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

Superconductivity with T c of 116 K discovered in antimony polyhydrides

Superconductivity (SC) was experimentally observed for the first time in antimony polyhydride. The diamond anvil cell combined with a laser heating system was used to synthesize the antimony polyhydride sample at high pressure and high temperature. In-situ high pressure transport measurements as a function of temperature with an applied magnetic field were performed to study the SC properties. It was found that the antimony polyhydride samples show superconducting transition with critical temperature T c 116 K at 184 GPa. The investigation of SC at magnetic field revealed the superconducting coherent length of ∼40 Å based on the Ginzburg Landau (GL) equation. Antimony polyhydride superconductor has the second highest T c in addition to sulfur hydride among the polyhydrides of elements from main groups IIIA to VIIA in the periodic table.

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.

Superconducting ternary hydrides: progress and challenges

Since the discovery of the high-temperature superconductors H3S and LaH10 under high pressure, compressed hydrides have received extensive attention as promising candidates for room-temperature superconductors. As a result of current high-pressure theoretical and experimental studies, it is now known that almost all the binary hydrides with a high superconducting transition temperature (T c) require extremely high pressure to remain stable, hindering any practical application. In order to further lower the stable pressure and improve superconductivity, researchers have started exploring ternary hydrides and had many achievements in recent years. Here, we discuss recent progress in ternary hydrides, aiming to deepen the understanding of the key factors regulating the structural stability and superconductivity of ternary hydrides, such as structural motifs, bonding features, electronic structures, electron-phonon coupling, etc. Furthermore, the current issues and challenges of superconducting ternary hydrides are presented, together with the prospects and opportunities for future research.

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.

Superconductivity above 105 K in Nonclathrate Ternary Lanthanum Borohydride below Megabar Pressure

Hydrides are promising candidates for achieving room-temperature superconductivity, but a formidable challenge remains in reducing the stabilization pressure below a megabar. In this study, we successfully synthesized a ternary lanthanum borohydride by introducing the nonmetallic element B into the La-H system, forming robust B-H covalent bonds that lower the pressure required to stabilize the superconducting phase. Electrical transport measurements confirm the presence of superconductivity with a critical temperature (Tc) of up to 106 K at 90 GPa, as evidenced by zero resistance and Tc shift under an external magnetic field. X-ray diffraction and transport measurements identify the superconducting compound as LaB2H8, a nonclathrate hydride, whose crystal structure remains stable at pressures as low as ∼ half megabar (59 GPa). Stabilizing superconductive stoichiometric LaB2H8 in a submegabar pressure regime marks a substantial advancement in the quest for high-Tc superconductivity in polynary hydrides, bringing us closer to the ambient pressure conditions.

Superior Superconducting Properties Realized in Quaternary La-Y-Ce Hydrides at Moderate Pressures

The recent revolution in the superconductivity field stems from hydride superconductors. Multicomponent hydrides provide a crucial platform for tracking high-temperature superconductors. Besides high superconducting transition temperature (Tc), achieving both giant upper critical magnetic field [μ0Hc2(0)] and high critical current density [Jc(0)] is also key to the latent potential of the application for hydride superconductors. In this work, we have successfully synthesized quaternary La-Y-Ce hydrides with excellent properties under moderate pressure by using the concept of "entropy engineering." The obtained temperature dependence of the resistance provides evidence for the superconductivity of Fm3m-(La,Y,Ce)H10, with the maximum Tc ∼ 190 K (at 112 GPa). Notably, Fm3m-(La,Y,Ce)H10 boasts exceptional properties: μ0Hc2(0) reaching 292 T and Jc(0) surpassing 4.61 × 107 A/cm2. Compared with the binary LaH10/YH10, we find that the Fm3m structure in (La,Y,Ce)H10 can be stable at relatively low pressures (112 GPa). These results indicate that multicomponent hydrides can significantly enhance the superconducting properties and regulate stabilizing pressure through the application of "entropy engineering." This work stimulates the experimental exploration of multihydride superconductors and also provides a reference for the search of room-temperature superconductors in more diversified hydride materials in the future.

Layered Hydride LiH4 with a Pressure-Insensitive Superconductivity

For hydride superconductors, each significant advance is built upon the discovery of novel H-based structural units, which in turn push the understanding of the superconducting mechanism to new heights. Based on first-principles calculations, we propose a metastable LiH4 with a wavy H layer composed of the edge-sharing pea-like H18 rings at high pressures. Unexpectedly, it exhibits pressure-insensitive superconductivity manifested by an extremely small pressure coefficient (dTc/dP) of 0.04 K/GPa. This feature is attributed to the slightly weakened electron-phonon coupling with pressure, caused by the reduced charge transfer from Li atoms to wavy H layers, significantly suppressing the substantial increase in the contribution of phonons to Tc. Its superconductivity originates from the strong coupling between the H 1s electrons and the high-frequency phonons associated with the H layer. Our study extends the list of H-based structural units and enhances the in-depth understanding of pressure-related superconductivity.

