Superconductivity of MgB2: covalent bonds driven metallic

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.

Unveiling a Family of Dimerized Quantum Magnets, Conventional Antiferromagnets, and Nonmagnets in Ternary Metal Borides

Dimerized quantum magnets are exotic crystalline materials where Bose-Einstein condensation of magnetic excitations can happen. However, known dimerized quantum magnets are limited to only a few oxides and halides. Here, we unveil 9 dimerized quantum magnets and 11 conventional antiferromagnets in ternary metal borides MTB4 (M = Sc, Y, La, Ce, Lu, Mg, Ca, and Al; T = V, Cr, Mn, Fe, Co, and Ni), where T atoms are arranged in structural dimers. Quantum magnetism in these compounds is dominated by strong antiferromagnetic (AFM) interactions between Cr (Cr and Mn for M = Mg and Ca) atoms within the dimers, with much weaker interactions between the dimers. These systems are proposed to be close to a quantum critical point between a disordered singlet spin-dimer phase, with a spin gap, and the ordered conventional Néel AFM phase. They greatly enrich the materials inventory that allows investigations of the spin-gap phase. Conventional antiferromagnetism in these compounds is dominated by ferromagnetic Mn (Fe for M = Mg and Ca) interactions within the dimers. The predicted stable and nonmagnetic (NM) YFeB4 phase is synthesized and characterized, providing a scarce candidate to study Fe dimers and Fe ladders in borides. The identified quantum, conventional, and NM systems provide a platform with abundant possibilities to tune the magnetic exchange coupling by doping and study the unconventional quantum phase transition and conventional magnetic transitions. This work opens new avenues for studying novel magnetism in borides arising from spin dimers and establishes a theoretical workflow for future searches for dimerized quantum magnets in other families of materials.

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.

Structure searches and superconductor discovery in XB2 (X = Sc, Ti, V, Cr, and Tc)

With extensive structure searches for XB2 (X = Sc, Ti, V, Cr, and Tc) under pressures up to 100 GPa, we uncovered that the crystal structures of these compounds with the lowest enthalpy have the same space group (P6/mmm) as MgB2 at ambient pressure. Among them, ScB2, TiB2 and VB2 are dynamically stable at ambient pressure, but they do not superconduct. CrB2 becomes dynamically stable at 108 GPa and shows superconductivity with a transition temperature (Tc) of 26.0 K. TcB2 is not dynamically stable until 9 GPa. At 20 GPa, it has a Tc of 23.5 K. Further calculations indicate that CrB2 and TcB2 are also thermodynamically stable, suggesting that it is highly likely that they can be synthesized successfully in the laboratory. We found that transition metal atoms (Cr/Tc) dominate soft phonon vibrations and make significant contributions to the electron-phonon coupling (EPC) and superconductivity in CrB2/TcB2, which is in strong contrast to the case of MgB2, where high-frequency B vibrations dominate the EPC and superconductivity. Our work enriches the understanding of superconductivity in transition metal borides.

Sampling the Materials Space for Conventional Superconducting Compounds

A large scale study of conventional superconducting materials using a machine-learning accelerated high-throughput workflow is performed, starting by creating a comprehensive dataset of around 7000 electron-phonon calculations performed with reasonable convergence parameters. This dataset is then used to train a robust machine learning model capable of predicting the electron-phonon and superconducting properties based on structural, compositional, and electronic ground-state properties. Using this machine, the transition temperatures (Tc ) of approximately 200 000 metallic compounds are evaluated, all of which are on the convex hull of thermodynamic stability (or close to it) to maximize the probability of synthesizability. Compounds predicted to have Tc values exceeding 5 K are further validated using density-functional perturbation theory. As a result, 541 compounds with Tc values surpassing 10 K, encompassing a variety of crystal structures and chemical compositions, are identified. This work is complemented with a detailed examination of several interesting materials, including nitrides, hydrides, and intermetallic compounds. Particularly noteworthy is LiMoN2 , which is predicted to be superconducting in the stoichiometric trigonal phase, with a Tc exceeding 38 K. LiMoN2 has previously been synthesized in this phase, further heightening its potential for practical applications.

Two-gap topological superconductor LaB2 with high Tc = 30 K

Since two gap superconductivity was discovered in MgB2, research on multigap superconductors has attracted increasing attention because of its intriguing fundamental physics. In MgB2, the Mg atom donates two electrons to the borophene layer, resulting in a stronger gap from the σ band and a weaker gap from the π bond. First-principles calculations demonstrate that the two gap anisotropic superconductivity strongly enhances the transition temperature of MgB2 in comparison with that given by the isotropic model. In this work, we report a three-band (B-σ, B-π, and La-d) two-gap superconductor LaB2 with very high Tc = 30 K by solving the fully anisotropic Migdal-Eliashberg equation. Because of the σ and π-d hybridization on the Fermi surface, the electron-phonon coupling constant λ = 1.5 is significantly larger than the λ = 0.7 of MgB2. Our work paves a new route to enhance the electron-phonon coupling strength of multigap superconductors with d orbitals. On the other hand, our analysis reveals that LaB2 belongs to the weak topological semimetal category, leading to a possible topological superconductor with the highest Tc to date. Moreover, upon applying pressure and/or doping, the topology is tunable between weak and strong with Tc varying from 15 to 30 K, opening up a flexible platform for manipulating topological superconductors.

