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

High-Tcsuperconductivity in doped molecular superconductors ofK4B8-xMxH32(M = C, N) under high pressure

Stabilized and metallic light elements hydrides have provided a potential route to achieve the goal of room-temperature superconductors at moderate or ambient pressures. Here, we have performed systematic DFT theoretical calculations to examine the effects of different light elements C and N atoms doped in cubic K4B8H32hydrides on the superconductivity at low pressures. As a result of various atoms substituting, we have found that metallic K4B_{8-x}MxH32(M = C, N) hydrides are dynamically stable at 50 GPa, band structures and density of states (DOS) indicate that sizeableTccorrelates with a high B-H DOS at the Fermi level. With the increasing of B atoms in K4B_{8-x}MxH32hydrides, the DOS values at Fermi level have been improved due to the delocalized electrons in B-H bonds, which result in strong electron-phonon coupling (EPC) interaction and increase theTcfrom 19.04 to 77.07 K for KC2H8and KB2H8at 50 GPa. The NH4unit in stable K4B7NH32hydrides has weakened the EPC and led to lowTcvalue of 21.47 K. Our results suggest the light elements hydrides KB2H8and K4B7CH32could estimate highTcvalues at 50 GPa, and the boron hydrides would be potential candidates to design or modulate hydrides superconductors with highTcat moderate or ambient pressures.

Prediction of Room-Temperature Superconductivity in Quasi-Atomic H2-Type Hydrides at High Pressure

Achieving superconductivity at room temperature (RT) is a holy grail in physics. Recent discoveries on high-Tc superconductivity in binary hydrides H3S and LaH10 at high pressure have directed the search for RT superconductors to compress hydrides with conventional electron-phonon mechanisms. Here, an exceptional family of superhydrides is predicated under high pressures, MH12 (M = Mg, Sc, Zr, Hf, Lu), all exhibiting RT superconductivity with calculated Tcs ranging from 313 to 398 K. In contrast to H3S and LaH10, the hydrogen sublattice in MH12 is arranged as quasi-atomic H2 units. This unique configuration is closely associated with high Tc, attributed to the high electronic density of states derived from H2 antibonding states at the Fermi level and the strong electron-phonon coupling related to the bending vibration of H2 and H-M-H. Notably, MgH12 and ScH12 remain dynamically stable even at pressure below 100 GPa. The findings offer crucial insights into achieving RT superconductivity and pave the way for innovative directions in experimental research.

Novel ground state structures of N-doped LuH3

Ab-initiocrystal structure searches have played a pivotal role in recent discoveries of high-Tc hydride superconductors under high pressure. Using evolutionary crystal searches, we predict novel ground state structures of N-doped LuH3at ambient conditions. We find an insulating ground state structure for LuN0.125H2.875(∼1.0 wt.% N), contrary to earlier studies where assumed structures were all metallic. This insulating behavior of ground state was found to persist up to ∼45 GPa. However our crystal structure searches revealed a metallic state for an H-deficient variant of LuN0.125H2.875. We study bonding characteristics of important structures by calculating electronic density of states, electronic-localization functions and Bader charges. Our Bader charge analysis shows that insulators have both H+and H-ions whereas metals have only H-ions. We find that H+ions are bonded to N atomsviaa very short covalent bond. Thus we identify a clear relationship between formation of N-H bonds and insulating behavior of materials. Besides this, we perform crystal structure searches for three more compositions with higher N-content (>1.0 wt.%). Analysis of electronic properties shows that the ground states of these compositions are insulator.

Surface inducing high-temperature superconductivity in layered metal carborides Li2BC3 and LiBC by metallizing σ electrons

Metallizing σ electrons provides a promising route to design high-temperature superconducting materials, such as MgB2 and high-pressure hydrides. Here, we focus on two MgB2-like layered carborides Li2BC3 and LiBC; their bulk does not have superconductivity because the B-C σ states are far away from the Fermi level (EF), however, based on first-principles calculations, we found that when their bulk systems are cleaved into surfaces with B-C termination, high Tc of ∼80 K could be observed in the exposed B-C layer on the surfaces. Detailed analysis reveals that surface symmetry reduction, due to lattice periodic breaking, not only introduces hole self-doping into surface B-C layers and shifts the σ-bonding states towards the EF - associated with emergent large electronic occupation, but also makes in-plane stretching modes on the surface layer experience significant softness. The enhanced σ states and softened phonon modes work to produce strong coupling, thus yielding high-Tc surface superconductivity, which distinctly differs from the superconducting features of the MgB2 film, which generates phonon stiffness accompanied by suppressed superconductivity. Our findings undoubtedly provide a novel platform to realize high-Tc surface superconductivity, and also clearly elucidate the microscopic mechanism of surface-enhanced superconductivity in favor of creating more high-Tc surface superconductors among MgB2-like layered materials.

