principles calculations. Cubic-Cu4H3 remains stable at ambient pressure after kinetic simulations from its experimentally synthesized pressure state. The incorporation of hydrogen impacts the ductility of Cu4H3 negligibly compared to copper, while enabling high-Tc superconductivity up to 77 K and non-trivial band topology at ambient pressure. The novel properties arise from the strong EPC, Fermi surface nesting and hydrogen-induced band inversion. This discovery may fill the gap in the lack of ductile superconductors in the liquid-nitrogen temperature range and pave a new way for realizing high-temperature topological superconductivity at atmospheric pressure.

Symmetry-Shaped Singularities in High-Temperature Superconductor H3S

The superconducting critical temperature of H3S ranks among the highest measured, at 203 K. This impressive value stems from a singularity in the electronic density-of-states, induced by a flat-band region that consists of saddle points. The peak sits right at the Fermi level, so that it gives rise to a giant electron-phonon coupling constant. In this work, we show how atomic orbital interactions and space group symmetry work in concert to shape the singularity. The body-centered cubic Brillouin Zone offers a unique 2D hypersurface in reciprocal space: fully connecting squares with two different high-symmetry points at the corners, Γ and H, and a third one in the center, N. Orbital mixing leads to the collapse of fully connected 1D saddle point lines around the square centers, due to a symmetry-enforced s-p energy inversion between Γ and H. The saddle-point states are invariably nonbonding, which explains the unconventionally weak response of the superconductor's critical temperature to pressure. Although H3S appears to be a unique case, the theory shows how it is possible to engineer flat bands and singularities in 3D lattices through symmetry considerations.

Clathrate metal superhydrides under high-pressure conditions: enroute to room-temperature superconductivity

Room-temperature superconductivity has been a long-held dream of mankind and a focus of considerable interest in the research field of superconductivity. Significant progress has recently been achieved in hydrogen-based superconductors found in superhydrides (hydrides with unexpectedly high hydrogen contents) that are stabilized under high-pressure conditions and are not capturable at ambient conditions. Of particular interest is the discovery of a class of best-ever-known superconductors in clathrate metal superhydrides that hold the record for high superconductivity (e.g. T c = 250-260 K for LaH10) among known superconductors and have great promise to be those that realize the long-sought room-temperature superconductivity. In these peculiar clathrate superhydrides, hydrogen forms unusual 'clathrate' cages containing encaged metal atoms, of which such a kind was first reported in a calcium hexa-superhydride (CaH6) showing a measured high T c of 215 K under a pressure of 170 GPa. In this review, we aim to offer an overview of the current status of research progress on the clathrate metal superhydride superconductors, discuss the superconducting mechanism and highlight the key features (e.g. structure motifs, bonding features, electronic structure, etc.) that govern the high-temperature superconductivity. Future research direction along this line to find room-temperature superconductors will be discussed.

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.

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.

Enhancement for phonon-mediated superconductivity up to 37 K in few-hydrogen metal-bonded layered magnesium hydride under atmospheric pressure

The discovery of superconductivity in layered MgB2 has renewed interest in the search for high-temperature conventional superconductors, leading to the synthesis of numerous hydrogen-dominated materials with high critical temperatures (Tc) under high pressures. However, achieving a high-Tc superconductor under ambient pressure remains a challenging goal. In this study, we propose a novel approach to realize a high-temperature superconductor under ambient pressure by introducing a hexagonal H monolayer into the hexagonal close-packed magnesium lattice, resulting in a new and stable few-hydrogen metal-bonded layered magnesium hydride (Mg4)2H1. This compound exhibits superior ductility compared to multi-hydrogen, cuprate, and iron-based superconductors due to its metallic bonding. Our unconventional strategy diverges from the conventional design principles used in hydrogen-dominated covalent high-temperature superconductors. Using anisotropic Migdal-Eliashberg equations, we demonstrate that the stable (Mg4)2H1 compound is a typical phonon-mediated superconductor, characterized by strong electron-phonon coupling and an excellent Tc of 37 K under ambient conditions, comparable to that of MgB2. Our findings not only present a new pathway for exploring high-temperature superconductors but also provide valuable insights for future experimental synthesis endeavors.