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.

Stability and superconductivity of freestanding two-dimensional transition metal boridene: M4/3B2

The small atomic mass of boron indicates strong electron-phonon coupling (EPC), so it may have a brilliant performance in superconductivity. Recently, a new 2D boride sheet with ordered metal vacancies and surface terminals (Mo4/3B2-x) was realized in experiments (Zhouet al2021Science373801). Here, the 2D monolayer freestanding Mo4/3B2is evidenced to be thermodynamically stable. Through electronic structure, phonon spectrum and EPC, monolayer Mo4/3B2is found to be an intrinsic phonon-mediated superconductor. The superconducting transition temperature (Tc) is determined to be 4.06 K by the McMillian-Allen-Dynes formula. Remarkably, theTcof monolayer Mo4/3B2can be increased to 6.78 K with an appropriate biaxial tensile strain (+5%). Moreover, we predict that other transition metal replacing Mo atoms is also stable and retaining the superconductivity. Such as monolayer W4/3B2is also a superconductor with theTcof 2.37 K. Our research results enrich the database of 2D monolayer superconductors and boron-related formed materials science.

Two-gap-like anisotropic superconductivity in a bulk boron kagome lattice

Since a report of superconductivity in elemental boron at high pressure [M. I. Eremets et al., Science, 2001, 293, 272-274], many efforts have been devoted to the search for superconductivity in diverse boron allotropes. However, there are few superconducting phenomena to be discovered theoretically and experimentally in elemental bulk boron crystals at normal pressure to date. In this paper, we propose a metastable but dynamically stable metallic bulk boron phase within the kagome lattice, and demonstrate from first principles good superconductivity with a high superconducting critical temperature Tc, e.g., ∼34-39 K, in the elemental bulk boron at ambient pressure. Our calculations indicate that such a high-Tc superconductivity is closely related to the Fermi surface displaying strong electron-phonon coupling with a two-region-like distribution feature, which resulted from two different types of covalent bonding crossing the Fermi level and also gives rise to a two-gap-like superconducting nature in the system. We uncover that the strong electron-lattice coupling is dominated by the transversal acoustic phonon modes around a degenerate softening kink that places the system on the verge of a latent charge density wave. The present findings shed light on a study of the high-Tc superconductivity of the elemental bulk boron phase at normal pressure.

Theoretical study on the superconductivity of graphene-like TMB6 (TM = Cr, Fe and Co) monolayer and its potential anchoring and catalytic properties for lithium-sulfur batteries

In recent years, two-dimensional materials have aroused enormous interest owing to their superior electrochemical performance, abundant exposed active sites, high specific surfaces and so on. Unlike many stable allotropes, honeycomb hexagonal borophene is kinetically unstable. In this study, we introduce transition metal atoms (Cr, Fe and Co) to stabilize honeycomb hexagonal borophene, forming stable graphene-like TMB6 (TM = Cr, Fe and Co) monolayers. Moreover, we explored the possibility of superconductivity and the anchoring materials of lithium-sulfur batteries using the first-principles density functional theory (DFT) calculation. Our results show that CoB6 exhibited the best superconductivity with a superconducting transition temperature of 33.3 K. Furthermore, CoB6 and FeB6 are promising anchoring materials because of the suppression of lithium polysulfides shuttling in lithium-sulfur batteries because they can accelerate sulfur reduction reaction kinetics.

Prediction of superconductivity in sandwich XB4 (X = Li, Be, Zn and Ga) films

Borophenes and 2D boron allotropes are metallic and exhibit a BCS superconducting state, unlike graphene. In-plane stretching vibrational modes in bulk MgB2 boron layers induce phonon-mediated superconductivity. However, the effect of stretching vibrational phonon modes on transition temperature (Tc) still requires further investigations. Here, we use first-principles calculations combined with conventional BCS theory to explore the superconducting properties in a series of dynamically stable boron-based sandwich films that have not been realized experimentally. The sandwich films of XB4 (where X = Li, Be, Zn, Ga) are predicted to exhibit good phonon-mediated superconductivity with high Tc values of 25.1 K, 28.7 K, 38.7 K, and 36.2 K, respectively. The origin of the superconducting states is mainly caused by the high metallicity and strong electron-phonon coupling (EPC), which can be attributed to the presence of intercalated atoms within the borophene layers. It is further demonstrated in the XB4 compounds (where X = Li, Be, Zn, Ga) that the pronounced EPC is not solely attributable to the in-plane vibrations of B atoms, but it is also influenced significantly by the out-of-plane vibrations of B atoms. Sandwich (Li,Be,Zn,Ga)B4 films may be a great choice for nanoscale superconductors as the electron-phonon coupling parameter becomes greater than unity, thereby providing a powerful approach for investigating these systems with high critical temperatures.