Anharmonic and quantum effects in Pm3̄ AlM(M = Hf, Zr)H6 under high pressure: A first-principles study

First-principles calculations were employed to investigate the impact of quantum ionic fluctuations and lattice anharmonicity on the crystal structure and superconductivity of Pm3̄ AlM(M = Hf, Zr)H6 at pressures of 0.3-21.2 GPa (AlHfH6) and 4.7-39.5 GPa (AlZrH6) within the stochastic self-consistent harmonic approximation. A correction is predicted for the crystal lattice parameters, phonon spectra, and superconducting critical temperatures, previously estimated without considering ionic fluctuations on the crystal structure and assuming the harmonic approximation for lattice dynamics. The findings suggest that quantum ionic fluctuations have a significant impact on the crystal lattice parameters, phonon spectra, and superconducting critical temperatures. Based on our anharmonic phonon spectra, the structures will be dynamically stable at 0.3 GPa for AlHfH6 and 6.2 GPa for AlZrH6, ∼6 and 7 GPa lower than pressures given by the harmonic approximation, respectively. Due to the anharmonic correction of their frequencies, the electron-phonon coupling constants (λ) are suppressed by 28% at 11 GPa for AlHfH6 and 22% at 30 GPa for AlZrH6, respectively. The decrease in λ causes Tc to be overestimated by ∼12 K at 11 GPa for AlHfH6 and 30 GPa for AlZrH6. Even if the anharmonic and quantum effects are not as strong as those of Pm3̄n-AlH3, our results also indicate that metal hydrides with hydrogen atoms in interstitial sites are subject to anharmonic effects. Our results will inevitably stimulate future high-pressure experiments on synthesis, structural, and conductivity measurements.

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.

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.

Structural Phase Transition and Decomposition of XeF2 under High Pressure and Its Formation of Xe-Xe Covalent Bonds

Noble gases with inert chemical properties have rich bonding modes under high pressure. Interestingly, Xe and Xe form covalent bonds, originating from the theoretical simulation of the pressure-induced decomposition of XeF2, which has yet to be experimentally confirmed. Moreover, the structural phase transition and metallization of XeF2 under high pressure have always been controversial. Therefore, we conducted extensive experiments using a laser-heated diamond anvil cell technique to investigate the above issues of XeF2. We propose that XeF2 undergoes a structural phase transition and decomposition above 84.1 GPa after laser heating, and the decomposed product Xe2F contains Xe-Xe covalent bonds. Neither the pressure nor temperature alone could bring about these changes in XeF2. With our UV-vis absorption experiment, I4/mmm-XeF2 was metalized at 159 GPa. This work confirms the existence of Xe-Xe covalent bonds and provides insights into the controversy surrounding XeF2, enriching the research on noble gas chemistry under high pressure.

Pressure-induced hydrogen-dominant high-temperature superconductors

The century-old pursuit of room temperature superconductivity has finally been reached in highly compressed hydrogen-dominant compounds. Future efforts will be focused on understanding the high-pressure hydrogen physics and ambient-pressure applications.

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.

Predicted hot superconductivity in LaSc2H24 under pressure

The recent theory-driven discovery of a class of clathrate hydrides (e.g., CaH6, YH6, YH9, and LaH10) with superconducting critical temperatures (Tc) well above 200 K has opened the prospects for "hot" superconductivity above room temperature under pressure. Recent efforts focus on the search for superconductors among ternary hydrides that accommodate more diverse material types and configurations compared to binary hydrides. Through extensive computational searches, we report the prediction of a unique class of thermodynamically stable clathrate hydrides structures consisting of two previously unreported H24 and H30 hydrogen clathrate cages at megabar pressures. Among these phases, LaSc2H24 shows potential hot superconductivity at the thermodynamically stable pressure range of 167 to 300 GPa, with calculated Tcs up to 331 K at 250 GPa and 316 K at 167 GPa when the important effects of anharmonicity are included. The very high critical temperatures are attributed to an unusually large hydrogen-derived density of states at the Fermi level arising from the newly reported peculiar H30 as well as H24 cages in the structure. Our predicted introduction of Sc in the La-H system is expected to facilitate future design and realization of hot superconductors in ternary clathrate superhydrides.

Structural and electronic properties of clathrate-like hydride: MH6 and MH9 (M = Sc, Y, La)