Diverse high-pressure chemistry in Y-NH3BH3 and Y-paraffin oil systems

The yttrium-hydrogen system has gained attention because of near-ambient temperature superconductivity reports in yttrium hydrides at high pressures. We conducted a study using synchrotron single-crystal x-ray diffraction (SCXRD) at 87 to 171 GPa, resulting in the discovery of known (two YH3 phases) and five previously unknown yttrium hydrides. These were synthesized in diamond anvil cells by laser heating yttrium with hydrogen-rich precursors-ammonia borane or paraffin oil. The arrangements of yttrium atoms in the crystal structures of new phases were determined on the basis of SCXRD, and the hydrogen content estimations based on empirical relations and ab initio calculations revealed the following compounds: Y3H11, Y2H9, Y4H23, Y13H75, and Y4H25. The study also uncovered a carbide (YC2) and two yttrium allotropes. Complex phase diversity, variable hydrogen content in yttrium hydrides, and their metallic nature, as revealed by ab initio calculations, underline the challenges in identifying superconducting phases and understanding electronic transitions in high-pressure synthesized materials.

Synthesis and superconductivity in yttrium-cerium hydrides at high pressures

Further increasing the critical temperature and/or decreasing the stabilized pressure are the general hopes for the hydride superconductors. Inspired by the low stabilized pressure associated with Ce 4f electrons in superconducting cerium superhydride and the high critical temperature in yttrium superhydride, we carry out seven independent runs to synthesize yttrium-cerium alloy hydrides. The synthetic process is examined by the Raman scattering and X-ray diffraction measurements. The superconductivity is obtained from the observed zero-resistance state with the detected onset critical temperatures in the range of 97-141 K. The upper critical field towards 0 K at pressure of 124 GPa is determined to be between 56 and 78 T by extrapolation of the results of the electrical transport measurements at applied magnetic fields. The analysis of the structural data and theoretical calculations suggest that the phase of Y0.5Ce0.5H9 in hexagonal structure with the space group of P63/mmc is stable in the studied pressure range. These results indicate that alloying superhydrides indeed can maintain relatively high critical temperature at relatively modest pressures accessible by laboratory conditions.

Anharmonic theory of superconductivity and its applications to emerging quantum materials

The role of anharmonicity on superconductivity has often been disregarded in the past. Recently, it has been recognized that anharmonic decoherence could play a fundamental role in determining the superconducting properties (electron-phonon coupling, critical temperature, etc) of a large class of materials, including systems close to structural soft-mode instabilities, amorphous solids and metals under extreme high-pressure conditions. Here, we review recent theoretical progress on the role of anharmonic effects, and in particular certain universal properties of anharmonic damping, on superconductivity. Our focus regards the combination of microscopic-agnostic effective theories for bosonic mediators with the well-established BCS theory and Migdal-Eliashberg theory for superconductivity. We discuss in detail the theoretical frameworks, their possible implementation within first-principles methods, and the experimental probes for anharmonic decoherence. Finally, we present several concrete applications to emerging quantum materials, including hydrides, ferroelectrics and systems with charge density wave instabilities.

High-temperature superconductivity up to 223 K in the Al stabilized metastable hexagonal lanthanum superhydride

As compressed hydrides constantly refresh the records of superconducting critical temperatures (Tc) in the vicinity of room temperature, this further reinforces the confidence to find more high-temperature superconducting hydrides. In this process, metastable phases of superhydrides offer enough possibilities to access superior superconducting properties. Here we report a metastable hexagonal lanthanum superhydride (P63/mmc-LaH10) stabilized at 146 GPa by introducing an appropriate proportion of Al, which exhibits high-temperature superconductivity with Tc ∼ 178 K, and this value is enhanced to a maximum Tc ∼ 223 K at 164 GPa. A huge upper critical magnetic field value Hc2(0) reaches 223 T at 146 GPa. The small volume expansion of P63/mmc-(La, Al) H10 compared with the binary LaH10 indicates the possible interstitial sites of Al atoms filling into the La-H lattice, instead of forming conventional ternary alloy-based superhydrides. This work provides a new strategy for metastable high-temperature superconductors through the multiple-element system.

Prediction of superconductivity in metallic boron-carbon compounds from 0 to 100 GPa by high-throughput screening

Boron-carbon compounds have been shown to have feasible superconductivity. In our earlier paper [Zheng et al., Phys. Rev. B, 2023, 107, 014508], we identified a new conventional superconductor of LiB3C at 100 GPa. Here, we aim to extend the investigation of possible superconductivity in this structural framework by replacing Li atoms with 27 different cations from periods 3, 4, and 5 under pressures ranging from 0 to 100 GPa. Using the high-throughput screening method of zone-center electron-phonon interaction, we found that ternary compounds like CaB3C, SrB3C, TiB3C, and VB3C are promising candidates for superconductivity. The consecutive calculations using the full Brillouin zone confirm that they have a Tc of <31 K at moderate pressures. Our study demonstrates that fast screening of superconductivity by calculating zone-center electron-phonon coupling strength is an effective strategy for high-throughput identification of new superconductors.