Superconducting H7 chain in gallium hydrides at high pressure

Pressure-stabilized hydrides have potential as an outstanding reservoir for high-temperature (T_c) superconductors. We undertook a systematic study of crystal structures and superconducting properties of gallium hydrides using an advanced structure-search method together with first-principles calculations. We identified an unconventional stoichiometric GaH₇ gallium hydride that is thermodynamically stable at pressures above 247 GPa. Interestingly, the H atoms are clustered to form a unique H₇ chain intercalating the Ga framework. Further calculations show a high estimated T_c above 100 K at 200-300 GPa for GaH₇, closely related to the strong coupling between electrons of Ga and H atoms, and phonon vibrations of H₇ chains. Our work provides an example of exploration for diverse superconducting hydrogen motifs under high pressure, and may stimulate further experimental syntheses.

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.

Predicted structures and superconductivity of LiYHn (n = 5-10) under high pressure

The structures of LiYH_n (n = 5-10) compounds in the pressure range of 0-300 GPa have been extensively explored using the CALYPSO structure prediction method based on the particle swarm optimization algorithm and first-principles calculation. Four stable structures (P2₁/m LiYH₆, C2/c LiYH₈, P1̄ LiYH₉, R3̄m LiYH₁₀) and three metastable phases (Pnma LiYH₆, P1̄ LiYH₈, Immm LiYH₉) were predicted. They all exhibit metallic and superconducting behavior in their respective stable pressure ranges, and the predicted superconducting transition temperature T_c is within 22-109 K when the pressure is greater than 100 GPa. It was found that after doping Li into YH_n (n = 6, 9, 10), the H₂ units in the system increased, the electron-phonon coupling interaction weakened, and T_c decreased when the structural characteristics, electronic density of states distribution, and superconductivity of LiYH_n and YH_n (n = 6, 8, 9, 10) were compared. Systems that have a high density of H_s states and a low number of Y_d states at the Fermi level have stronger electron-phonon coupling (EPC) interactions and higher T_c.

The 2021 room-temperature superconductivity roadmap

Designing materials with advanced functionalities is the main focus of contemporary solid-state physics and chemistry. Research efforts worldwide are funneled into a few high-end goals, one of the oldest, and most fascinating of which is the search for an ambient temperature superconductor (A-SC). The reason is clear: superconductivity at ambient conditions implies being able to handle, measure and access a single, coherent, macroscopic quantum mechanical state without the limitations associated with cryogenics and pressurization. This would not only open exciting avenues for fundamental research, but also pave the road for a wide range of technological applications, affecting strategic areas such as energy conservation and climate change. In this roadmap we have collected contributions from many of the main actors working on superconductivity, and asked them to share their personal viewpoint on the field. The hope is that this article will serve not only as an instantaneous picture of the status of research, but also as a true roadmap defining the main long-term theoretical and experimental challenges that lie ahead. Interestingly, although the current research in superconductor design is dominated by conventional (phonon-mediated) superconductors, there seems to be a widespread consensus that achieving A-SC may require different pairing mechanisms.In memoriam, to Neil Ashcroft, who inspired us all.

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.

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.

The electron–phonon coupling constant and the Debye temperature in polyhydrides of thorium, hexadeuteride of yttrium, and metallic hydrogen phase III

A milestone experimental discovery of superconductivity above 200 K in highly compressed sulfur hydride by Drozdov et al. [Nature 525, 73 (2015)] sparked experimental and theoretical investigations of metallic hydrides. Since then, a dozen of superconducting binary and ternary polyhydrides have been discovered. For instance, there are three superconducting polyhydrides of thorium: Th4H15, ThH9, and ThH10 and four polyhydrides of yttrium: YH4, YH6, YH7, and YH9. In addition to binary and ternary hydrogen-based metallic compounds, recently Eremets et al. (arXiv:2109.11104) reported on the metallization of hydrogen, which exhibits a phase transition into metallic hydrogen phase III at P ≥ 330 GPa and T ∼ 200 K. Here, we analyzed temperature-dependent resistance, R(T), in polyhydrides of thorium, hexadeuteride of yttrium, and in hydrogen phase III and deduced the Debye temperature, Tθ, and the electron–phonon coupling constant, λe−ph, for these conductors. We found that I-43d-Th4H15 exhibits λe−ph = 0.82–0.99, which is in very good agreement with the experimental value of λe−ph = 0.84 deduced from heat capacity measurements [Miller et al., Phys. Rev. B 14, 2795 (1976)]. For P63/mmc-ThH9 (P = 170 GPa), we deduced λe−ph(170 GPa) = 1.46 ± 0.01, which is in reasonable agreement with λe−ph computed by first-principles calculations [Semenok et al. Mater. Today 33, 36 (2020)]. Deduced λe−ph(170 GPa) = 1.70 ± 0.04 for Fm-3m-ThH10 is in remarkable agreement with first-principles calculated λe−ph(174 GPa) = 1.75 [Semenok et al., Mater. Today 33, 36 (2020)]. Deduced λe−ph(172 GPa) = 1.90 ± 0.02 for Im-3m-YD6 is also in excellent agreement with first-principles calculated λe−ph(165 GPa) = 1.80 [Troyan et al., Adv. Mater. 33, 2006832 (2021)]. Finally, we deduced Tθ(402 GPa) = 727 ± 6 K for hydrogen phase III, which implies that λe−ph(402 GPa) ≤ 1.7 in this metal.