Strong electron-phonon coupling driven pseudogap modulation and density-wave fluctuations in a correlated polar metal

There is tremendous interest in employing collective excitations of the lattice, spin, charge, and orbitals to tune strongly correlated electronic phenomena. We report such an effect in a ruthenate, Ca3Ru2O7, where two phonons with strong electron-phonon coupling modulate the electronic pseudogap as well as mediate charge and spin density wave fluctuations. Combining temperature-dependent Raman spectroscopy with density functional theory reveals two phonons, B2P and B2M, that are strongly coupled to electrons and whose scattering intensities respectively dominate in the pseudogap versus the metallic phases. The B2P squeezes the octahedra along the out of plane c-axis, while the B2M elongates it, thus modulating the Ru 4d orbital splitting and the bandwidth of the in-plane electron hopping; Thus, B2P opens the pseudogap, while B2M closes it. Moreover, the B2 phonons mediate incoherent charge and spin density wave fluctuations, as evidenced by changes in the background electronic Raman scattering that exhibit unique symmetry signatures. The polar order breaks inversion symmetry, enabling infrared activity of these phonons, paving the way for coherent light-driven control of electronic transport.

The Structure Evolution of Hydroxyl-Reacted LiBC to Improve the Capacity for Li-Ion Batteries

As a graphite-like material, the LiBC can deliver a high capacity up to 500 mA h g^-1 in Li-ion batteries, which is dependent on the carbon precursor, the high-temperature treatment, and the lithium insufficiency. However, the underlying mechanism is still not clear for the electrochemical reactions of LiBC. In this work, the pristine LiBC was reacted with aqueous solutions of different alkalinity, which was delithiated chemically and retained the layered structure. According to the XPS and NMR results, the B-B bond might be produced through the aqueous reaction or the initial charge process, which can be oxidized (charged) and reduced (discharged) in the electrochemical measurements. In the Li-ion battery, the reversible capacity of LiBC increases evidently with the alkalinity of aqueous solution and significantly rises to a similar value of ca. 285 mA h g^-1 under 200 cycles. Therefore, the specific capacity of LiBC should be contributed by the active sites of B-B bonds, which can be significantly increased through the reaction with the hydroxyl ions, and this strategy might be adopted to activate more graphite-like materials.

Pressure-induced superconductivity at 32 K in MoB2

Since the discovery of superconductivity in MgB2 (Tc ∼ 39 K), the search for superconductivity in related materials with similar structures or ingredients has never stopped. Although about 100 binary borides have been explored, only a few of them show superconductivity with relatively low Tc. In this work, we report the discovery of superconductivity up to 32 K, which is the highest Tc in transition-metal borides, in MoB2 under pressure. The Tc of MoB2 in the α phase can be well explained by theoretical calculations in the framework of electron-phonon coupling. Furthermore, the coupling between the d electrons of Mo and the out-of-plane Mo-phonon modes are the main driving force of the 32 K superconductivity of MoB2. Our study sheds light on the exploration of high-Tc superconductors in transition metal borides.

Dominant Two-Dimensional Electron-Phonon Interactions in the Bulk Dirac Semimetal Na3Bi

Bulk Dirac semimetals (DSMs) exhibit unconventional transport properties and phase transitions due to their peculiar low-energy band structure, yet the electronic interactions governing nonequilibrium phenomena in DSMs are not fully understood. Here we show that electron-phonon (e-ph) interactions in a prototypical bulk DSM, Na₃Bi, are predominantly two-dimensional (2D). Our first-principles calculations reveal a 2D optical phonon with strong e-ph interactions associated with in-plane vibrations of Na atoms. We show that this 2D mode governs e-ph scattering and charge transport in Na₃Bi and induces a dynamical phase transition to a Weyl semimetal. Our work advances the quantitative analysis of electron interactions in Na₃Bi and reveals a dominant low-dimensional interaction in a bulk Dirac semimetal.

Prediction ofπ-electrons mediated high-temperature superconductivity in monolayer LiC12

Prediction and synthesis of two-dimensional high transition temperature (T_C) superconductors is an area of extensive research. Based on calculations of the electronic structures and lattice dynamics, we predict that graphene-like layered monolayer LiC₁₂is aπ-electrons mediated Bardeen-Cooper-Schrieffer-type superconductor. Monolayer LiC₁₂is theoretically stable and expected to be synthesized experimentally. From the band structures and the phonon dispersion spectrum, it is found that the saddle point ofπ-bonding bands induces large density of states at the Fermi energy level. There is strongly coupled between the vibration mode in the in-plane direction of the lithium atoms and theπ-electrons of carbon atoms, which induces the high-T_Csuperconductivity in LiC₁₂. TheT_Ccan reach to 41 K under an applied 10% biaxial tensile strain based on the anisotropic Eliashberg equation. Our results show that monolayer LiC₁₂is a good candidate asπ-electrons mediated electron-phonon coupling high-T_Csuperconductor.

Polymeric Hydronitrogen N4H: A Promising High-Energy-Density Material and High-Temperature Superconductor

Solid nitrogen-rich compounds are potential high-energy-density materials (HEDMs). The enormous challenge in this area is to synthesize and stabilize these energetic materials at moderate pressure and better under near-ambient conditions. Here, we perform an extensive theoretical study on hydronitrogens by the reverse design method considering both energies and energy densities. Four hydronitrogens with different stoichiometries, that is, N4H, N3H, N2H, and NH, are found to be stable at pressures of about 80-300 GPa and metastable with pressure releasing to ambient pressure. The energy densities of these hydronitrogens are about 5.6-6.5 kJ/g and 1.3-1.5 times larger than that of trinitrotoluene (TNT). Most importantly, the Pbam phase of the N4H compound is an excellent high-temperature superconductor with a Tc of 37.7 K at 72 GPa. The present findings enrich new phases of hydronitrogens under high pressure and characterize their structural and energetic properties and superconductivity, which offer crucial insights for further design and synthesis of exceptional materials with high energy density and high-temperature superconductivity.