CONTEXT

The addition of central metal atoms to hydrogen clathrate structures is thought to provide a certain amount of "internal chemical pressure" to offset some of the external physical pressure required for compound stability. The size and valence of the central atoms significantly affect the minimum pressure required for the stabilization of hydrogen-rich compounds and their superconducting transition temperature. In recent years, many studies have calculated the minimum stable pressure and superconducting transition temperature of compounds with H24, H29, and H32 hydrogen clathrates, with centrally occupied metal atoms. In order to investigate the stability and physical properties of compounds with H cages in which the central atoms change in the same third group B, herein, based on first-principles calculations, we systematically investigated the lattice parameters, crystal volume, band structures, density of states, Mulliken analysis, charge density, charge density difference, and electronic localization function in I m 3 ¯ m -MH6 and P63/mmc-MH9 systems with different centered rare earth atoms M (M = Sc, Y, La) under a series of pressures. We find that for MH9, the pressure mainly changes the crystal lattice parameters along the c-axis, and the contributions of the different H atoms in MH9 to the Fermi level are H3 > H1 > H2. The density of states at the Fermi level of MH6 is mainly provided by H 1 s. Moreover, the size of the central atom M is particularly important for the stability of the crystal. By observing a series of properties of the structures with H24 and H29 cages wrapping the same family of central atoms under a series of pressures, our theoretical study is helpful for further understanding the formation mechanism of high-temperature superconductors and provides a reference for future research and design of high-temperature superconductors.

METHODS

The first principles based on the density functional theory and density functional perturbation theory were employed to execute all calculations by using the CASTEP code in this work.

Discovery of superconductivity in technetium borides at moderate pressures

Advances in theoretical calculations have boosted the search for high-temperature superconductors, such as sulfur hydrides and rare-earth polyhydrides. However, the required extremely high pressures for stabilizing these superconductors has handicapped further implementation. Based upon thorough structural searches, we identified a series of unprecedented superconducting technetium borides at moderate pressures, including TcB (P63/mmc) with a superconducting transition temperature of Tc = 20.2 K at ambient pressure and TcB2 (P6/mmm) with Tc = 23.1 K at 20 GPa. Superconductivity in these technetium borides mainly originates from the coupling between the low-frequency vibrations of technetium atoms and the dominant technetium-4d electrons at the Fermi level. Our work therefore presents a fresh group in the family of superconducting borides, whose diversified crystal structures suggest rich possibilities in the discovery of other superconducting transition-metal borides.

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 of thulium substituted clathrate hexahydrides at moderate pressure

Due to the BCS theory, hydrogen, the lightest element, would be the prospect of room-temperature superconductor after metallization, but because of the difficulty of the hydrogen metallization, the theory about hydrogen pre-compression was proposed that the hydrogen-rich compounds could be a great option for the high Tc superconductors. The superior properties of TmH6, YbH6 and LuH6 indicated the magnificent potential of heavy rare earth elements for low-pressure stability. Here, we designed XTmH12 (X = Y, Yb, Lu, and La) to obtain higher Tc while maintaining low pressure stability. Most prominently, YbTmH12 can stabilize at a pressure of 60 GPa. Compared with binary TmH6 hydride, its Tc was increased to 48 K. The results provide an effective method for the rational design of moderate pressure stabilized hydride superconductors.

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.

Small-pore hydridic frameworks store densely packed hydrogen

Nanoporous materials have attracted great attention for gas storage, but achieving high volumetric storage capacity remains a challenge. Here, by using neutron powder diffraction, volumetric gas adsorption, inelastic neutron scattering and first-principles calculations, we investigate a magnesium borohydride framework that has small pores and a partially negatively charged non-flat interior for hydrogen and nitrogen uptake. Hydrogen and nitrogen occupy distinctly different adsorption sites in the pores, with very different limiting capacities of 2.33 H2 and 0.66 N2 per Mg(BH4)2. Molecular hydrogen is packed extremely densely, with about twice the density of liquid hydrogen (144 g H2 per litre of pore volume). We found a penta-dihydrogen cluster where H2 molecules in one position have rotational freedom, whereas H2 molecules in another position have a well-defined orientation and a directional interaction with the framework. This study reveals that densely packed hydrogen can be stabilized in small-pore materials at ambient pressures.

Chemical bonding dictates drastic critical temperature difference in two seemingly identical superconductors

Though YB6 and LaB6 share the same crystal structure, atomic valence electron configuration, and phonon modes, they exhibit drastically different phonon-mediated superconductivity. YB6 superconducts below 8.4 K, giving it the second-highest critical temperature of known borides, second only to MgB2. LaB6 does not superconduct until near-absolute zero temperatures (below 0.45 K), however. Though previous studies have quantified the canonical superconductivity descriptors of YB6's greater Fermi-level (Ef) density of states and higher electron-phonon coupling (EPC), the root of this difference has not been assessed with full detail of the electronic structure. Through chemical bonding, we determine low-lying, unoccupied 4f atomic orbitals in lanthanum to be the key difference between these superconductors. These orbitals, which are not accessible in YB6, hybridize with π B-B bonds and bring this π-system lower in energy than the σ B-B bonds otherwise at Ef. This inversion of bands is crucial: the optical phonon modes we show responsible for superconductivity cause the σ-orbitals of YB6 to change drastically in overlap, but couple weakly to the π-orbitals of LaB6. These phonons in YB6 even access a crossing of electronic states, indicating strong EPC. No such crossing in LaB6 is observed. Finally, a supercell (the M k-point) is shown to undergo Peierls-like effects in YB6, introducing additional EPC from both softened acoustic phonons and the same electron-coupled optical modes as in the unit cell. Overall, we find that LaB6 and YB6 have fundamentally different mechanisms of superconductivity, despite their otherwise near-identity.