Crystal structure prediction and non-superconductivity of N-doped LuH3at near ambient pressure

Lanthanide polyhydrides, which have attracted the attention of researchers, are considered as a potential candidate material for high-temperature superconductivity. Especially, it is reported that N-doped LuH3exhibits near ambient superconductivity recently. It has attracted attention to room temperature superconductivity of ternary Lu-N-H systems at near ambient pressure. Here, we constructed a LuNH3(N-doped LuH3) compound to predict the crystal structural at relatively low pressures. We found a stable ternary LuNH3structure with a tetragonalP4mmphase under 5 GPa. In addition, ourTccalculations show that theP4mmLuNH3structure does not exhibit superconductivity down to 0.3 K at near ambient pressure due to the H atoms hardly contribute to acoustical phonons.

Synthesis of superconducting phase of La0.5Ce0.5H10at high pressures

Clathrate hydrideFm3-m-LaH10has been proven as the most extraordinary superconductor with the critical temperatureTcabove 250 K upon compression of hundreds of GPa in recent years. A general hope is to reduce the stabilization pressure and maintain the highTcvalue of the specific phase in LaH10. However, strong structural instability distortsFm3-mstructure and leads to a rapid decrease ofTcat low pressures. Here, we investigate the phase stability and superconducting behaviors ofFm3-m-LaH10with enhanced chemical pre-compression through partly replacing La by Ce atoms from both experiments and calculations. For explicitly characterizing the synthesized hydride, we choose lanthanum-cerium alloy with stoichiometry composition of 1:1. X-ray diffraction and Raman scattering measurements reveal the stabilization ofFm3-m-La0.5Ce0.5H10in the pressure range of 140-160 GPa. Superconductivity withTcof 175 ± 2 K at 155 GPa is confirmed with the observation of the zero-resistivity state and supported by the theoretical calculations. These findings provide applicability in the future explorations for a large variety of hydrogen-rich hydrides.

First-principles study of the structures and superconductivity of H-S-La systems under high pressure

Recent experimental and theoretical studies have shown that a La-H system displays remarkable superconducting properties, and it is also possible to improve the superconducting state by introducing other elements into this system. In this study, we systematically investigated the crystal structures and physical properties of an H-S-La system by using first-principles calculations combined with the CALYPSO structure exploration technique. We predicted four stable stoichiometries containing H2SLa, H3SLa, H4Sla, and H6SLa. These compounds undergo a series of phase transitions under 50-300 GPa. The bonding characters and electronic properties were calculated. It was found that Cm-H2SLa, C2/c-H2SLa, and Cmcm-H6SLa exhibit good metallic nature, which stimulates us to further study their superconducting properties. The calculated superconducting transition temperatures (Tc) of Cm-H2SLa, C2/c-H2Sla, and Cmcm-H6SLa are 15.0 K at 200 GPa, 6.9 K at 300 GPa, and 23.6 K at 300 GPa, respectively.

Absence of near-ambient superconductivity in LuH2±xNy

A recent study demonstrated near-ambient superconductivity in nitrogen-doped lutetium hydride1. This stimulated a worldwide interest in exploring room-temperature superconductivity at low pressures. Here, by using a high-pressure and high-temperature synthesis technique, we have obtained nitrogen-doped lutetium hydride (LuH2±xNy), which has a dark-blue colour and a structure with the space group [Formula: see text] as evidenced by X-ray diffraction. This structure is the same as that reported in ref. 1, with a slight difference in lattice constant. Raman spectroscopy of our samples also showed patterns similar to those observed in ref. 1. Energy-dispersive X-ray spectroscopy confirmed the presence of nitrogen in the samples. We observed a metallic behaviour from 350 K to 2 K at ambient pressure. On applying pressures from 2.1 GPa to 41 GPa, we observed a gradual colour change from dark blue to violet to pink-red. By measuring the resistance at pressures ranging from 0.4 GPa to 40.1 GPa, we observed a progressively improved metallic behaviour; however, superconductivity was not observed above 2 K. Temperature dependence of magnetization at high pressure shows a very weak positive signal between 100 K and 320 K, and the magnetization increases with an increase in magnetic field at 100 K. All of these are not expected for superconductivity above 100 K. Thus, we conclude the absence of near-ambient superconductivity in this nitrogen-doped lutetium hydride at pressures below 40.1 GPa.