Superconducting ScH3 and LuH3 at Megabar Pressures

Rare-earth (RE) superhydrides have great potential as high-temperature superconductors, with recent discoveries almost achieving room-temperature superconductivity in compressed LaH₁₀ and YH₉. Here, we continue to study the rare-earth hydrides by focusing on the new hydrides that the lightest element Sc and the heaviest element Lu formed under pressure. Two new superconducting hydrides ScH₃ (T_c ∼ 18.5 K at 131 GPa) and LuH₃ (T_c ∼ 12.4 K at 122 GPa) have been identified both with cubic structure by combining X-ray diffraction and electrical resistance techniques. Among all of the REH₃, only the superconducting properties of ScH₃ and LuH₃ have been experimentally confirmed. Our current results may offer guidance to other REH₃, which were predicted to be superconductors but have not been experimentally confirmed.

Pressure-induced superconducting CS2H10 with an H3S framework

The discovery of the high-temperature superconducting state in the compounds of hydrogen, carbon and sulfur with a critical temperature (T_c) of 288 K at high pressure is an important milestone towards room-temperature superconductors. Here, we have extensively investigated the high-pressure phases of CS₂H₁₀, and found four phases Cmc2₁, P3m1, P3̄m1 and Pm. Among them, P3m1 can be dynamically stable at a pressure as low as 50 GPa, and Cmc2₁ has a high T_c of 155 K at 150 GPa. Both Cmc2₁ and P3m1 are host-guest hydrides, in which CH₄ molecules are inserted into Im3̄m-H₃S and R3m-H₃S sublattices, respectively. Their T_c is dominated by the H₃S lattice inside. The insertion of CH₄ molecules greatly reduces the pressure required for the stability of the original H₃S lattice, but it has a negative impact on superconductivity which cannot be ignored. By studying the effect of CH₄ insertion in the H₃S lattice, we can design hydrides with a T_c close to that of H₃S and a greatly reduced pressure required for stability.

Classifying Charge Carrier Interaction in Highly Compressed Elements and Silane

Since the pivotal experimental discovery of near-room-temperature superconductivity (NRTS) in highly compressed sulphur hydride by Drozdov et al. (Nature 2015, 525, 73-76), more than a dozen binary and ternary hydrogen-rich phases exhibiting superconducting transitions above 100 K have been discovered to date. There is a widely accepted theoretical point of view that the primary mechanism governing the emergence of superconductivity in hydrogen-rich phases is the electron-phonon pairing. However, the recent analysis of experimental temperature-dependent resistance, R(T), in H₃S, LaH_x, PrH₉ and BaH₁₂ (Talantsev, Supercond. Sci. Technol. 2021, 34, accepted) showed that these compounds exhibit the dominance of non-electron-phonon charge carrier interactions and, thus, it is unlikely that the electron-phonon pairing is the primary mechanism for the emergence of superconductivity in these materials. Here, we use the same approach to reveal the charge carrier interaction in highly compressed lithium, black phosphorous, sulfur, and silane. We found that all these superconductors exhibit the dominance of non-electron-phonon charge carrier interaction. This explains the failure to demonstrate the high-T_c values that are predicted for these materials by first-principles calculations which utilize the electron-phonon pairing as the mechanism for the emergence of their superconductivity. Our result implies that alternative pairing mechanisms (primarily the electron-electron retraction) should be tested within the first-principles calculations approach as possible mechanisms for the emergence of superconductivity in highly compressed lithium, black phosphorous, sulfur, and silane.