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.

High-temperature superconductivities and crucial factors influencing the stability of LaThH12 under moderate pressures

The recent discovery of high-temperature superconductivity in compressed hydrides has reignited the long-standing quest for room-temperature superconductors. However, the synthesis of superconducting hydrides under moderate pressure and the identification of crucial factors that affect their stability remain challenges. Here, we predicted the ternary clathrate phases of LaThH12 with potential superconductivity under high pressures and specifically proposed a novel R3̄c-LaThH12 phase exhibiting a remarkable Tc of 54.95 K at only 30 GPa to address these confusions. Our first-principles studies show that the high-Tc value of Pm3̄m and Cmmm-LaThH12 phases was induced by the strong electron-phonon coupling driven by the synergy of the electron-phonon matrix element and phonon softening caused by Fermi surface nesting. Importantly, we demonstrate the dual effects of enhanced ionic bonding and expanded orbital hybridization between Th-6f and H-sp3 orbitals during depressurization are primary factors governing the dynamic stability of R3̄c-LaThH12 at low pressures. Our findings offer crucial insights into the underlying mechanisms governing low-pressure stability and provide guidance for experimental efforts aimed at realizing hydrogen-based superconductors with both low synthesis pressures and high-Tc.

Absence of superconductivity in I4/mmm-FeH5: experimental evidence

The experimentally discovered FeH5 exhibits a structure built of atomic hydrogen that only has bonding between hydrogen and iron atoms [C. M. Pepin, G. Geneste, A. Dewaele, M. Mezouar and P. Loubeyre, Science, 2017, 357, 382]. However, its superconductivity has remained unsolved since its discovery. In this work, we have synthesized I4/mmm-FeH5 at 139 GPa combined with laser-heating conditions. The electrical resistance measurements at ultrahigh pressures indicate that no evidence of superconducting transition of FeH5 is observed in the temperature range of 1.5 K to 270 K. These results indicate that I4/mmm-FeH5 does not exhibit superconductivity within the experimental temperature range, and the introduction of iron atoms is not beneficial to the formation of the superconducting phase.

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.

Metal-bonded perovskite lead hydride with phonon-mediated superconductivity exceeding 46 K under ambient pressure

In the search for high-temperature superconductivity in hydrides, a plethora of multi-hydrogen superconductors have been theoretically predicted, and some have been synthesized experimentally under ultrahigh pressures of several hundred GPa. However, the impracticality of these high-pressure methods has been a persistent issue. In response, we propose a new approach to achieve high-temperature superconductivity under ambient pressure by implanting hydrogen into lead to create a stable few-hydrogen binary perovskite, Pb4H. This approach diverges from the popular design methodology of multi-hydrogen covalent high critical temperature (Tc) superconductors under ultrahigh pressure. By solving the anisotropic Migdal-Eliashberg equations, we demonstrate that perovskite Pb4H presents a phonon-mediated superconductivity exceeding 46 K with inclusion of spin-orbit coupling, which is six times higher than that of bulk Pb (7.22 K) and comparable to that of MgB2, the highestTcachieved experimentally at ambient pressure under the Bardeen, Cooper, and Schrieffer framework. The highTccan be attributed to the strong electron-phonon coupling strength of 2.45, which arises from hydrogen implantation in lead that induces several high-frequency optical phonon modes with a relatively large phonon linewidth resulting from H atom vibration. The metallic-bonding in perovskite Pb4H not only improves the structural stability but also guarantees better ductility than the widely investigated multi-hydrogen, iron-based and cuprate superconductors. These results suggest that there is potential for the exploration of new high-temperature superconductors under ambient pressure and may reignite interest in their experimental synthesis in the near future.

Superconductivity of cubic MB6 (M = Na, K, Rb, Cs)

Previous studies have shown that NaB6, KB6, and RbB6 adopting Pm3̄m are superconductors with a relatively high Tc under ambient conditions. In this paper, we conducted systematic structural and related properties research on CsB6 through a genetic evolution algorithm and total energy calculations based on density functional theory between 0 and 20 GPa. Our results reveal a cubic Pm3̄m CsB6, which is dynamically stable under the pressures we studied. We systematically calculated the formation enthalpies, electronic properties, and superconducting properties of Pm3̄m MB6 (M = Na, K, Rb, Cs). They all exhibit metallic features, and boron has high contributions to band structures, density of states, and electron-phonon coupling (EPC). The calculated results about the Helmholtz free energy difference of Pm3̄m CsB6 at 0, 10, and 20 GPa indicate that it is stable upon chemical decomposition (decomposition to simple substances Cs and B) from 0 to 400 K. The phonon density of states indicates that boron atoms occupy the high frequency area. The EPC results show that Pm3̄m CsB6 is a superconductor with Tc = 11.7 K at 0 GPa, close to NaB6 (13.1 K), KB6 (11.7 K), and RbB6 (11.3 K) at 0 GPa in our work, which indicates that boron atoms play an essential role in superconductivity: vibrations of B6 regular octagons lead to the high Tc of Pm3̄m MB6. Our work about Pm3̄m hexaborides provides a supplementary study on the borides of the group IA elements (without Fr and Li) and has an important guiding significance for the experimental synthesis of CsB6.