Stoichiometric Ternary Superhydride LaBeH_{8} as a New Template for High-Temperature Superconductivity at 110 K under 80 GPa

The search for high-temperature superconducting superhydrides has recently moved into a new phase by going beyond extensively probed binary compounds and focusing on ternary ones with vastly expanded material types and configurations for property optimization. Theoretical and experimental works have revealed promising ternary compounds that superconduct at or above room temperature, but it remains a pressing challenge to synthesize stoichiometric ternary compounds with a well-resolved crystal structure that can host high-temperature superconductivity at submegabar pressures. Here, we report on the successful synthesis of ternary LaBeH_{8} obtained via compression in a diamond anvil cell under 110-130 GPa. X-ray diffraction unveils a rocksalt-like structure composing La and BeH_{8} units in the lattice. Transport measurements determined superconductivity with critical temperature T_{c} up to 110 K at 80 GPa, as evidenced by a sharp drop of resistivity to zero and a characteristic shift of T_{c} driven by a magnetic field. Our experiment establishes the first superconductive ternary compound with a resolved crystal structure. These findings raise the prospects of rational development of the class of high-T_{c} superhydrides among ternary compounds, opening greatly expanded and more diverse structural space for exploration and discovery of superhydrides with enhanced high-T_{c} superconductivity.

Structures of LaH10, EuH9, and UH8 superhydrides rationalized by electron counting and Jahn-Teller distortions in a covalent cluster model

The superconducting hydrides LaH₁₀, EuH₉ and UH₈ are studied using chemically intuitive bonding analysis of periodic and molecular models. We find trends in the crystallographic and electronic structures of the materials by focusing on chemically meaningful building blocks in the predicted H sublattices. Atomic charge calculations, using two complementary techniques, allow us to assign oxidation states to the metals and divide the H sublattice into neutral and anionic components. Cubic [H₈]^q- clusters are an important structural motif, and molecular orbital analysis of this cluster in isolation shows the crystal structures to be consistent with our oxidation state assignments. Crystal orbital Hamilton population analysis confirms the applicability of the cluster model to the periodic electronic structure. A Jahn-Teller distortion predicted by MO analysis rationalises the distortion observed in a prior study of EuH₉. The impact of this distortion on superconductivity is determined, and implications for crystal structure prediction in other metal-hydrogen systems are discussed. Additionally, the performance of electronic structure analysis methods at high pressures are tested and recommendations for future studies are given. These results demonstrate the value of simple bonding models in rationalizing chemical structures under extreme conditions.

Enhancement of superconducting properties in the La-Ce-H system at moderate pressures

Ternary hydrides are regarded as an important platform for exploring high-temperature superconductivity at relatively low pressures. Here, we successfully synthesized the hcp-(La,Ce)H_9-10 at 113 GPa with the initial La/Ce ratio close to 3:1. The high-temperature superconductivity was strikingly observed at 176 K and 100 GPa with the extrapolated upper critical field H_c2(0) reaching 235 T. We also studied the binary La-H system for comparison, which exhibited a T_c of 103 K at 78 GPa. The T_c and H_c2(0) of the La-Ce-H are respectively enhanced by over 80 K and 100 T with respect to the binary La-H and Ce-H components. The experimental results and theoretical calculations indicate that the formation of the solid solution contributes not only to enhanced stability but also to superior superconducting properties. These results show how better superconductors can be engineered in the new hydrides by large addition of alloy-forming elements.

Quantum structural fluxion in superconducting lanthanum polyhydride

The discovery of 250-kelvin superconducting lanthanum polyhydride under high pressure marked a significant advance toward the realization of a room-temperature superconductor. X-ray diffraction (XRD) studies reveal a nonstoichiometric LaH_9.6 or LaH_10±δ polyhydride responsible for the superconductivity, which in the literature is commonly treated as LaH₁₀ without accounting for stoichiometric defects. Here, we discover significant nuclear quantum effects (NQE) in this polyhydride, and demonstrate that a minor amount of stoichiometric defects will cause quantum proton diffusion in the otherwise rigid lanthanum lattice in the ground state. The diffusion coefficient reaches ~10^-7 cm²/s in LaH_9.63 at 150 gigapascals and 240 kelvin, approaching the upper bound value of interstitial hydrides at comparable temperatures. A puzzling phenomenon observed in previous experiments, the positive pressure dependence of the superconducting critical temperature T_c below 150 gigapascals, is explained by a modulation of the electronic structure due to a premature distortion of the hydrogen lattice in this quantum fluxional structure upon decompression, and resulting changes of the electron-phonon coupling. This finding suggests the coexistence of the quantum proton fluxion and hydrogen-induced superconductivity in this lanthanum polyhydride, and leads to an understanding of the structural nature and superconductivity of nonstoichiomectric hydrogen-rich materials.

Symmetry of Identical Particles, Modern Achievements in the Pauli Exclusion Principle, in Superconductivity and in Some Other Phenomena

In this review, the modern achievements in studies of the Pauli exclusion principle (PEP) and the properties of the identical particle systems when PEP is not fulfilled are discussed. The validity of conception of the spin in the framework of density functional theory (DFT) approaches is analyzed. The modern state of the recently discovered Fe-based superconductors is discussed in detail. These materials belong to the paramagnetic semimetal family and become superconductors upon doping. Recently, in 2020, room-temperature superconductivity was realized. However, from the following discussion in the SC community, it was not evident that the results of room-temperature superconductivity have been repeated by other laboratories. Thus, the question “is room temperature really achieved?” is still open. In the concluding remarks, we present the explanation of why the PEP limitations on the symmetry of identical particles system exist in nature, and following from it, some important consequences.