Triplet Superconductivity from Nonlocal Coulomb Repulsion in an Atomic Sn Layer Deposited onto a Si(111) Substrate

Atomic layers deposited on semiconductor substrates introduce a platform for the realization of the extended electronic Hubbard model, where the consideration of electronic repulsion beyond the on-site term is paramount. Recently, the onset of superconductivity at 4.7 K has been reported in the hole-doped triangular lattice of tin atoms on a silicon substrate. Through renormalization group methods designed for weak and intermediate coupling, we investigate the nature of the superconducting instability in hole-doped Sn/Si(111). We find that the extended Hubbard nature of interactions is crucial to yield triplet pairing, which is f-wave (p-wave) for moderate (higher) hole doping. In light of persisting challenges to tailor triplet pairing in an electronic material, our finding promises to pave unprecedented ways for engineering unconventional triplet superconductivity.

The 2021 room-temperature superconductivity roadmap

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

THz/Far infrared synchrotron observations of superlattice frequencies in MgB2

THz/Far Infrared synchrotron absorption experiments on pure and doped MgB₂ samples show that the absorption spectral weight at low wavenumber (i.e., <110 cm^-1) evolves as the temperature is reduced to 10 K. Distinct spectral peak intensities increase as the temperature of MgB₂ and doped MgB₂ approaches, and then crosses, the superconducting transition temperature. These experimental data suggest a strong link to superconductivity induced by subtle shifts in structural symmetry. Significant increases in absorption are observed at frequencies that correspond to the superconducting gaps for doped and pure MgB₂, and at fractions of these frequency (or energy) values. This low wavenumber spectral transition is consistent with the notion that superlattice frequencies contribute to the optic modes of the MgB₂ phonon dispersion and are critical to the superconducting transition for this structure. Key integer ratios are identified in real and reciprocal spaces that link bonding character, Fermi vectors and Fermi surfaces as well as phonon properties with geometric parameters and specific superlattice symmetries for MgB₂. Similarly consistent spectral data at low wavenumber are also obtained for carbon doped Mg¹¹B₂. Density Functional Theory calculations of superlattice phonon dispersions result in folded mode frequencies that match these observed low wavenumber experiments. These results show that symmetry reductions, largely electronic in character although coupled to vibrations, occur with change in temperature and imply strong links to superconductivity mechanisms.

Charge Density Waves and Electronic Properties of Superconducting Kagome Metals

Kagome metals AV_{3}Sb_{5} (A=K, Rb, and Cs) exhibit intriguing superconductivity below 0.9∼2.5  K, a charge density wave (CDW) transition around 80∼100  K, and Z_{2} topological surface states. The nature of the CDW phase and its relation to superconductivity remains elusive. In this work, we investigate the electronic and structural properties of CDW by first-principles calculations. We reveal an inverse Star of David deformation as the 2×2×2 CDW ground state of the kagome lattice. The kagome lattice shows softening breathing-phonon modes, indicating the structural instability. However, electrons play an essential role in the CDW transition via Fermi surface nesting and van Hove singularity. The inverse Star of David structure agrees with recent experiments by scanning tunneling microscopy (STM). The CDW phase inherits the nontrivial Z_{2}-type topological band structure. Further, we find that the electron-phonon coupling is too weak to account for the superconductivity T_{c} in all three materials. It implies the existence of unconventional pairing of these kagome metals. Our results provide essential knowledge toward understanding the superconductivity and topology in kagome metals.

The Emergence and Evolution of Borophene

Neighboring carbon and sandwiched between non-metals and metals in the periodic table of the elements, boron is one of the most chemically and physically versatile elements, and can be manipulated to form dimensionally low planar structures (borophene) with intriguing properties. Herein, the theoretical research and experimental developments in the synthesis of borophene, as well as its excellent properties and application in many fields, are reviewed. The decade-long effort toward understanding the size-dependent structures of boron clusters and the theory-directed synthesis of borophene, including bottom-up approaches based on different foundations, as well as up-down approaches with different exfoliation modes, and the key factors influencing the synthetic effects, are comprehensively summarized. Owing to its excellent chemical, electronic, mechanical, and thermal properties, borophene has shown great promise in supercapacitor, battery, hydrogen-storage, and biomedical applications. Furthermore, borophene nanoplatforms used in various biomedical applications, such as bioimaging, drug delivery, and photonic therapy, are highlighted. Finally, research progress, challenges, and perspectives for the future development of borophene in large-scale production and other prospective applications are discussed.

Prediction of Phonon-Mediated Superconductivity with High Critical Temperature in the Two-Dimensional Topological Semimetal W2N3

Two-dimensional superconductors attract great interest both for their fundamental physics and for their potential applications, especially in the rapidly growing field of quantum computing. Despite intense theoretical and experimental efforts, materials with a reasonably high transition temperature are still rare. Even more rare are those that combine superconductivity with a nontrivial band topology that could potentially give rise to exotic states of matter. Here, we predict a remarkably high superconducting critical temperature of 21 K in the easily exfoliable, topologically nontrivial 2D semimetal W₂N₃. By studying its electronic and superconducting properties as a function of doping and strain, we also find large changes in the electron-phonon interactions that make this material a unique platform to study different coupling regimes and test the limits of current theories of superconductivity. Last, we discuss the possibility of tuning the material to achieve coexistence of superconductivity and topologically nontrivial edge states.