Room-temperature-superconducting Tc driven by electron correlation

Room-temperature-superconducting Tc measured by high pressure in hydrides can be theoretically explained by a Brinkman-Rice (BR)-Bardeen-Cooper-Schrieffer (BCS) Tc combining both the generalized BCS Tc and the diverging effective mass, m*/m = 1/(1 - (U/Uc)2), with the on-site Coulomb interaction U in the BR picture. A transition from U in a correlated metal of the normal state to Uc in the superconducting state can lead to superconductivity, which can be caused by volume contraction induced by high pressure or low temperature.

High-temperature superconductivity in transition metallic hydrides MH11 (M = Mo, W, Nb, and Ta) under high pressure

The discovery of H₃S and LaH₁₀ is an important step towards the development of room temperature superconductors which fuels the enthusiasm for finding promising superconductors among hydrides at high pressure. In the present study, three new and stable stoichiometric MoH₅, MoH₆ and MoH₁₁ compounds were found in the pressure range of 100-300 GPa. The highly hydrogen-rich phase of Cmmm-MoH₁₁ has a layered structure that contains various forms of hydrogen: H, H₂^- and H₃^- units. It is a high-T_c material with an estimated T_c value in the range of 165-182 K at 250 GPa. The same structures are also found in NbH₁₁, TaH₁₁, and WH₁₁, each material showing T_c ranging from 117 to 168 K. By combining the method of using two coupling constants λ_opt and λ_ac, and two characteristic frequencies (optical and acoustic) with first-principle calculations, we found that the high values of T_c are mainly caused by the presence of high frequency optical modes, but the acoustic modes also play a noticeable role.

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.

Origin of enhanced chemical precompression in cerium hydride [Formula: see text]

The rare-earth metal hydrides with clathrate structures have been highly attractive because of their promising high-[Formula: see text] superconductivity at high pressure. Recently, cerium hydride [Formula: see text] composed of Ce-encapsulated clathrate H cages was synthesized at much lower pressures of 80-100 GPa, compared to other experimentally synthesized rare-earth hydrides such as [Formula: see text] and [Formula: see text]. Based on density-functional theory calculations, we find that the Ce 5p semicore and 4f/5d valence states strongly hybridize with the H 1s state, while a transfer of electrons occurs from Ce to H atoms. Further, we reveal that the delocalized nature of Ce 4f electrons plays an important role in the chemical precompression of clathrate H cages. Our findings not only suggest that the bonding nature between the Ce atoms and H cages is characterized as a mixture of ionic and covalent, but also have important implications for understanding the origin of enhanced chemical precompression that results in the lower pressures required for the synthesis of [Formula: see text].

Structural, mechanical and electronic properties and hardness of ionic vanadium dihydrides under pressure from first-principles computations

Based on a combination of the CALYPSO method for crystal structure prediction and first-principles calculations, we explore the crystal structures of VH2 under the pressure range of 0-300 GPa. The cubic Fm-3m phase with regular VH8 cubes is predicted to transform into orthorhombic Pnma structure with fascinating distorted VH9 tetrakaidecahedrons at 47.36 GPa. Both the Fm-3m phase at 0 GPa and the Pnma phase at 100 GPa are mechanically and dynamically stable, as verified with the calculations of elastic constants and phonon dispersions, respectively. Moreover, the calculated electronic band structure and density of states indicate both stable phases are metallic. Remarkably, the analyses of the Poisson's ratio, electron localization function (ELF) and Bader charge substantiate that both stable phases are ionic crystals on account of effective charges transferring from V atom to H. On the basis of the microscopic hardness model, the Fm-3m and Pnma crystals of VH2 are potentially incompressible and hard materials with the hardness values of 17.83 and 17.68 GPa, respectively.

Superconducting Zirconium Polyhydrides at Moderate Pressures

Highly compressed hydrides have been at the forefront of the search for high-T_c superconductivity. The recent discovery of record-high T_c's in H₃S and LaH_10±x under high pressure fuels the enthusiasm for finding good superconductors in similar hydride groups. Guided by first-principles structure prediction, we successfully synthesized ZrH₃ and Zr₄H₁₅ at modest pressures (30-50 GPa) in diamond anvil cells by two different reaction routes: ZrH₂ + H₂ at room temperature and Zr + H₂ at ∼1500 K by laser heating. From the synchrotron X-ray diffraction patterns, ZrH₃ is found to have a Pm3̅n structure corresponding to the familiar A15 structure, and Zr₄H₁₅ has an I4̅3d structure isostructural to Th₄H₁₅. Electrical resistance measurement and the dependence of T_c on the applied magnetic field of the sample showed the emergence of two superconducting transitions at 6.4 and 4.0 K at 40 GPa, which correspond to the two T_c's for ZrH₃ and Zr₄H₁₅.