A systematic study on the phase diagram and superconductivity of ternary clathrate Ca-Sc-H at high pressures

This work explores potential high-temperature superconductor materials in hydrogen-rich systems. Here, the crystal structure stabilities of ternary Ca-Sc-H systems under high-pressure (P = 100-250 GPa) and their superconductivities are investigated using the particle swarm optimization methodology combined with first-principles calculations. For the predicted candidate structures of Ca-Sc-H systems, the pressure-dependent phase diagram and thermodynamic convex hull were investigated across a wide range of compositions; the electronic properties of all the predicted phases were analyzed in detail to study the bonding behavior of these stable phases. We identified the crystal structures of four thermodynamically stable compounds: R3̄m-CaScH6, Immm-CaSc2H9,C2/m-Ca2ScH10, and R3̄m-CaScH12. Among them, R3̄m-CaScH12 was predicted to have the highest Tc value (i.e., 173 K) at 200 GPa. The discovery of this previously unreported pressure-induced decomposition of Ca-Sc-H systems will pave the way for investigations on the nature of hydrogen-metal interactions.

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

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

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.

Data-driven Design of High Pressure Hydride Superconductors using DFT and Deep Learning

The observation of superconductivity in hydride-based materials under ultrahigh pressures (for example, H3S and LaH10) has fueled the interest in a more data-driven approach to discovering new high-pressure hydride superconductors. In this work, we performed density functional theory (DFT) calculations to predict the critical temperature (Tc) of over 900 hydride materials under a pressure range of (0 to 500) GPa, where we found 122 dynamically stable structures with a Tc above MgB2 (39 K). To accelerate screening, we trained a graph neural network (GNN) model to predict Tc and demonstrated that a universal machine learned force-field can be used to relax hydride structures under arbitrary pressures, with significantly reduced cost. By combining DFT and GNNs, we can establish a more complete map of hydrides under pressure.

Pressure-Induced Metallization of BaH2 and the Effect of Hydrogenation

Using optical spectroscopy, X-ray diffraction, and electrical transport measurements, we have studied the pressure-induced metallization in BaH2 and Ba8H46. Our combined measurements suggest a structural phase transition from BaH2-II to BaH2-III accompanied by band gap closure and transformation to a metallic state at 57 GPa. The metallization is confirmed by resistance measurements as a function of the pressure and temperature. We also confirm that, with further hydrogenation, BaH2 forms the previously observed Weaire-Phelan Ba8H46, synthesized at 45 GPa and 1200 K. In this compound, metallization pressure is shifted to 85 GPa. Through a comparison of the properties of these two compounds, a question is raised about the importance of the hydrogen content in the electronic properties of hydride systems.

Phase diagrams and superconductivity of ternary Ca-Al-H compounds under high pressure

The search for high-temperature superconductors in hydrides under high pressure has always been a research hotspot. Hydrogen-based superconductors offer an avenue to achieve the long-sought goal of superconductivity at room temperature. Here we systematically explored the high-pressure phase diagram, electronic properties, lattice dynamics and superconductivity of the ternary Ca-Al-H system using ab initio methods. At 80 GPa, CaAlH5 transforms from Cmcm to P21/m phase. Both of Cmcm-CaAlH5 and Pnnm-CaAl2H8 are semiconductors. At 200 GPa, P4/mmm-CaAlH7 and a metastable compound Immm-Ca2AlH12 were found. Furthermore, P4/mmm-CaAlH7 shows obvious softening of the high frequency vibration modes, which improves the strength of electron-phonon coupling. Therefore, a superconducting transition temperature Tc of 71 K is generated in P4/mmm-CaAlH7 at 50 GPa. In addition, the thermodynamic metastable Immm-Ca2AlH12 exhibits a superconducting transition temperature of 118 K at 250 GPa. These results are very useful for the experimental searching of new high-Tc superconductors in ternary hydrides. Our work may provide an opportunity to search for high Tc superconductors at lower pressure.

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.