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.

Evidence of near-ambient superconductivity in a N-doped lutetium hydride

The absence of electrical resistance exhibited by superconducting materials would have enormous potential for applications if it existed at ambient temperature and pressure conditions. Despite decades of intense research efforts, such a state has yet to be realized1,2. At ambient pressures, cuprates are the material class exhibiting superconductivity to the highest critical superconducting transition temperatures (Tc), up to about 133 K (refs. 3-5). Over the past decade, high-pressure 'chemical precompression'6,7 of hydrogen-dominant alloys has led the search for high-temperature superconductivity, with demonstrated Tc approaching the freezing point of water in binary hydrides at megabar pressures8-13. Ternary hydrogen-rich compounds, such as carbonaceous sulfur hydride, offer an even larger chemical space to potentially improve the properties of superconducting hydrides14-21. Here we report evidence of superconductivity on a nitrogen-doped lutetium hydride with a maximum Tc of 294 K at 10 kbar, that is, superconductivity at room temperature and near-ambient pressures. The compound was synthesized under high-pressure high-temperature conditions and then-after full recoverability-its material and superconducting properties were examined along compression pathways. These include temperature-dependent resistance with and without an applied magnetic field, the magnetization (M) versus magnetic field (H) curve, a.c. and d.c. magnetic susceptibility, as well as heat-capacity measurements. X-ray diffraction (XRD), energy-dispersive X-ray (EDX) and theoretical simulations provide some insight into the stoichiometry of the synthesized material. Nevertheless, further experiments and simulations are needed to determine the exact stoichiometry of hydrogen and nitrogen, and their respective atomistic positions, in a greater effort to further understand the superconducting state of the material.

Effect of Pressure on the Distribution of Electrons in a Cluster of H2S

We carry out a theoretical study of the effect of pressure on the atomic and electronic distribution of a cluster made of 155 H₂S molecules. The pressure was modeled by bringing the cluster into a spherical container made of 500 helium atoms and reducing the diameter of the container. We did ab initio molecular calculations using DFT. At the lowest pressure, the S-H-S angle between two neighboring H₂S molecules has a distribution with a mean value of 167.1°. This angle will be shorter as pressure increases, reaching a distribution with a mean value of 125.5° at the highest pressure. Changes in this angle result from a strong S-S interaction, displacing the H atoms from the line joining the sulfur atoms. This rearrangement of the atomic distribution generates hydrogen-rich spatial regions. We analyzed the evolution of Mulliken charges on S and H atoms in the cluster with pressure, finding that electrons move from S to H atoms, suggesting that these hydrogen-rich regions should be responsible for the electrical conductivity and, consequently, also for the superconductivity in solid H₂S under pressure.

High-pressure synthesis of seven lanthanum hydrides with a significant variability of hydrogen content

The lanthanum-hydrogen system has attracted significant attention following the report of superconductivity in LaH10 at near-ambient temperatures and high pressures. Phases other than LaH10 are suspected to be synthesized based on both powder X-ray diffraction and resistivity data, although they have not yet been identified. Here, we present the results of our single-crystal X-ray diffraction studies on this system, supported by density functional theory calculations, which reveal an unexpected chemical and structural diversity of lanthanum hydrides synthesized in the range of 50 to 180 GPa. Seven lanthanum hydrides were produced, LaH3, LaH~4, LaH4+δ, La4H23, LaH6+δ, LaH9+δ, and LaH10+δ, and the atomic coordinates of lanthanum in their structures determined. The regularities in rare-earth element hydrides unveiled here provide clues to guide the search for other synthesizable hydrides and candidate high-temperature superconductors. The hydrogen content variability in lanthanum hydrides and the samples’ phase heterogeneity underline the challenges related to assessing potentially superconducting phases and the nature of electronic transitions in high-pressure hydrides.

Prediction for high superconducting ternary hydrides below megabar pressure

The recent findings of high-temperature hydrides ushered a new era of superconductivity research under high pressure. However, the stable pressure for these remarkable hydrides remains extremely high. In this work, we performed the extensive simulations on a series of hydrides with the prototype structure of UH₈and UH₇. Our results indicate several compounds possess superconducting critical temperature (T_c) above liquid nitrogen temperature below 100 GPa, such as CeBeH₈and ThBeH₈that are dynamical stable with aT_cof 201 K at 30 GPa and aT_cof 98 K at 10 GPa, respectively. Further formation enthalpy calculations suggest that thermodynamical stable pressure of CeBeH₈and ThBeH₈compounds is above 50 GPa and 88 GPa with respect to binary compounds and solid elements. Moreover, we also found that ThBeH₇could be dynamically stable down to 20 GPa with aT_cof 70 K. Our further simulations suggested this newly predicted ThBeH₇is thermodynamically stable above pressure of 33 GPa with respect to binary compounds and solid elements. The present results shed light on future design and discovery of high-temperature superconductor at moderate pressure.

