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

Synthesis and Superconductivity of Ternary A15-(Lu, Y)4H23 at High Pressures

Ternary hydrides, formed by introducing new elements into binary hydrides, are a crucial pathway for enhancing superconducting transition temperatures (Tc) or reducing the stable pressures. In this work, we have acquired the ternary hydride formed by Lu and Y atoms, inspired by the low stabilization pressure of the Lu-H system with its fully filled 4f electrons, as well as the higher Tc of the Y-H system. By effectively controlling the high-pressure and high-temperature conditions, we have successfully synthesized Pm-3n (Lu, Y)4H23 (A15-type). The synthesized Pm-3n (Lu, Y)4H23 reveals the highest Tc of 112 K at 215 GPa, which is the record Tc among A15-type superconductors. Compared to the binary Pm-3n Lu4H23, the Pm-3n (Lu, Y)4H23 exhibits a 60% increase in Tc and a 61% enhancement in the upper critical field μ0Hc2(0). Interestingly, Pm-3n (Lu, Y)4H23 displays minimal volume expansion and a slight increase in the H-H bond distance relative to Pm-3n Lu4H23 due to the introduction of Y atoms. Combined theoretical and experimental analyses indicate that the substitution of Lu atoms with Y atoms enhances electron-phonon coupling (EPC) through modified electronic bands and phonon softening caused by the expansion of H-H bonds, collectively driving the significant enhancement of Tc in Pm-3n (Lu, Y)4H23. Our work demonstrates a crucial strategy for adjusting and enhancing the superconducting performance of hydrides and offers valuable practical experience for developing ternary hydrides.

Hydrogen-Vacancy-Induced Stable Superconducting Niobium Hydride at High Pressure

In recent years, the discovery of unconventional polyhydrides under high pressure, including notable instances like CaH6, YH9, and LaH10, with superconducting critical temperature (Tc) above 200 K, has ignited considerable interest in the quest for high-temperature superconductivity in hydrogen-based materials. Recent studies have suggested the highly probable existence of hydrogen vacancies in these high-Tc superconducting hydrides, although there is no conclusive evidence. In this study, taking niobium (Nb) hydride as a model, we showcase the observation of nonstoichiometric face-centered cubic (fcc) NbH4-δ (δ∼0.23-0.51) at pressures ranging from 113 to 175 GPa, employing in situ high-pressure X-ray diffraction experiments in conjunction with first-principles calculations. Remarkably, our further analyses indicate that the hydrogen vacancies, along with the resulting configurational entropy, play crucial roles in stabilizing this nonstoichiometric fcc NbH4-δ. Electrical transport measurements confirmed the superconductivity, as evidenced by zero resistance as well as suppression of Tc with applying magnetic fields, with a Tc reaching up to 34 K. Our current results not only confirm the presence of hydrogen vacancies in high-Tc hydrides, but also provide key insights into the understanding of hydrogen-vacancy-induced stability for nonstoichiometric hydrides under high pressure.

Superconductivity in hexagonal Ce0.5La0.5H9 under high pressure

Recently, experimental observation has shown that the substitutional alloy (Ce,La)H9 can be successfully synthesized under high pressure, approximately 90-170 GPa, and become a superconductor with a high critical temperature (Tc) superconductivity in ternary rare-earth clathrate hydrides between 148-178 K. In this work, we theoretically simplified the hydride alloy (Ce,La)H9, a compound in a series that could function as a potential superconductor, with Ce0.5La0.5H9 exhibiting strong electron-phonon coupling (EPC). The Ce0.5La0.5H9 alloy is scrutinized for its lattice dynamical stability in the pressure range of 100 to 150 GPa. Remarkably, we have first unlocked the theoretical structure of Ce0.5La0.5H9, which remains ambiguous in identifying its crystal structure through experimental measurements. With these remarkable results, the Ce0.5La0.5H9 begins to exhibit structural stability at 110 GPa. The superconducting spectral function is also calculated. We found that the EPC reaches strong-coupling at a pressure of 120 GPa. Using the Allen-Dynes-modified McMillan equation in the strong coupling regime, the Ce0.5La0.5H9 exhibits superconductivity with a Tc of approximately 127 K.

Possible Superconductivity Transition in Nitrogen-Doped Lutetium Hydride Observed at Megabar Pressure

The pursuit of room-temperature superconductivity at an accessible synthetic pressure has been a long-held dream for both theoretical and experimental physicists. Recently, a controversial report by Dasenbrock-Gammon et al. claims that the nitrogen-doped lutetium trihydride exhibits room-temperature superconductivity at near-ambient pressure. However, many researchers have failed to independently reproduce these results, which has sparked intense skepticism on this report. In this work, a LuH2±xNy sample is fabricated using high-pressure and high-temperature methods. The composition and structural characterization are the same as the aforementioned near-ambient superconductor. In situ X-ray diffraction investigations indicate that a high-pressure phase transition toward Fm3 ¯ $\bar{3}$ m-LuH3±xNy occurred in the sample at 59 GPa. The temperature-dependent resistance measurements reveal that two possible superconductivity transition are observed at 95 GPa, with Tc1 ≈6.5 K for high-Tc phase and Tc2 ≈2.1 K for low-Tc phase, arising from the disparate phases in the sample. Resistivity measurements in the Fm3 ¯ $\bar{3}$ m-LuH3±xNy phase under varying magnetic fields exhibited characteristics consistent with superconductivity, with an upper critical field μ0Hc2(0) of 3.3 T measured at 163 GPa. This work is expected to shed some light on the controversy surrounding superconductivity in the nitrogen-doped lutetium hydride system.