Predicted superconductivity in one-dimensional A3Hf2B3-type electrides

Inorganic electrides are considered potential superconductors due to the unique properties of their anionic electrons. However, most electrides require external high-pressure conditions to exhibit considerable superconducting transition temperatures (Tc). Therefore, searching for superconducting electrides under low or moderate external pressures is of significant research interest and importance. In this work, a series of A3Hf2B3-type compounds (A = Mg, Ca, Sr, Ba; B = Si, Ge, Sn, Pb) were constructed and systematically studied based on density functional theory calculations. According to the analysis of the electronic structures and phonon dispersion spectrums, stable one-dimensional electrides Ca3Hf2Ge3, Ca3Hf2Sn3, and Sr3Hf2Pb3, were screened out. Interestingly, the superconductivity of these electrides were predicted from electron phonon coupling calculations. It is highlighted that Sr3Hf2Pb3 showed the highest Tc, reaching 4.02 K, while the Tc values of Ca3Hf2Ge3 and Ca3Hf2Sn3 were 1.16 K and 1.04 K, respectively. Moreover, the Tc value of Ca3Hf2Ge3 can be increased to 1.96 K under 20 GPa due to the effect of phonon softening. This work enriches the types of superconducting electrides and has important guiding significance for the research on constructing electrides and related superconducting materials.

Microscopic theory of colour in lutetium hydride

Nitrogen-doped lutetium hydride has recently been proposed as a near-ambient-conditions superconductor. Interestingly, the sample transforms from blue to pink to red as a function of pressure, but only the pink phase is claimed to be superconducting. Subsequent experimental studies have failed to reproduce the superconductivity, but have observed pressure-driven colour changes including blue, pink, red, violet, and orange. However, discrepancies exist among these experiments regarding the sequence and pressure at which these colour changes occur. Given the claimed relationship between colour and superconductivity, understanding colour changes in nitrogen-doped lutetium hydride may hold the key to clarifying the possible superconductivity in this compound. Here, we present a full microscopic theory of colour in lutetium hydride, revealing that hydrogen-deficient LuH2 is the only phase which exhibits colour changes under pressure consistent with experimental reports, with a sequence blue-violet-pink-red-orange. The concentration of hydrogen vacancies controls the precise sequence and pressure of colour changes, rationalising seemingly contradictory experiments. Nitrogen doping also modifies the colour of LuH2 but it plays a secondary role compared to hydrogen vacancies. Therefore, we propose hydrogen-deficient LuH2 as the key phase for exploring the superconductivity claim in the lutetium-hydrogen system. Finally, we find no phonon-mediated superconductivity near room temperature in the pink phase.

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.

Superconductivity Above 100 K Predicted in Carbon-Cage Network

To explore carbide superconductors with higher transition temperature, two novel carbon structures of cage-network are designed and their superconductivity is studied by doping metals. MC6 and MC10 are respectively identified as C24 and C32 cage-network structures. This study finds that both carbon structures drive strong electron-phonon interaction and can exhibit superconductivity above liquid nitrogen temperature. Importantly, the superconducting transition temperatures above 100 K are predicted to be achieved in C24 -cage-network systems doped by Na, Mg, Al, In, and Tl at ambient pressure, which is far higher than those in graphite, fullerene, and other carbides. Meanwhile, the superconductivity of cage-network carbides is also found to be sensitive to the electronegativity and concentration of dopant M. The result indicates that the higher transition temperatures can be obtained by optimizing the carbon-cage-network structures and the doping conditions. The study suggests that the carbon-cage-network structure is a direction to explore high-temperature superconducting carbides.

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.

Composition and structural characteristics of compressed alkaline earth metal hydrides

The metallization of alkaline earth metal hydrides offers a way to achieve near-room temperature superconductivity. In order to explore the metallization mechanism of these hydrides under pressure, a detailed understanding of the property changes of alkaline earth metal hydrides is required. Based on first-principles calculations, we have systematically investigated the dihydrides (XH2, X = Be, Mg, Ca, Sr, Ba) and tetrahydrides (XH4, X = Mg, Ca, Sr, Ba) of alkaline earth metals, respectively. By applying external pressure, we show that the structures of these alkaline earth metal hydrides undergo a series of phase transitions. Moreover, we investigate how the size of the bandgap decreases and eventually closes and reveal the role of electronegativity of metal elements in the critical pressure of hydride metallization. Remarkably, the hydrogen units (H6 or H8) formed in XH4 can accelerate the metallization process. The increase of the energy level difference in hydrogen units promotes the electroacoustic coupling effect, which is conducive to realization of high superconducting transition temperature (Tc). Our theoretical findings identify MgH4-I4/mmm as having potential to be a high-temperature superconductor and provide unusual ideas for the search of unknown high-temperature superconducting materials.

