Phonon-mediated Superconductivity Research Articles

Van Hove singularity, flat band, and phonon-mediated superconductivity in topological perovskite carbides

Van Hove singularity, flat band, and phonon-mediated superconductivity in topological perovskite carbides

Superconductivity in CaH6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_{6}$$\\end{document} and ThH10\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_{10}$$\\end{document} through fully ab initio Eliashberg method and self-consistent Green’s function

Pressurized hydrogen-based superconductors are phonon-mediated superconductors that exhibit high phonon frequencies. In these superconductors, in addition to the density of states (DOS) at the Fermi energy (EF\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$E_F$$\\end{document}), the energy dependence of the DOS around EF\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$E_F$$\\end{document} becomes important for evaluating their transition temperature (Tc\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_c$$\\end{document}). Systems with peak structures in the DOS around EF\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$E_F$$\\end{document}, such as Im3¯m\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Im\\bar{3}m$$\\end{document} H3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_{3}$$\\end{document}S and Fm3¯m\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Fm\\bar{3}m$$\\end{document} LaH10\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_{10}$$\\end{document}, highlight this point. We use the fully ab initio Eliashberg method to investigate this phenomenon in Im3¯m\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Im\\bar{3}m$$\\end{document} CaH6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_{6}$$\\end{document} and Fm3¯m\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Fm\\bar{3}m$$\\end{document} ThH10\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_{10}$$\\end{document} with a dip structure in their DOS around EF\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$E_F$$\\end{document}. Our calculated Tc\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_c$$\\end{document} values (225–235 K for CaH6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_{6}$$\\end{document} at 200 GPa and 156–158 K for ThH10\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_{10}$$\\end{document} at 170 GPa) are quantitatively consistent with the experimental results. Remarkably, our results from the self-consistent treatment of the electron Green’s function contrasts with those cases with a peak structure in the DOS. This finding unifies the understanding of how DOS structures influence the evaluation of Tc\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_c$$\\end{document}.

Phonon-mediated unconventional superconductivity in rhombohedral stacked multilayer graphene

Understanding the origin of superconductivity in correlated two-dimensional materials is a key step in leveraging material engineering techniques for next-generation nanoscale devices. While it is widely accepted that phonons fluctuations only mediate conventional (s-wave) superconductivity, the common phenomenology of superconductivity in Bernal bilayer and rhombohedral trilayer graphene, as well as in a large family of graphene-based moiré systems, suggests a common superconducting mechanism across these platforms. In particular, in all these platforms some superconducting regions violate the Pauli limit, indicating unconventional superconductivity, naively ruling out conventional phonon-mediated pairing as the underlying mechanism. Here we combine first principles simulations with effective low-energy theories to investigate the superconducting mechanism and pairing symmetry in rhombohedral stacked graphene multilayers. We find that phonon-mediated superconductivity explains the main experimental findings, namely the displacement field and doping level dependence of the critical temperature, and the presence of two superconducting regions with different pairing symmetries that depend on the parent normal state. In particular, we find that intra-valley phonon scattering favors a triplet f-wave pairing when combined with electronic correlations stabilizing a spin- and valley-polarized normal state. We also propose a so far unexplored superconducting region at higher hole doping densities nh ≈ 4 × 1012 cm−2, and demonstrate how this highly hole-doped regime can be reached in heterostructures consisting of monolayer α-RuCl3 and rhombohedral trilayer graphene. Our findings promote phonon-mediated pairing as a strong contender to explain superconductivity across a wide range of graphene platforms, and demonstrate that phonons can, in fact, stabilize unconventional superconducting orders.

Superconductivity in monolayer Janus titanium-sulfur hydride (TiSH) at ambient pressure

Janus two dimensional (2D) materials are new and novel materials. As they break out-of-plane symmetry, they possess several fascinating properties which can be applied in catalytic reactions and opto-electronics. Recent synthesis of MoSH and the prediction of phonon-mediated superconductivity have opened a new way to investigate the properties of hydrogenated Janus materials (Novoselov et al 2004 Science 306 666–9; Mehta et al 2023 Solid State Commun. 375 115347; Naik et al 2023 Comput. Theor. Chem. 1228 114278). In this work, we performed the density functional theory calculations to demonstrate that titanium sulfur hydride (TiSH) is dynamically stable and becomes phonon-mediated superconductor with the superconducting critical temperature, Tc = 9.24 K with the corresponding value of electron–phonon coupling constant, λ = 0.71, in the weak interaction limits, under ambient conditions. Eliashberg spectral function α2F(ω) was well converged for dense grid of q1 × q2 × q3 = 12 × 12 × 1 and nk1 × nk2 × nk3 = 140 × 140 × 1. The effect of smearing broadening was also considered for determining well converged value of Tc and λ. Figure (b) shows that after smearing broadening of 0.02 Ry, λ shows convergent values, and subsequent changes are as low as less that 5% of the peak value. Overall, our findings predicted a new member in the 2D Janus hydride family with possible applications in 2D nanomaterials and superconducting devices applications.