Theoretical Insights into High-T c Superconductivity of Structurally Ordered YThH18: A First-Principles Study

There has been a marked increase in interest in high-temperature superconductors over the past few years, sparked by their potential to revolutionize multiple fields, including energy generation and transportation. A particularly promising avenue of exploration has emerged in the form of ternary superhydrides, compounds composed of hydrogen along with two other rare-earth elements. Our investigation focuses on the search for Y-Th-H ternary compounds; employing an evolutionary search methodology complemented by electron-phonon calculations reveals a stable superhydride, P6̅m2-YThH18, capable of exhibiting a critical temperature (T c) as high as 222 K at 200 GPa along a few low-T c novel hydrides. Our analysis explores the possibility of alloyed structure formation from the disordered condition of Th-doped YH9 and establishes that the P6̅m2-YThH18 is indeed a structurally ordered structure. This opens up an exciting avenue for research on multinary superhydrides, which could facilitate experimental synthesis and provides potential implications for high-temperature superconductivity research.

Compact vacuum transfer devices for highly air-sensitive materials in scanning electron microscopy

Surface analysis experiments on air-sensitive substances are challenging to avoid their contact with air, leading to inaccurate results due to oxidation or hygroscopicity. To address this issue, we designed a compact vacuum transfer device (VTD) and applied it to scanning electron microscopy (SEM) and energy-dispersive X-ray spectroscopy (EDS) experiments. Our VTD features a split structure that can be opened and separated in the SEM specimen exchange chamber via magnetic control. This design allows the SEM manufacturer's stub to be fed directly into the SEM specimen chamber, preventing damage to the instrument's internal components and avoiding restrictions on specimen height. Additionally, the compact design maximizes the utilization of sample accommodation space. Besides, it can be flexibly customized in different sizes and types of stubs to adapt electron microscopes from various manufacturers. To confirm the reliability of our device, we applied it to several highly air-sensitive samples for morphology and chemical composition analysis by SEM and EDS. The EDS results showed that the atomic percentage of Na reaches 94.55 % after 14 minutes and 93.44 % after 30 minutes of storage when transferring metallic sodium. Furthermore, our VTD enables airtight recycling and re-transfer of samples after the SEM (-EDS) experiments. These results demonstrate that our device has excellent practicality and airtightness, making it suitable for medium- and long-distance sample transfer between laboratories on the campus.

Unusual metallic state in superconducting A15-type La4H23

Hydride superconductors continue to fascinate the communities of condensed matter physics and material scientists because they host the promising near room-temperature superconductivity. Current research has concentrated on the new hydride superconductors with the enhancement of the superconducting transition temperature (T c). The multiple extreme conditions (high pressure/temperature and magnetic field) will introduce new insights into hydride superconductors. The study of transport properties under very high magnetic fields facilitates the understanding of superconductivity in conventional hydride superconductors. In the present work, we report experimental evidence of an unusual metal state in a newly synthesized cubic A15-type La4H23 that exhibits superconductivity with a T c reaching 105 K at 118 GPa. A large negative magnetoresistance is observed in strong pulsed magnetic fields in the non-superconducting state of this compound below 40 K. Moreover, we construct the full magnetic phase diagram of La4H23 up to 68 T at high pressure. The present work reveals anomalous electronic structural properties of A15-La4H23 under high magnetic fields, and therefore has great importance with regard to advancing the understanding of quantum transport behaviors in hydride superconductors.

High-Temperature Superconductivity in Perovskite Hydride Below 10 GPa

Hydrogen and hydride materials have long been considered promising materials for high-temperature superconductivity. However, the extreme pressures required for the metallization of hydrogen-based superconductors limit their applications. Here, a series of high-temperature perovskite hydrides is designed that can be stable within 10 GPa. The research covered 182 ternary systems and ultimately determined that eight new compounds are stable within 20 GPa, of which five exhibited superconducting transition temperatures exceeding 120 K within 10 GPa, including KGaH3 (146 K at 10 GPa), RbInH3 (130 K at 6 GPa), CsInH3 (153 K at 9 GPa), RbTlH3 (170 K at 4 GPa) and CsTlH3 (163 K at 7 GPa). Excitingly, KGaH3 and RbGaH3 are thermodynamically stable at 50 GPa. Among these perovskite hydrides, alkali metals are responsible for providing a fixed amount of charge and supporting alloy framework composed of hydrogen and IIIA group elements to maintain stable crystal structure, while the cubic hydrogen alloy framework formed by IIIA group elements and hydrogen is crucial for high-temperature superconductivity. This work will inspire further experimental exploration and take an important step in the exploration of low-pressure stable high-temperature superconductors.