Giant enhancement of superconducting critical temperature in substitutional alloy (La,Ce)H9

A sharp focus of current research on superconducting superhydrides is to raise their critical temperature T_c at moderate pressures. Here, we report a discovery of giant enhancement of T_c in CeH₉ obtained via random substitution of half Ce by La, leading to equal-atomic (La,Ce)H₉ alloy stabilized by maximum configurational entropy, containing the LaH₉ unit that is unstable in pure compound form. The synthesized (La,Ce)H₉ alloy exhibits T_c of 148–178 K in the pressure range of 97–172 GPa, representing up to 80% enhancement of T_c compared to pure CeH₉ and showcasing the highest T_c at sub-megabar pressure among the known superhydrides. This work demonstrates substitutional alloying as a highly effective enabling tool for substantially enhancing T_c via atypical compositional modulation inside suitably selected host crystal. This optimal substitutional alloying approach opens a promising avenue for synthesis of high-entropy multinary superhydrides that may exhibit further increased T_c at even lower pressures.

Superconductivity was recently discovered in the clathrate hydride CeH₉ with superconducting temperature (T_c) of 57 K at pressures below 1 megabar. Here, the authors show that T_c can be increased to 148 K in the substitutional alloy (La,Ce)H₉, while maintaining a pressure below 1 megabar.

Effect of Magnetic Impurities on Superconductivity in LaH10

Polyhydrides are a novel class of superconducting materials with extremely high critical parameters, which is very promising for sensor applications. On the other hand, a complete experimental study of the best so far known superconductor, lanthanum superhydride LaH₁₀ , encounters a serious complication because of the large upper critical magnetic field H_C2 (0), exceeding 120-160 T. It is found that partial replacement of La atoms by magnetic Nd atoms results in significant suppression of superconductivity in LaH₁₀ : each at% of Nd causes a decrease in T_C by 10-11 K, helping to control the critical parameters of this compound. Strong pulsed magnetic fields up to 68 T are used to study the Hall effect, magnetoresistance, and the magnetic phase diagram of ternary metal polyhydrides for the first time. Surprisingly, (La,Nd)H₁₀ demonstrates completely linear H_C2 (T) ∝ |T - T_C |, which calls into question the applicability of the Werthamer-Helfand-Hohenberg model for polyhydrides. The suppression of superconductivity in LaH₁₀ by magnetic Nd atoms and the robustness of T_C with respect to nonmagnetic impurities (e.g., Y, Al, C) under Anderson's theorem gives new experimental evidence of the isotropic (s-wave) character of conventional electron-phonon pairing in lanthanum decahydride.

Second harmonic AC calorimetry technique within a diamond anvil cell

Tuning the energy density of matter at high pressures gives rise to exotic and often unprecedented properties, e.g., structural transitions, insulator-metal transitions, valence fluctuations, topological order, and the emergence of superconductivity. The study of specific heat has long been used to characterize these kinds of transitions, but their application to the diamond anvil cell (DAC) environment has proved challenging. Limited work has been done on the measurement of specific heat within DACs, in part due to the difficult experimental setup. To this end, we have developed a novel method for the measurement of specific heat within a DAC that is independent of the DAC design and is, therefore, readily compatible with any DACs already performing high pressure resistance measurements. As a proof-of-concept, specific heat measurements of the MgB₂ superconductor were performed, showing a clear anomaly at the transition temperature (T_c), indicative of bulk superconductivity. This technique allows for specific heat measurements at higher pressures than previously possible.

Carbon content drives high temperature superconductivity in a carbonaceous sulfur hydride below 100 GPa

We report a previously unobserved superconducting state of the photosynthesized carbonaceous sulfur hydride (C-S-H) system with a maximum TC of 191(1) K below 100 GPa. The properties of C-S-H are dependent on carbon content, and X-ray diffraction and simulations reveal the system remains molecular-like up to 100 GPa.

Prediction of Above-Room-Temperature Superconductivity in Lanthanide/Actinide Extreme Superhydrides

Achieving room-temperature superconductivity has been an enduring scientific pursuit driven by broad fundamental interest and enticing potential applications. The recent discovery of high-pressure clathrate superhydride LaH₁₀ with superconducting critical temperatures (T_c) of 250-260 K made it tantalizingly close to realizing this long-sought goal. Here, we report a remarkable finding based on an advanced crystal structure search method of a new class of extremely hydrogen-rich clathrate superhydride MH₁₈ (M: rare-earth/actinide atom) stoichiometric compounds stabilized at an experimentally accessible pressure of 350 GPa. These compounds are predicted to host T_c up to 330 K, which is well above room temperature. The bonding and electronic properties of these MH₁₈ clathrate superhydrides closely resemble those of atomic metallic hydrogen, giving rise to the highest T_c hitherto found in a thermodynamically stable hydride compound. An in-depth study of these extreme superhydrides offers insights for elucidating phonon-mediated superconductivity above room temperature in hydrogen-rich and other low-Z materials.