Multiband superconductors with degenerate excitation gaps

There is a tacit assumption that multiband superconductors are essentially the same as multigap superconductors. More precisely, it is usually assumed that the number of excitation gaps in the single-particle energy spectrum of a uniform superconductor (i.e. number of peaks in the density of states of the superconducting electrons) determines the number of contributing bands in the corresponding superconducting model. Here we demonstrate that contrary to this widely accepted viewpoint, the superconducting magnetic properties are sensitive to the number of contributing bands even when the spectral gaps are degenerate and cannot be distinguished. In particular, we find that the crossover between superconductivity types I and II-the intertype regime-is strongly affected by the difference between characteristic lengths of multiple contributing condensates. The reason for this is that condensates with diverse characteristic lengths, when coexisting in one system, interfere constructively or destructively, which results in multi-condensate magnetic phenomena regardless of the presence/absence of the multigap spectrum of a superconducting multiband material.

Superconductivity in Compression-Shear Deformed Diamond

Diamond is a prototypical ultrawide band gap semiconductor, but turns into a superconductor with a critical temperature T_{c}≈4  K near 3% boron doping [E. A. Ekimov et al., Nature (London) 428, 542 (2004)NATUAS0028-083610.1038/nature02449]. Here we unveil a surprising new route to superconductivity in undoped diamond by compression-shear deformation that induces increasing metallization and lattice softening with rising strain, producing phonon mediated T_{c} up to 2.4-12.4 K for a wide range of Coulomb pseudopotential μ^{*}=0.15-0.05. This finding raises intriguing prospects of generating robust superconductivity in strained diamond crystal, showcasing a distinct and hitherto little explored approach to driving materials into superconducting states via strain engineering. These results hold promise for discovering superconductivity in normally nonsuperconductive materials, thereby expanding the landscape of viable nontraditional superconductors and offering actionable insights for experimental exploration.

Ultrafast Hot Phonon Dynamics in MgB_{2} Driven by Anisotropic Electron-Phonon Coupling

The zone-center E_{2g} modes play a crucial role in MgB_{2}, controlling the scattering mechanisms in the normal state as well the superconducting pairing. Here, we demonstrate via first-principles quantum-field theory calculations that, due to the anisotropic electron-phonon interaction, a hot-phonon regime where the E_{2g} phonons can achieve significantly larger effective populations than other modes, is triggered in MgB_{2} by the interaction with an ultrashort laser pulse. Spectral signatures of this scenario in ultrafast pump-probe Raman spectroscopy are discussed in detail, revealing also a fundamental role of nonadiabatic processes in the optical features of the E_{2g} mode.

Pressure-induced phase transitions and superconductivity in magnesium carbides

Crystal structure prediction and in silico physical property observations guide experimental synthesis in high-pressure research. Here, we used magnesium carbides as a representative example of computational high-pressure studies. We predicted various compositions of Mg–C compounds up to 150 GPa and successfully reproduced previous experimental results. Interestingly, our proposed MgC₂ at high pressure >7 GPa consists of extended carbon bonds, one-dimensional graphene layers, and Mg atomic layers, which provides a good platform to study superconductivity of metal intercalated graphene nano-ribbons. We found that this new phase of MgC₂ could be recovered to ambient pressure and exhibited a strong electron-phonon coupling (EPC) strength of 0.6 whose corresponding superconductivity transition temperature reached 15 K. The EPC originated from the cooperation of the out-of-plane and the in-plane phonon modes. The geometry confinement and the hybridization between the Mg s and C p_z orbitals significantly affect the coupling of phonon modes and electrons. These results show the importance of the high-pressure route to the synthesis of novel functional materials, which can promote the search for new phases of carbon-based superconductors.

Simultaneous Enhancement of the Thermoelectric and Mechanical Performance in One-Step Sintered n-Type Bi2Te3-Based Alloys via a Facile MgB2 Doping Strategy

The Bi₂Te₃-based alloys have been commercialized for the applications of energy harvesting and refrigeration for decades. However, the commercial Bi₂Te₃-based alloys produced by the zone-melting (ZM) method usually show poor mechanical strength and crack problems as well as the sluggish figure of merit ZT, especially for the less-progressed n-type samples. In this work, we have simultaneously enhanced the thermoelectric and mechanical performance of the one-step spark plasma sintering (SPS)-derived n-type Bi₂Te_2.7Se_0.3 alloys just by doping a small amount of superconducting material MgB₂ where Mg and B atoms can play significant roles in carrier density optimization and hardness enhancement. Besides the optimization of carrier density, the MgB₂ doping can also increase the carrier mobility but decrease the lattice and bipolar thermal conductivity, leading to a peak ZT of 0.96 at 325 K and an average ZT of 0.88 within 300-500 K in the 0.5% MgB₂-doped Bi₂Te_2.7Se_0.3 (BTSMB) alloys. The peak ZT and average ZT of our optimized BTSMB samples are comparable and higher than those of the state-of-the-art commercial ZM ingot. Moreover, the optimized BTSMB sample also exhibits almost 70% enhancement in hardness compared with the ZM ingot. Our results demonstrate the great potential of the MgB₂ doping strategy for mass production of SPS-derived Bi₂Te₃-based alloys in one-step sintering.