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.

High-temperature superconductivity in sulfur hydride evidenced by alternating-current magnetic susceptibility

The search for high-temperature superconductivity is one of the research frontiers in physics. In the sulfur hydride system, an extremely high T _c (∼200 K) has been recently developed at pressure. However, the Meissner effect measurement above megabar pressures is still a great challenge. Here, we report the superconductivity identification of sulfur hydride at pressure, employing an in situ alternating-current magnetic susceptibility technique. We determine the superconducting phase diagram, finding that superconductivity suddenly appears at 117 GPa and T _c reaches 183 K at 149 GPa before decreasing monotonically with increasing pressure. By means of theoretical calculations, we elucidate the variation of T _c in the low-pressure region in terms of the changing stoichiometry of sulfur hydride and the further decrease in T _c owing to a drop in the electron-phonon interaction parameter λ. This work provides a new insight into clarifying superconducting phenomena and anchoring the superconducting phase diagram in the hydrides.

Atomic and Electronic Properties of a 155 H2S Cluster under Pressure

This is an all-electron density functional study of a cluster with 155 H2S molecules subjected to pressures between 0.2 and 681.2 GPa. For modeling pressure, the cluster was in a container made of 500 He atoms. As the pressure increased, the bond length between the atoms decreased. This decrease changed the atomic distribution of the cluster. Initially, the H2S molecules interacted weakly through hydrogen bonds. Then, the pressure moved the H atoms along the axis connecting two sulfur atoms, with S-H bond lengths between 1.4 and 1.6 Å. At high pressures, the atomic distribution consisted of interleaved layers of H and S atoms. The energy density of states of the valence band had two sub-bands with an energy gap between them. The overlapping of the 2a1 molecular orbitals of the H2S molecules determined the molecular orbitals in the low-energy sub-band. In this sub-band, the molecular orbital with the lowest energy has no nodes; at high pressures, it has non-zero values for all the internuclear regions of the cluster. The overlapping of the molecular orbitals 1b2, 3a1, and 1b1 of the H2S molecules determined the orbitals in the high-energy sub-band. The energy band gap (lowest unoccupied molecular orbital-highest occupied molecular orbital) decreased with the pressure, from 5.3906 eV for 0.2 GPa to 0.4980 eV for 681.2 GPa, whereas the gap between the sub-bands decreased from 4.7729 eV for 0.2 GPa to 0.03 eV for pressures higher than 125.5 GPa. The present study provides, from first principles, an idea on the role of hydrogen atoms in the evolution of solid phases of H2S with pressure, which is difficult to obtain from experiments.

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.

Stoichiometric evolutions of PH3 under high pressure: implication for high-T c superconducting hydrides

The superconductivity of hydrides under high pressure has attracted a great deal of attention since the recent observation of the superconducting transition at 203 K in strongly compressed H2S. It has been realized that the stoichiometry of hydrides might change under high pressure, which is crucial in understanding the superconducting mechanism. In this study, PH3 was studied to understand its superconducting transition and stoichiometry under high pressure using Raman, IR and X-ray diffraction measurements, as well as theoretical calculations. PH3 is stable below 11.7 GPa and then it starts to dehydrogenate through two dimerization processes at room temperature and pressures up to 25 GPa. Two resulting phosphorus hydrides, P2H4 and P4H6, were verified experimentally and can be recovered to ambient pressure. Under further compression above 35 GPa, the P4H6 directly decomposed into elemental phosphorus. Low temperature can greatly hinder polymerization/decomposition under high pressure and retains P4H6 up to at least 205 GPa. The superconductivity transition temperature of P4H6 is predicted to be 67 K at 200 GPa, which agrees with the reported result, suggesting that it might be responsible for superconductivity at higher pressures. Our results clearly show that P2H4 and P4H6 are the only stable P-H compounds between PH3 and elemental phosphorus, which is helpful for shedding light on the superconducting mechanism.