Sr-Doped Superionic Hydrogen Glass: Synthesis and Properties of SrH22

Recently, several research groups announced reaching the point of metallization of hydrogen above 400 GPa. Despite notable progress, detecting superconductivity in compressed hydrogen remains an unsolved problem. Following the mainstream of extensive investigations of compressed metal polyhydrides, here small doping of molecular hydrogen by strontium is demonstrated to lead to a dramatic reduction in the metallization pressure to ≈200 GPa. Studying the high-pressure chemistry of the Sr-H system, the formation of several new phases is observed: C2/m-Sr₃ H₁₃ , pseudocubic SrH₆ , SrH₉ with cubic F 4 ¯ 3 m $F\bar{4}3m$ -Sr sublattice, and pseudo tetragonal superionic P1-SrH₂₂ , the metal hydride with the highest hydrogen content (96 at%) discovered so far. High diffusion coefficients of hydrogen in the latter phase D_H  = 0.2-2.1 × 10^-9 m² s^-1 indicate an amorphous state of the H-sublattice, whereas the strontium sublattice remains solid. Unlike Ca and Y, strontium forms molecular semiconducting polyhydrides, whereas calcium and yttrium polyhydrides are high-T_C superconductors with an atomic H sublattice. The discovered SrH₂₂ , a kind of hydrogen sponge, opens a new class of materials with ultrahigh content of hydrogen.

Stable structures and superconducting properties of Ca-La-H compounds under pressure

The calcium hydrides and lanthanum hydrides under high pressures have been reported to have good superconducting properties with high-T_C. In this work, the structures and superconductivities of Ca-La-H ternary hydrides have been studied by genetic algorithm and density functional theory calculations. Our results show that at the pressure range of 100-300 GPa, the most stable structure of CaLaH₁₂has aCmmmsymmetry, in which there is a H₂₄hydrogen cage. It can be expected to have high possibility to be synthesized due to its large stability. Furthermore, the predictedT_Cof theCmmm-CaLaH₁₂structure is about 140 K at 150 GPa, and when the pressure decreases to 30 GPa, the CaLaH₁₂structure with aC2/msymmetry has a predictedT_Cof about 49 K. The CaLaH₁₂is suggested to be a stable good superconductor with large stability and performs well at relatively low pressures.

Synthesis, Structure, and Electric Conductivity of Higher Hydrides of Ytterbium at High Pressure

While most of the rare-earth metals readily form trihydrides, due to increased stability of the filled 4f electronic shell for Yb(II), only YbH_2.67, formally corresponding to Yb^II(Yb^IIIH₄)₂ (or Yb₃H₈), remains the highest hydride of ytterbium. Utilizing the diamond anvil cell methodology and synchrotron powder X-ray diffraction, we have attempted to push this limit further via hydrogenation of metallic Yb and Yb₃H₈. Compression of the latter has also been investigated in a neutral pressure-transmitting medium (PTM). While the in situ heating of Yb facilitates the formation of YbH_2+x hydrides, we have not observed clear qualitative differences between the systems compressed in H₂ and He or Ne PTM. In all of these cases, a sequence of phase transitions occurred within ca. 13–18 GPa (P3̅1m–I4/m phase) and around 27 GPa (to the I4/mmm phase). The molecular volume of the systems compressed in H₂ PTM is ca. 1.5% larger than of those compressed in inert gases, suggesting a small hydrogen uptake. Nevertheless, hydrogenation toward YbH₃ is incomplete, and polyhydrides do not form up to the highest pressure studied here (ca. 75 GPa). As pointed out by electronic transport measurements, the mixed-valence Yb₃H₈ retains its semiconducting character up to >50 GPa, although the very low remnant activation energy of conduction (<5 meV) suggests that metallization under further compression should be achievable. Finally, we provide a theoretical description of a hypothetical stoichiometric YbH₃.

Hydrogenation of Yb and Yb₃H₈ has been attempted under high pressure (≤75 GPa); the latter compound has also been investigated in Ne and He. The same sequence of phase transitions observed in all of these systems, with only minor differences in molar volume (1.5%), indicates that the limiting composition remains not far from YbH_2.67. The latter retains its semiconducting character up to >50 GPa, with a very low remnant activation energy of conduction (<5 meV).

Machine learning accelerated random structure searching: Application to yttrium superhydrides