Tunable broadband hyperbolic light dispersion in metal diborides

The naturally hyperbolic materials that conquer the limitations of artificially structured hyperbolic metamaterials are promising candidates for the emerging devices based on light. However, the variety of natural hyperbolic materials and their hyperbolic frequency regime are presently limited. Here, on the basis of first-principles calculations, we demonstrated a family of natural hyperbolic materials, graphite-like metal diborides, with a broadband hyperbolic region from near-IR (∼2.5µm) to the ultraviolet regime (∼248 nm). The operating hyperbolic window and negative refraction can be effectively modulated by extracting electrons from the materials, offering a promising strategy for regulating the optical properties.

Pressure induced semiconductor-semimetal-superconductor transition of magnesium hexaborides

A thorough structural exploration was performed for MgB₆ combining the global structure searching method with first-principles calculations. Besides the known Cmcm phase, new phases, i.e. I4/mmm, C2/m-I, C2/m-II and P2₁/m, were predicted to be stable in the pressure range of 18-100 GPa. Unexpectedly, Cmcm-MgB₆ was found to be a semiconductor with an indirect band gap of 0.38 eV with the HSE06 functional, in good agreement with the experimental finding. I4/mmm-MgB₆ stabilized above 18 GPa exhibits semimetallic behaviour with a topological node-line near the Fermi level. Consequently, C2/m-I MgB₆ with a sandwich structure similar to MgB₂ is predicted to be a superconductor with a critical temperature (T_c) of 9.5 K. By analysing the electronic structure, the intriguing semiconductor-semimetal-superconductor transition may be ascribed to the delocalization of more B-p electrons in the boron sublattice. The novel functions uncovered for MgB₆ may inspire more efforts to discover materials with intriguing properties.

Intrinsic phonon-mediated superconductivity in graphene-like BSi lattice

The research of new superconductors is an ongoing field for the fundamental significances and potential applications, and two-dimensional (2D) nanomaterials open a new alluring branch for exploration. Here we predict by first-principles calculations that 2D pristine graphene-like BSi monolayer is a phonon-mediated superconductor above the boiling point of liquid helium. The intrinsic covalent-metallic ground state, large density of states at Fermi energy, proper electronic organization as well as strong coupling of out-of-plane phonons and electrons endow an intermediate electron-phonon coupling of ~1.12, rendering this honeycomb sheet as a conventional superconductor with a relatively high T _c ~ 11 K. As the global minimum structure in the 2D space previously predicted, this superconducting BSi monolayer may be feasible experimentally. Our finding provides a new field of superconducting nanomaterials for study.

Viewpoint: the road to room-temperature conventional superconductivity

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

Why have band theorists been so successful in explaining and predicting novel superconductors?

In this contribution to the J. Phys.: Condens. Matter memorial issue in honor of Sandro Massidda I reflect on a phenomenon Sandro had been a part of. While theoretical condensed matter physicists have made, over the years, exciting and most elegant contributions to the theory of superconductivity (which, in and by itself, is one of the most beautiful constructs in theoretical physics), some of them of utmost importance, they have had less success in predicting and explaining superconducting states and mechanisms in specific materials. More down-to-earth computational materials scientists, who often go by the moniker 'band theorists', have been much more successful in applying (usually other people's) ideas in such circumstances. In this essay I give some examples, largely drawn from my own experience, and speculate on their meaning.

First-principles prediction of phonon-mediated superconductivity in XBC (X = Mg, Ca, Sr, Ba)

From first-principles calculations, we predict four new intercalated hexagonal XBC (X = Mg, Ca, Sr, Ba) compounds to be dynamically stable and phonon-mediated superconductors. These compounds form a LiBC like structure but are metallic. The calculated superconducting critical temperature, Tc, of MgBC is 51 K. The strong attractive interaction between σ-bonding electrons and the B1g phonon mode gives rise to a larger electron-phonon coupling constant (1.135) and hence high Tc; notably, higher than that of MgB2. The other compounds have a low superconducting critical temperature (4-17 K) due to the interaction between σ-bonding electrons and low energy phonons (E2u modes). Due to their energetic and dynamic stability, we envisage that these compounds can be synthesized experimentally.

Ab Initio Study of the Electronic, Vibrational, and Mechanical Properties of the Magnesium Diboride Monolayer

Magnesium diboride gained significant interest in the materials science community after the discovery of its superconductivity, with an unusually high critical temperature of 39 K. Many aspects of the electronic properties and superconductivity of bulk MgB 2 and thin sheets of MgB 2 have been determined; however, a single layer of MgB 2 has not yet been fully theoretically investigated. Here, we present a detailed study of the structural, electronic, vibrational, and elastic properties of monolayer MgB 2 , based on ab initio methods. First-principles calculations reveal the importance of reduction of dimensionality on the properties of MgB 2 and thoroughly describe the properties of this novel 2D material. The presence of a negative Poisson ratio, higher density of states at the Fermi level, and a good dynamic stability under strain make the MgB 2 monolayer a prominent material, both for fundamental research and application studies.