Preempted phonon-mediated superconductivity in the infinite-layer nickelates

Preempted phonon-mediated superconductivity in the infinite-layer nickelates

Feasible Route to High-Temperature Ambient-Pressure Hydride Superconductivity.

A key challenge in materials discovery is to find high-temperature superconductors. Hydrogen and hydride materials have long been considered promising materials displaying conventional phonon-mediated superconductivity. However, the high pressures required to stabilize these materials have restricted their application. Here, we present results from high-throughput computation, considering a wide range of high-symmetry ternary hydrides from across the periodic table at ambient pressure. This large composition space is then reduced by considering thermodynamic, dynamic, and magnetic stability before direct estimations of the superconducting critical temperature. This approach has revealed a metastable ambient-pressure hydride superconductor, Mg_{2}IrH_{6}, with a predicted critical temperature of 160K, comparable to the highest temperature superconducting cuprates. We propose a synthesis route via a structurally related insulator, Mg_{2}IrH_{7}, which is thermodynamically stable above 15GPa, and discuss the potential challenges in doing so.

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.

Superconductivity induced by ionized σ-bond at 10 GPa

Discovering high-temperature superconductors under low pressures and elucidating the underlying critical factors governing superconductivity are central issues in condensed matter physics. Here, we developed a strategy for the metallization of σ-bonds through incorporating NH3-units into the filled f-shell Lu-lattice and obtained a Luδ+(NH3)4σ− hydride to investigate the potential high-temperature superconductivity. Based on the density-functional theory calculations, our proposed I-43m-Luδ+(NH3)4σ− phase exhibits a Tc of 33.44 K at 10 GPa. Further analyses unveil that the Tc is attributed to strong electron-phonon coupling (EPC), which originated from the electron-phonon matrix element primarily driven by H–N–H bending and twisting vibrations, and Fermi surface nesting induced softening of optical phonons to scatter itinerant electrons on phonon-coupling bands to form Cooper pairs. Importantly, the emergence of phonon-coupling bands is mainly dependent on the ionization of sp3-hybridized σ-bonds within NH3, resulting in the manifestation of metallicity. Due to the enhanced ionization of σ-bands and strengthened interatomic coupling effect with pressurization, the Tc is further enhanced to 130 K. Our study offers novel insights towards the realization of phonon-mediated high-temperature superconductivity at comparatively low-pressures and highlights the potential for achieving high-Tc in filled f-shell metal hydrides through strategic engineering of metallized σ-bonds.

Van Hove singularity driven enhancement of superconductivity in two-dimensional tungsten monofluoride (WF)

Superconductivity in two-dimensional materials has gained significant attention in the last few years. In this work, we report phonon-mediated superconductivity investigations in monolayer Tungsten monofluoride (WF) by solving anisotropic Migdal Eliashberg equations as implemented in EPW. By employing first-principles calculations, our examination of phonon dispersion spectra suggests that WF is dynamically stable. Our results show that WF has weak electron–phonon coupling (EPC) strength (λ) of 0.49 with superconducting transition temperature (T c ) of 2.6 K. A saddle point is observed at 0.11 eV below the Fermi level (E F ) of WF, which corresponds to the Van Hove singularity (VHS). On shifting the Fermi level to the VHS by hole doping (3.7 × 1014 cm−2), the EPC strength increases to 0.93, which leads to an increase in the T c to 11 K. However, the superconducting transition temperature of both pristine and doped WF increases to approximately 7.2 K and 17.2 K, respectively, by applying the Full Bandwidth (FBW) anisotropic Migdal–Eliashberg equations. Our results provide a platform for the experimental realization of superconductivity in WF and enhancement of the superconducting transition temperature by adjusting the position of E F to the VHS.

Build Borophite from Borophenes: A Boron Analogue Graphite.

Unlike graphene derived from graphite, borophenes represent a distinct class of synthetic two-dimensional materials devoid of analogous bulk-layered allotropes, leading to covalent bonding within borophenes instead of van der Waals (vdW) stacking. Our investigation focuses on 665 vdW-stacking boron bilayers to uncover potential bulk-layered boron allotropes through vdW stacking. Systematic high-throughput screening and stability analysis reveal a prevailing inclination toward covalently bonded layers in the majority of boron bilayers. However, an intriguing outlier emerges in δ5 borophene, demonstrating potential as a vdW-stacking candidate. We delve into electronic and topological structural similarities between δ5 borophene and graphene, shedding light on the structural integrity and stability of vdW-stacked boron structures across bilayers, multilayers, and bulk-layered allotropes. The δ5 borophene analogues exhibit metallic properties and characteristics of phonon-mediated superconductors, boasting a critical temperature near 22 K. This study paves the way for the concept of "borophite", a long-awaited boron analogue of graphite.