The search for new superhydrides, promising materials for both hydrogen storage and high temperature superconductivity, made great progress, thanks to atomistic simulations and Crystal Structure Prediction (CSP) algorithms. When they are combined with Density Functional Theory (DFT), these methods are highly reliable and often match a great part of the experimental results. However, systems of increasing complexity (number of atoms and chemical species) become rapidly challenging as the number of minima to explore grows exponentially with the number of degrees of freedom in the simulation cell. An efficient sampling strategy preserving a sustainable computational cost then remains to be found. We propose such a strategy based on an active-learning process where machine learning potentials and DFT simulations are jointly used, opening the way to the discovery of complex structures. As a proof of concept, this method is applied to the exploration of tin crystal structures under various pressures. We showed that the α phase, not included in the learning process, is correctly retrieved, despite its singular nature of bonding. Moreover, all the expected phases are correctly predicted under pressure (20 and 100 GPa), suggesting the high transferability of our approach. The method has then been applied to the search of yttrium superhydrides (YH x) crystal structures under pressure. The YH6 structure of space group Im-3m is successfully retrieved. However, the exploration of more complex systems leads to the appearance of a large number of structures. The selection of the relevant ones to be included in the active learning process is performed through the analysis of atomic environments and the clustering algorithm. Finally, a metric involving a distance based on x-ray spectra is introduced, which guides the structural search toward experimentally relevant structures. The global process (active-learning and new selection methods) is finally considered to explore more complex and unknown YH x phases, unreachable by former CSP algorithms. New complex phases are found, demonstrating the ability of our approach to push back the exponential wall of complexity related to CSP.

Superconductivity above 200 K discovered in superhydrides of calcium

Searching for superconductivity with T_c near room temperature is of great interest both for fundamental science & many potential applications. Here we report the experimental discovery of superconductivity with maximum critical temperature (T_c) above 210 K in calcium superhydrides, the new alkali earth hydrides experimentally showing superconductivity above 200 K in addition to sulfur hydride & rare-earth hydride system. The materials are synthesized at the synergetic conditions of 160~190 GPa and ~2000 K using diamond anvil cell combined with in-situ laser heating technique. The superconductivity was studied through in-situ high pressure electric conductance measurements in an applied magnetic field for the sample quenched from high temperature while maintained at high pressures. The upper critical field Hc(0) was estimated to be ~268 T while the GL coherent length is ~11 Å. The in-situ synchrotron X-ray diffraction measurements suggest that the synthesized calcium hydrides are primarily composed of CaH₆ while there may also exist other calcium hydrides with different hydrogen contents.

The discovery of superconductivity in hydrides at critical temperature (T_c) near room temperature receives intensive attentions. Here the authors report experimental synthesis and discovery of superconductivity with T_c above 210 K in calcium superhydrides at 160–190 GPa.

High-Temperature Superconducting Phase in Clathrate Calcium Hydride CaH_{6} up to 215 K at a Pressure of 172 GPa

The recent discovery of superconductive rare earth and actinide superhydrides has ushered in a new era of superconductivity research at high pressures. This distinct type of clathrate metal hydrides was first proposed for alkaline-earth-metal hydride CaH_{6} that, however, has long eluded experimental synthesis, impeding an understanding of pertinent physics. Here, we report successful synthesis of CaH_{6} and its measured superconducting critical temperature T_{c} of 215 K at 172 GPa, which is evidenced by a sharp drop of resistivity to zero and a characteristic decrease of T_{c} under a magnetic field up to 9 T. An estimate based on the Werthamer-Helfand-Hohenberg model gives a giant zero-temperature upper critical magnetic field of 203 T. These remarkable benchmark superconducting properties place CaH_{6} among the most outstanding high-T_{c} superhydrides, marking it as the hitherto only clathrate metal hydride outside the family of rare earth and actinide hydrides. This exceptional case raises great prospects of expanding the extraordinary class of high-T_{c} superhydrides to a broader variety of compounds that possess more diverse material features and physics characteristics.

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.

Superconducting hydrides on a quantum landscape

Reaching superconductivity at ambient conditions is one of the biggest scientific dreams. The discoveries in the last few years at high pressures place hydrogen-based compounds as the best candidates for making it true. As the recent history shows, first-principles calculations are expected to continue guiding the experimental quest in the right track in the coming years. Considering that ionic quantum fluctuations largely affect the crystal structure and the vibrational properties of superconducting hydrides, in many cases making them thermodynamically stable at much lower pressures than expected, it will be crucial to include such effects on the futureab initiopredictions. The prospects for low-pressure high critical-temperature compounds are wide open, even at ambient pressure.

Caging-Pnictogen-Induced Superconductivity in Skutterudites IrX3 (X = As, P)

Here, we report on a new kind of compound, X_δIr₄X_12-δ (X = P, As), the first hole-doped skutterudites superconductor. We provide atomic-resolution images of the caging As atoms using scanning transmission electron microscopy (STEM). By inserting As atoms into the caged structure under a high pressure, superconductivity emerges with a maximum transition temperature (T_c) of 4.4 K (4.8 K) in IrAs₃ (IrP₃). In contrast to all of the electron-doped skutterudites, the electronic states around the Fermi level in X_δIr₄X_12-δ are dominated by the caged X atom, which can be described by a simple body-centered tight-binding model, implying a distinct pairing mechanism. Our density functional theory (DFT) calculations reveal an intimate relationship between the pressure-dependent local-phonon mode and the enhancement of T_c. The discovery of X_δIr₄X_12-δ provides an arena to investigate the uncharted territory of hole-doped skutterudites, and the method proposed here represents a new strategy of carrier doping in caged structures, without introducing extra elements.

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.

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.