Extrinsic Two-Dimensional Flux Pinning Centers in MgB2 Superconductors Induced by Graphene-Coated Boron

Extrinsic two-dimensional flux pinning centers, via graphene-encapsulated boron powder as precursors, have been introduced into MgB₂ superconductors by means of in situ and diffusion sintering methods. Uniform graphene encapsulation of the boron powders was achieved by the hydrothermal method with highly dispersed graphene oxide as the precursor. The graphene coating layers induce remaining graphene layers and other defects acting as flux pinning centers in the matrix as well as improved connectivity in between grains. The increased critical current density ( J_c) is attributed to the enhanced flux pinning force and improved connectivity. Two-dimensional flux pinning centers provided by thin graphene layers and grain boundaries in MgB₂ possess high flux pinning efficiency without suppressing the connectivity of the MgB₂ superconductor.

Superconductivity of boron-doped graphane under high pressure

Based on first-principles calculations, the properties of B-doped graphane under high pressure up to 380 GPa are investigated. We find that B-doped graphane undergoes a phase transition from phase-α to phase-β at 6 GPa. Different from pristine graphane (X. Wen, L. Hand, V. Labet, T. Yang, R. Hoffmann, N. W. Ashcroft, A. R. Oganov and A. O. Lyakhov, Graphane sheets and crystals under pressure, Proc. Natl. Acad. Sci. U. S. A., 2011, 108, 6833–6837), phase-γ of B-doped graphane is kinetically unstable. The calculated superconducting transition temperature of B-doped graphane at ambient pressure is 45 K, and pressurization can increase the transition temperature notably, e.g., 77 K at 100 GPa. Both the electronic states at the Fermi level and the electron–phonon coupling are mainly contributed by B–C characteristics, indicating that the B-doping plays a key role in the superconductivity.

Under high-pressure, the most stable two configurations of B-doped graphane are phase-α and phase-β, and pressurization can increase their T_c significantly.

Crystallinity-dependent capacity of a LiBC anode material in Li-ion batteries

LiBC is a layered boron carbide material that was first studied as a superconducting material. Theoretical study showed that LiBC is a promising cathode material in Li-ion batteries, while our early computational and experimental studies demonstrated the feasibility of LiBC as a high-capacity anode material for Li-ion batteries. In this work, LiBC has been synthesized by a solid-state method using different carbon precursors of acetylene black and graphite, marked a-LiBC and g-LiBC, respectively, and their electrochemical properties and corresponding structure evolutions have been investigated in Li-ion batteries. As a result, a-LiBC delivers a higher specific capacity than g-LiBC, 500 mA h g-1vs. 200 mA h g-1, after 50 cycles at a rate of 0.1C. Actually, a significant structural evolution of a-LiBC was observed by in situ XRD during the charge/discharge processes, while a nearly constant structure was detected for g-LiBC. Meanwhile, in situ Raman results revealed the evolution of vibrational beating modes at different charge/discharge states. Therefore, the specific capacity of LiBC is closely related to its crystallinity, and LiBC with amorphous carbon precursors could be adopted as a promising anode material for Li-ion batteries.

Phonon-mediated superconductivity in Mg intercalated bilayer borophenes

Using first-principles calculations, we investigate the structural, electronic and superconducting properties of Mg intercalated bilayer borophenes B_xMgB_x (x = 2-5). Remarkably, B₂MgB₂ and B₄MgB₄ are predicted to exhibit good phonon-mediated superconductivity with a high transition temperature (T_c) of 23.2 K and 13.3 K, respectively, while B₄MgB₄ is confirmed to be more practical based on the analyses of its stability. The densities of states of in-plane orbitals at the Fermi level are found to be dominant at the superconducting transition temperature in Mg intercalated bilayer borophenes, providing an effective avenue to explore Mg-B systems with high T_cs.

Two dimensional boron nanosheets: synthesis, properties and applications

As a material generating increasing interest, boron nanosheets have been reviewed from the perspective of their synthesis, properties, application and possible research directions.

Nonempirical Calculation of Superconducting Transition Temperatures in Light-Element Superconductors

Recent progress in the fully nonempirical calculation of the superconducting transition temperature (T_c ) is reviewed. Especially, this study focuses on three representative light-element high-T_c superconductors, i.e., elemental Li, sulfur hydrides, and alkali-doped fullerides. Here, it is discussed how crucial it is to develop the beyond Migdal-Eliashberg (ME) methods. For Li, a scheme of superconducting density functional theory for the plasmon mechanism is formulated and it is found that T_c is dramatically enhanced by considering the frequency dependence of the screened Coulomb interaction. For sulfur hydrides, it is essential to go beyond not only the static approximation for the screened Coulomb interaction, but also the constant density-of-states approximation for electrons, the harmonic approximation for phonons, and the Migdal approximation for the electron-phonon vertex, all of which have been employed in the standard ME calculation. It is also shown that the feedback effect in the self-consistent calculation of the self-energy and the zero point motion considerably affect the calculation of T_c . For alkali-doped fullerides, the interplay between electron-phonon coupling and electron correlations becomes more nontrivial. It has been demonstrated that the combination of density functional theory and dynamical mean field theory with the ab initio downfolding scheme for electron-phonon coupled systems works successfully. This study not only reproduces the experimental phase diagram but also obtains a unified view of the high-T_c superconductivity and the Mott-Hubbard transition in the fullerides. The results for these high-T_c superconductors will provide a firm ground for future materials design of new superconductors.