Few-Hydrogen High-Tc Superconductivity in (Be4)2H Nanosuperlattice with Promising Ductility under Ambient Pressure

The multi-hydrogen lanthanum hydride LaH10 is well recognized as having the highest critical temperature (Tc) of 250-260 K under unrealistically ultrahigh pressures of about 170-200 GPa. Here, we propose a novel idea for designing a new ambient-pressure high-Tc superconductor by inserting a hexagonal H-monolayer into two close-packed Be monolayers to form a new and stable few-hydrogen metal-bonded layered beryllium hydride (Be4)2H nanosuperlattice, with better ductility than multi-hydrogen, cuprate, and iron-based superconductors, completely contrary to the conventional design strategy for multi-hydrogen covalent high-Tc superconductors with poor ductility at several hundred GPa. We find that (Be4)2H is a phonon-mediated Eliashberg superconductor with a large electron-phonon coupling constant of 1.41 and a high Tc of 84-72 K with Coulomb repulsion pseudopotential μ* = 0.07-0.13. Importantly, (Be4)2H is the only new high-Tc superconductor and fills the gap in the absence of ambient-pressure superconductors around the liquid-nitrogen temperature with good ductility, which is highly beneficial for practical applications.

Pressure-induced superconductivity of Ac-B-H hydrides

The search for room-temperature superconductors among high-pressure hydrides is a hot research topic. In this study, the structures, stabilities and superconducting properties of ternary Ac-B-H hydrides were studied using a genetic algorithm (GA) combined with density functional theory (DFT) calculations. It was shown that the R3̄m-AcBH8 and I4/mmm-AcB2H8 structures were thermodynamically and dynamically stable above 70 and 125 GPa, respectively. In the R3̄m-AcBH8 structure, the BH6 unit and the dispersed H atoms were bonded to form a corrugated structure. The I4/mmm-AcB2H8 structure contained a cage and the Ac atom located at the cage center. The calculations of the electron-phonon coupling showed that the R3̄m-AcBH8 and I4/mmm-AcB2H8 structures had Tc values of 140 K (70 GPa) and 99 K (125 GPa), respectively. The analyses of the phonon dispersion curves revealed that electron-phonon coupling was closely related to the vibrations of the B-H bonds.

Superconductivity determined by the S-H framework in CH4-inserted S-H framework hydrides under high pressures

Recently, a debate is raising the concern of possible carbonaceous sulfur hydrides with room-temperature superconductivity around 270 GPa. In order to systematically investigate the structural information and relevant natures of C-S-H superconductors, we performed an extremely extensive structure search and first-principles calculations under high pressures. As a result, the metastable stoichiometries of CSH7, C2SH14, CS2H10, and CS2H11 were unveiled under high pressure, which can be viewed as CH4 units inserted into the S-H framework. Given the super-high superconductivity of Im3̄m-SH3, we performed electron-phonon coupling calculations of these compounds,the metastable of R3m-CSH7, Cm-CSH7, Cm-CS2H10, P3m1-CS2H10, Cm-CS2H11, and Fmm2-CS2H11 are predicted to become good phonon-mediated superconductors that could reach Tc of 130, 120, 72, 74, 92, and 70 K at 270 GPa, respectively. Furthermore, we identified that high Tc is associated with the large contribution of the S-H framework to the electron density of states near the Fermi level. Our results highlight the importance of the S-H framework in superconductivity and verify that the suppression of density of states of these carbonaceous sulfur hydrides by CH4 units results in Tc lower than that of Im3̄m-SH3, which could act as a useful guidance in the design and optimization of high-Tc superconductors in these and related systems.

MAGUS: machine learning and graph theory assisted universal structure searcher

Crystal structure predictions based on first-principles calculations have gained great success in materials science and solid state physics. However, the remaining challenges still limit their applications in systems with a large number of atoms, especially the complexity of conformational space and the cost of local optimizations for big systems. Here, we introduce a crystal structure prediction method, MAGUS, based on the evolutionary algorithm, which addresses the above challenges with machine learning and graph theory. Techniques used in the program are summarized in detail and benchmark tests are provided. With intensive tests, we demonstrate that on-the-fly machine-learning potentials can be used to significantly reduce the number of expensive first-principles calculations, and the crystal decomposition based on graph theory can efficiently decrease the required configurations in order to find the target structures. We also summarized the representative applications of this method on several research topics, including unexpected compounds in the interior of planets and their exotic states at high pressure and high temperature (superionic, plastic, partially diffusive state, etc.); new functional materials (superhard, high-energy-density, superconducting, photoelectric materials), etc. These successful applications demonstrated that MAGUS code can help to accelerate the discovery of interesting materials and phenomena, as well as the significant value of crystal structure predictions in general.

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.

Versatile transition metal monolayers with catalytic and superconducting properties: a computational study

Due to their abundant valence electrons and unique electronic properties, transition metals have garnered great interest in the search for novel materials displaying various properties, including superconductivity, catalysis and so on. XRu₂ (X: V, Mn, Fe, etc.) compounds, which are isostructural to AlB₂, were used as examples for which we performed extensive simulations to screen for superconductivity and possible potential catalytic activity. On this basis, we found that VRu₂ could achieve a superconducting critical temperature (T_c) of about 13 K. Meanwhile, our simulations showed the lowest adsorption free energy of atomic hydrogen (ΔG_H) on the (0 0 1) surface of VRu₂ to be about 2 meV, indicating its almost zero free energy of hydrogen adsorption with excellent catalytic performance. In addition, the results suggested potential superconducting and catalytic properties of VXRu (X = Os, Fe). Our current results have shed light on possible applications of Ru-based AlB₂-type intermetallic compounds and have presented a new strategy for further designing superconductors and catalysts based on transition metals.