Anomalously high value of Coulomb pseudopotential for the H5S2 superconductor

The H₅S₂ and H₂S compounds are the two candidates for the low-temperature phase of compressed sulfur-hydrogen system. We have shown that the value of Coulomb pseudopotential (μ*) for H₅S₂ ([T_C]_exp = 36 K and p = 112 GPa) is anomalously high. The numerical results give the limitation from below to μ* that is equal to 0.402 (μ* = 0.589), if we consider the first order vertex corrections to the electron-phonon interaction). Presented data mean that the properties of superconducting phase in the H₅S₂ compound can be understood within the classical framework of Eliashberg formalism only at the phenomenological level (μ* is the parameter of matching the theory to the experimental data). On the other hand, in the case of H₂S it is not necessary to take high value of Coulomb pseudopotential to reproduce the experimental critical temperature relatively well (μ* = 0.15). In our opinion, H₂S is mainly responsible for the observed superconductivity state in the sulfur-hydrogen system at low temperature.

Key Role of Lanthanum Oxychloride: Promotional Effects of Lanthanum in NiLaOy /NaCl for Hydrogen Production from Ethyl Acetate and Water

The hydrogen economy is accelerating technological evolutions toward highly efficient hydrogen production. In this work, the catalytic performance of NiO/NaCl for hydrogen production via autothermal reforming of ethyl acetate and water is further improved through lanthanum modification, and the resulted 3%-NiLaO_y /NaCl catalyst achieves as high as 93% H₂ selectivity and long-term stability at 600 °C. The promoting effect is caused by the strong interactions between lanthanum and NiO/NaCl, by which LaNiO₃ and a novel LaOCl phase are formed. The key role of LaOCl in promoting low-temperature hydrogen production is highlighted, while effects of LaNiO₃ are well known. The LaOCl (010) facet possesses high adsorption capacity toward co-chemisorbing ethyl acetate and water. LaOCl strongly interacts with ethyl acetate and H₂ O in the form of hydrogen bonding and coordination effect. The interactions induce tensions inside ethyl acetate and H₂ O, activate the molecules, and hence decrease the energy barrier for reaction. In situ Fourier transform infrared spectroscopy (FTIR) reveals that LaOCl along with NaCl enhances the adsorption ability of NiO/NaCl. Moreover, LaOCl improves the dispersion of Ni species in NiO-LaNiO₃ -LaOCl nanosheets, which possess abundant active sites. The effects together promote hydrogen evolution. Furthermore, the NiLaO_y /NaCl catalyst can be easily reborn after deactivation due to the water solubility of NaCl.

Superconductivity in solid benzene molecular crystal

Light-element compounds hold great promise of high critical temperature superconductivity judging from the theoretical perspective. A hydrogen-rich material, benzene, is such a kind of candidate but also an organic compound. A series of first-principles calculations are performed on the electronic structures, dynamics properties, and electron-phonon interactions of solid benzene at high pressures. Benzene is found to be dynamically stable in the pressure range of 180-200 GPa and to exhibit superconductivity with a maximum transition temperature of 20 K at 195 GPa. The phonon modes of carbon atoms are identified to mainly contribute to the electron-phonon interactions driving this superconductivity. The predicted superconductivity in this simplest pristine hydrocarbon shows a common feature in aromatic hydrocarbons and also makes it a bridge to organic and hydrogen-rich superconductors.

Dynamic electron-ion collisions and nuclear quantum effects in quantum simulation of warm dense matter

The structural, thermodynamic and transport properties of warm dense matter (WDM) are crucial to the fields of astrophysics and planet science, as well as inertial confinement fusion. WDM refers to the states of matter in a regime of temperature and density between cold condensed matter and hot ideal plasmas, where the density is from near-solid up to ten times solid density, and the temperature between 0.1 and 100 eV. In the WDM regime, matter exhibits moderately or strongly coupled, partially degenerate properties. Therefore, the methods used to deal with condensed matter and isolated atoms need to be properly validated for WDM. It is therefore a big challenge to understand WDM within a unified theoretical description with reliable accuracy. Here, we review the progress in the theoretical study of WDM with state-of-the-art simulations, i.e. quantum Langevin molecular dynamics and first principles path integral molecular dynamics. The related applications for WDM are also included.

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.

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.