Formation of novel transition metal hydride complexes with ninefold hydrogen coordination

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

Coexistence of Superconductivity and Superhardness in Beryllium Hexaboride Driven by Inherent Multicenter Bonding

Unique multicenter bonding in boron-rich materials leads to the formation of complex structures and intriguing properties. Here global structural searches are performed to unearth the structure of beryllium hexaboride (BeB₆) synthesized decades ago. Three BeB₆ phases (α, β, and γ) were predicted to be stable at ambient and high pressures. The ground state at ambient pressure, α-BeB₆, consists of a strong and uniformly distributed covalent B-B network, which results in exceptional elastic properties and a hardness of 46 GPa comparable to γ-B. Even more surprisingly, α-BeB₆ retains credible electron phonon coupling in the boron sublattice, and is predicted to be superconducting at 9 K. Above 4 GPa, β-BeB₆ is stabilized with alternating boron slabs and triangular beryllium layers analogous to the structure of MgB₂. The β-BeB₆ is predicted to be superconducting at 24 K, similar to Nb₃(Al,Ge). The γ-BeB₆ is stable above 340 GPa. The understanding of intrinsic multicenter-bonding mechanism and related properties demonstrated in the very example of BeB₆ provides new insights for the design of tunable multifunctional materials.

Can Two-Dimensional Boron Superconduct?

Two-dimensional boron is expected to exhibit various structural polymorphs, all being metallic. Additionally, its small atomic mass suggests strong electron-phonon coupling, which in turn can enable superconducting behavior. Here we perform first-principles analysis of electronic structure, phonon spectra, and electron-phonon coupling of selected 2D boron polymorphs and show that the most stable structures predicted to feasibly form on a metal substrate should also exhibit intrinsic phonon-mediated superconductivity, with estimated critical temperature in the range of Tc ≈ 10-20 K.

New class of photocatalytic materials and a novel principle for efficient water splitting under infrared and visible light: MgB2 as unexpected example

Water splitting is unanimously recognized as environment friendly, potentially low cost and renewable energy solution based on the future hydrogen economy. Especially appealing is photocatalytic water splitting whereby a suitably chosen catalyst dramatically improves efficiency of the hydrogen production driven by direct sunlight and allows it to happen even at zero driving potential. Here, we suggest a new class of stable photocatalysts and the corresponding principle for catalytic water splitting in which infrared and visible light play the main role in producing the photocurrent and hydrogen. The new class of catalysts - ionic or covalent binary metals with layered graphite-like structures - effectively absorb visible and infrared light facilitating the reaction of water splitting, suppress the inverse reaction of ion recombination by separating ions due to internal electric fields existing near alternating layers, provide the sites for ion trapping of both polarities, and finally deliver the electrons and holes required to generate hydrogen and oxygen gases. As an example, we demonstrate conversion efficiency of ~27% at bias voltage V_bias = 0.5V for magnesium diboride working as a catalyst for photoinduced water splitting. We discuss its advantages over some existing materials and propose the underlying mechanism of photocatalytic water splitting by binary layered metals.

Spontaneous symmetry breaking in vortex systems with two repulsive lengthscales

Scanning Hall probe microscopy (SHPM) has been used to study vortex structures in thin epitaxial films of the superconductor MgB₂. Unusual vortex patterns observed in MgB₂ single crystals have previously been attributed to a competition between short-range repulsive and long-range attractive vortex-vortex interactions in this two band superconductor; the type 1.5 superconductivity scenario. Our films have much higher levels of disorder than bulk single crystals and therefore both superconducting condensates are expected to be pushed deep into the type 2 regime with purely repulsive vortex interactions. We observe broken symmetry vortex patterns at low fields in all samples after field-cooling from above T_c. These are consistent with those seen in systems with competing repulsions on disparate length scales, and remarkably similar structures are reproduced in dirty two band Ginzburg-Landau calculations, where the simulation parameters have been defined by experimental observations. This suggests that in our dirty MgB₂ films, the symmetry of the vortex structures is broken by the presence of vortex repulsions with two different lengthscales, originating from the two distinct superconducting condensates. This represents an entirely new mechanism for spontaneous symmetry breaking in systems of superconducting vortices, with important implications for pinning phenomena and high current density applications.

Phase Diagram and High-Temperature Superconductivity of Compressed Selenium Hydrides

Recent discovery of high-temperature superconductivity (Tc = 190 K) in sulfur hydrides at megabar pressures breaks the traditional belief on the Tc limit of 40 K for conventional superconductors, and opens up the doors in searching new high-temperature superconductors in compounds made up of light elements. Selenium is a sister and isoelectronic element of sulfur, with a larger atomic core and a weaker electronegativity. Whether selenium hydrides share similar high-temperature superconductivity remains elusive, but it is a subject of considerable interest. First-principles swarm structure predictions are performed in an effort to seek for energetically stable and metallic selenium hydrides at high pressures. We find the phase diagram of selenium hydrides is rather different from its sulfur analogy, which is indicated by the emergence of new phases and the change of relative stabilities. Three stable and metallic species with stoichiometries of HSe2, HSe and H3Se are identified above ~120 GPa and they all exhibit superconductive behaviors, of which the hydrogen-rich HSe and H3Se phases show high Tc in the range of 40-110 K. Our simulations established the high-temperature superconductive nature of selenium hydrides and provided useful route for experimental verification.