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

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

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.

Structural and Electronic Properties of the Magnetic and Nonmagnetic X0.125Mg0.875B2 (X = Nb, Ni, Fe) Materials: A DFT/HSE06 Approach to Investigate Superconductor Behavior

MgB2 material has a simple composition and structure that is well-reported and characterized. This material has been widely studied and applied in the last 20 years as a superconductor in wire devices and storage material for H in the hydride form. MgB2 doped with transition metals improves the superconductor behavior, such as the critical temperature (T cs) or critical current (J sc) for the superconducting state. The results obtained in this manuscript indicate that Nb-, Fe-, and Ni-doping in the Mg site leads to a contraction of the unit cell through the spin polarization on the electronic resonance of the boron layer. Fe and Ni transition metals doping perturb the electronic resonance because of stronger dopant-boron bonds. The unpaired electrons are transferred from 3d orbitals to the empty 2p z orbitals of the boron atoms, locating α electrons in the σ bonds and β electrons in the π orbitals. The observed influence of magnetic dopants on MgB2 enables the proposal of an electronic mechanism to explain the spin polarization of boron hexagonal rings.

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.

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.

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.

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.

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.

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.

D-Wave Superconducting Gap Symmetry as a Model for Nb1−xMoxB2 (x = 0.25; 1.0) and WB2 Diborides

Recently, Pei et al. (National Science Review2023, nwad034, 10.1093/nsr/nwad034) reported that ambient pressure β-MoB2 (space group: R3¯m) exhibits a phase transition to α-MoB2 (space group: P6/mmm) at pressure P~70 GPa, which is a high-temperature superconductor exhibiting Tc=32 K at P~110 GPa. Although α-MoB2 has the same crystalline structure as ambient-pressure MgB2 and the superconducting critical temperatures of α-MoB2 and MgB2 are very close, the first-principles calculations show that in α-MoB2, the states near the Fermi level, εF, are dominated by the d-electrons of Mo atoms, while in MgB2, the p-orbitals of boron atomic sheets dominantly contribute to the states near the εF. Recently, Hire et al. (Phys. Rev. B2022, 106, 174515) reported that the P6/mmm-phase can be stabilized at ambient pressure in Nb1−xMoxB2 solid solutions, and that these ternary alloys exhibit Tc~8 K. Additionally, Pei et al. (Sci. China-Phys. Mech. Astron. 2022, 65, 287412) showed that compressed WB2 exhibited Tc~15 K at P~121 GPa. Here, we aimed to reveal primary differences/similarities in superconducting state in MgB2 and in its recently discovered diboride counterparts, Nb1−xMoxB2 and highly-compressed WB2. By analyzing experimental data reported for P6/mmm-phases of Nb1−xMoxB2 (x = 0.25; 1.0) and highly compressed WB2, we showed that these three phases exhibit d-wave superconductivity. We deduced 2Δm(0)kBTc=4.1±0.2 for α-MoB2, 2Δm(0)kBTc=5.3±0.1 for Nb0.75Mo0.25B2, and 2Δm(0)kBTc=4.9±0.2 for WB2. We also found that Nb0.75Mo0.25B2 exhibited high strength of nonadiabaticity, which was quantified by the ratio of TθTF=3.5, whereas MgB2, α-MoB2, and WB2 exhibited TθTF~0.3, which is similar to the TθTF in pnictides, A15 alloys, Heusler alloys, Laves phase compounds, cuprates, and highly compressed hydrides.

Quantifying Nonadiabaticity in Major Families of Superconductors

The classical Bardeen−Cooper−Schrieffer and Eliashberg theories of the electron−phonon-mediated superconductivity are based on the Migdal theorem, which is an assumption that the energy of charge carriers, kBTF, significantly exceeds the phononic energy, ℏωD, of the crystalline lattice. This assumption, which is also known as adiabatic approximation, implies that the superconductor exhibits fast charge carriers and slow phonons. This picture is valid for pure metals and metallic alloys because these superconductors exhibit ℏωDkBTF<0.01. However, for n-type-doped semiconducting SrTiO3, this adiabatic approximation is not valid, because this material exhibits ℏωDkBTF≅50. There is a growing number of newly discovered superconductors which are also beyond the adiabatic approximation. Here, leaving aside pure theoretical aspects of nonadiabatic superconductors, we classified major classes of superconductors (including, elements, A-15 and Heusler alloys, Laves phases, intermetallics, noncentrosymmetric compounds, cuprates, pnictides, highly-compressed hydrides, and two-dimensional superconductors) by the strength of nonadiabaticity (which we defined by the ratio of the Debye temperature to the Fermi temperature, TθTF). We found that the majority of analyzed superconductors fall into the 0.025≤TθTF≤0.4 band. Based on the analysis, we proposed the classification scheme for the strength of nonadiabatic effects in superconductors and discussed how this classification is linked with other known empirical taxonomies in superconductivity.