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.

Leading components and pressure-induced color changes in N-doped lutetium hydride

Recent experimental study by Dasenbrock-Gammon et al. (Nature 2023;615:244) claims to have discovered room-temperature superconductivity in lutetium-nitrogen-hydrogen system at 1 GPa, which sheds light on the long-held dream of ambient superconductivity. However, all follow-up experiments found no evidence of superconductivity. The compositions and the crystal structures of the lutetium-nitrogen-hydrogen system remain unknown. By employing the density functional theory based structure prediction algorithm, we suggest that in lutetium-nitrogen-hydrogen the major component is LuH₂ (Fm3¯m), together with minor LuN (Fm3¯m). The blue LuH₂ at ambient pressure will turn into purple and red color at higher pressures, possibly accompanied by the formation of vacancies at hydrogen-sites. In LuH₂ and LuN, the density of states at the Fermi level is dominated by the Lu-5d orbitals, while those from hydrogen and nitrogen are very small, leading to the absence of superconductivity in these two compounds. Nitrogen-doping to LuH₂ fails to enhance the superconductivity as well. In this work, we identify the leading components in N-doped lutetium hydride, explain its intriguing color changes under pressure, and elucidate why superconductivity is absent in the follow-up experiments.

Modulations in Superconductors: Probes of Underlying Physics

The importance of modulations is elevated to an unprecedented level, due to the delicate conditions required to bring out exotic phenomena in quantum materials, such as topological materials, magnetic materials, and superconductors. Recently, state-of-the-art modulation techniques in material science, such as electric-double-layer transistor, piezoelectric-based strain apparatus, angle twisting, and nanofabrication, have been utilized in superconductors. They not only efficiently increase the tuning capability to the broader ranges but also extend the tuning dimensionality to unprecedented degrees of freedom, including quantum fluctuations of competing phases, electronic correlation, and phase coherence essential to global superconductivity. Here, for a comprehensive review, these techniques together with the established modulation methods, such as elemental substitution, annealing, and polarization-induced gating, are contextualized. Depending on the mechanism of each method, the modulations are categorized into stoichiometric manipulation, electrostatic gating, mechanical modulation, and geometrical design. Their recent advances are highlighted by applications in newly discovered superconductors, e.g., nickelates, Kagome metals, and magic-angle graphene. Overall, the review is to provide systematic modulations in emergent superconductors and serve as the coordinate for future investigations, which can stimulate researchers in superconductivity and other fields to perform various modulations toward a thorough understanding of quantum materials.

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.

Universal correlation of the superconducting transition temperature with the linear-in-T coefficient, electron packing parameter, and the numbers of valence and conduction electrons

A generic conductivity equation, developed in our previous work, is used to predict the universal superconducting transition temperature, T_c. Our prediction shows that T_c and the linear-in-T scattering coefficient, A₁, have a scaling relationship of T_c ∼ A₁^0.5, where A₁ comes from the empirical experimental equation ρ = ρ₀ + A₁T with ρ as the resistivity, which is consistent with recent experimental observations. However, our theory suggests that 1/ρ has a linear relationship with 1/T, rather than the empirical relationship between ρ and T postulated in the literature. The physical meaning of A₁ is made clear by the equations, and it is related to the electron packing parameter, α, the number of valence electrons per unit cell, the number of conduction electrons in the entire system, and the volume of the material under study, among others. In general, T_c increases with α and the number of valence electrons per unit cell, but decreases sharply with the number of conduction electrons. A ridge appears when α is around 30, suggesting that T_c may reach a maximum at this point. Our findings not only provide theoretical support for recent experimental observations but also offer insight into achieving high T_c by fine-tuning material properties and have broader implications for understanding superconductivity in a universal manner.

Superatomic states under high pressure

The study of superatoms has attracted great interest since they apparently go beyond the traditional understanding of the periodic table of elements. In this work, we clearly show that superatoms can be extended from conventional structures to states under pressure condition. By studying the compression process of the CH₄@C₆₀ system formed via embedding methane molecules inside fullerene C₆₀, it is found that the system maintains superatomic properties in both static states, and even dynamic rotation situations influenced by quantum tunneling. Remarkably, the simulations reveal the emergence of new superatomic molecular orbitals by decreasing the confined space to approach the van der Waals boundary between CH₄ and C₆₀. Our current results not only establish a complete picture of superatoms from ambient condition to high pressure, but also offer a perspective for the discovery and exploration of new properties in superatom systems under extreme conditions.