Investigation of superconductivity in compressed vanadium hydrides

Aiming at finding new superconducting materials, we performed systematical simulations on phase diagrams, crystal structures, and electronic properties of vanadium hydrides under high pressures. The VH, VH₂, VH₃, and VH₅ species were found to be stable under high pressures; among these, VH₂ had previously been investigated. Moreover, all three novel stoichiometries showed a strong ionic character as a result of the charge transfer from V to H. The electron-phonon coupling calculations revealed the potentially superconductive nature of these vanadium hydrides, with estimated superconducting critical temperature (T_c) values of 6.5-10.7 K for R3[combining overline]m (VH), 8.0-1.6 K for Fm3[combining overline]m (VH₃), and 30.6-22.2 K for P6/mmm (VH₅) within the pressure range from 150 GPa to 250 GPa.

High-pressure structures of yttrium hydrides

In this work, the crystal structures of YH₃ and YH₄ at high pressure (100-250 GPa) have been explored using a genetic algorithm combined with first-principles calculations. New structures of YH₃ with space group symmetries of P21/m and I4/mmm were predicted. The electronic structures and the phonon dispersion properties of various YH₃ and YH₄ structures at different temperatures and pressures were investigated. Among YH₃ phases, the P21/m structure of YH₃ was found to have a relatively high superconducting transformation temperature T _c of 19 K at 120 GPa, which is reduced to 9 K at 200 GPa. Other YH₃ structures have much lower T _cs. Compared with YH₃, the T _c of the YH₄ compound is much higher, i.e. 94 K at 120 GPa and 55 K at 200 GPa.

Emergence of superconductivity in doped H2O ice at high pressure

We investigate the possibility of achieving high-temperature superconductivity in hydrides under pressure by inducing metallization of otherwise insulating phases through doping, a path previously used to render standard semiconductors superconducting at ambient pressure. Following this idea, we study H2O, one of the most abundant and well-studied substances, we identify nitrogen as the most likely and promising substitution/dopant. We show that for realistic levels of doping of a few percent, the phase X of ice becomes superconducting with a critical temperature of about 60 K at 150 GPa. In view of the vast number of hydrides that are strongly covalent bonded, but that remain insulating up to rather large pressures, our results open a series of new possibilities in the quest for novel high-temperature superconductors.

Potential high-Tc superconducting lanthanum and yttrium hydrides at high pressure

A systematic structure search in the La-H and Y-H systems under pressure reveals some hydrogen-rich structures with intriguing electronic properties. For example, LaH₁₀ is found to adopt a sodalite-like face-centered cubic (fcc) structure, stable above 200 GPa, and LaH₈ a C2/m space group structure. Phonon calculations indicate both are dynamically stable; electron phonon calculations coupled to Bardeen-Cooper-Schrieffer (BCS) arguments indicate they might be high-T_c superconductors. In particular, the superconducting transition temperature T_c calculated for LaH₁₀ is 274-286 K at 210 GPa. Similar calculations for the Y-H system predict stability of the sodalite-like fcc YH₁₀ and a T_c above room temperature, reaching 305-326 K at 250 GPa. The study suggests that dense hydrides consisting of these and related hydrogen polyhedral networks may represent new classes of potential very high-temperature superconductors.

Formation of novel transition metal hydride complexes with ninefold hydrogen coordination

Ninefold coordination of hydrogen is very rare, and has been observed in two different hydride complexes comprising rhenium and technetium. Herein, based on a theoretical/experimental approach, we present evidence for the formation of ninefold H- coordination hydride complexes of molybdenum ([MoH₉]³⁻), tungsten ([WH₉]³⁻), niobium ([NbH₉]⁴⁻) and tantalum ([TaH₉]⁴⁻) in novel complex transition-metal hydrides, Li₅MoH₁₁, Li₅WH₁₁, Li₆NbH₁₁ and Li₆TaH₁₁, respectively. All of the synthesized materials are insulated with band gaps of approximately 4 eV, but contain a sufficient amount of hydrogen to cause the H 1s-derived states to reach the Fermi level. Such hydrogen-rich materials might be of interest for high-critical-temperature superconductivity if the gaps close under compression. Furthermore, the hydride complexes exhibit significant rotational motions associated with anharmonic librations at room temperature, which are often discussed in relation to the translational diffusion of cations in alkali-metal dodecahydro-closo-dodecaborates and strongly point to the emergence of a fast lithium conduction even at room temperature.