Hydrogenation-induced superconductivity in monolayer

Here, we construct a new two-dimensional hydrogenated transition metal dichalcogenide material, the Janus WSH monolayer, which is created by replacing the top-layer S atoms in the 2H-WS2 monolayer with H atoms. Then we use first-principles calculations to investigate its electronic structure, phonon dispersion, and superconductivity. The results show that hydrogenation breaks the reflection symmetry, which helps orbital hybridization and to flatten the electronic bands. Thus, it leads to a high electronic density of states near the Fermi level. Additionally, the electron-phonon coupling is enhanced by the softening of phonon modes from the in-plane vibrations of W. The strong interactions between electrons and phonons result in phonon-mediated superconductivity in Janus WSH monolayer. The calculated critical temperature (T c ) is approximately 23.1 K at atmospheric pressure. This T c is about twice higher than that of existing WS2-based materials.

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 highest Tc achieved experimentally at ambient pressure under the Bardeen, Cooper, and Schrieffer framework. The high Tc can 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.

Strain-tunable Dirac semimetal phase transition and emergent superconductivity in a borophane

A two-dimensional (2D) Dirac semimetal with concomitant superconductivity has been long sought but rarely reported. It is believed that light-element materials have the potential to realize this goal owing to their intrinsic lightweight and metallicity. Here, based on the recently synthesized β12 hydrogenated borophene, we investigate its counterpart named β12-B5H3. Our first-principles calculations suggest it has good stability. β12-B5H3 is a scarce Dirac semimetal demonstrating a strain-tunable phase transition from three Dirac cones to a single Dirac cone. Additionally, β12-B5H3 is also a superior phonon-mediated superconductor with a superconducting critical temperature of 32.4 K and can be further boosted to 42 K under external strain. The concurrence of Dirac fermions and superconductivity, supplemented with dual tunabilities, reveals β12-B5H3 is an attractive platform to study either quantum phase transition in 2D Dirac semimetal or the superconductivity or the exotic physics brought about by their interplay.

Coexistence of topological node surface and Dirac fermions in phonon-mediated superconductor YB2C2.

The interaction between nontrivial topology and superconductivity in condensed matter physics has attracted tremendous research interest as it could give rise to exotic phenomena. Herein, based on first-principles calculations, we investigate the electronic structures, mechanical properties, topological properties, dynamic stability, electron-phonon coupling (EPC), and superconducting properties of the synthesized real material YB2C2. It is a tetragonal structure with P4/mbm symmetry and exhibits excellent stability. The calculated electronic band structures reveal that a zero-dimension (0D) Dirac point and two-dimensional (2D) nodal surface coexist near the Fermi level. A spin-orbit coupling (SOC) Dirac point with the topological Fermi arc is observed on the (001) surface. These nodal surfaces are protected by a two-fold screw axis and time-reversal symmetry. Based on the Bardeen-Cooper-Schrieffer theory, the superconducting transition temperature (Tc) in the range 1.25-4.45 K with different Coulomb repulsion constant μ* for YB2C2 is estimated to be consistent with previous experimental results. In addition, the EPC is mainly from the coupling between the dx2-y2 and dz2 orbitals of the Y atom and low-energy phonon modes. The presence of superconductivity and nontrivial topological surface state in YB2C2 suggests that it may be a candidate material for topological superconductors.

Hardness and superconductivity in tetragonal LiB4 and NaB4.

Boron-based compounds have triggered substantial attention due to their multifunctional properties, incorporating excellent hardness and superconductivity. While tetragonal metal borides LiB4 and NaB4 with BaAl4-type structure and striking clathrate boron motif have been induced under compression, there is still a lack of deep understanding of their potential properties at ambient pressure. We herein conduct a comprehensive study on I4/mmm-structured LiB4 and NaB4 under ambient pressure via first-principles calculations. Remarkably, both LiB4 and NaB4 are found to possess high Vickers hardness of 39GPa, which is ascribed to the robust boron framework with strong covalency. Furthermore, their high hardness values together with distinguished stability make them highly potential superhard materials. Meanwhile, electron-phonon coupling analysis reveals that both LiB4 and NaB4 are conventional phonon-mediated superconductors, with critical temperatures of 6 and 8K at 1 atmosphere pressure (atm), respectively, mainly arising from the coupling of B 2p electronic states and the low-frequency phonon modes associated with Li-, Na-, and B-derived vibrations. This work provides valuable insights into the mechanical and superconducting behaviors of metal borides and will boost further studies of emergent borides with multiple functionalities.

Superconducting two-dimensional penta materials

Successful experimental synthesis and theoretical prediction of two-dimensional (2D) penta materials with various properties have enriched the family of 2D materials. In this work, based on first-principles calculations, we systematically study the electronic structures, phonon dispersions, and electron-phonon coupling (EPC) of four metallic penta materials ‘XY2’ (NC2, PC2, BN2, and BP2). Three of them display weak phonon-mediated superconductivity with different low superconducting transition temperatures (Tc). The highest Tc among them is 12 K for BP2. Through applying biaxial tensile strain, the λ and Tc of PC2 (BN2) can be enhanced up to 1.64 (2.68) and 49.77 (52.29) K, respectively. By solving the anisotropic Eliashberg equations, single-gap superconducting nature is predicted for PC2 and BN2. The high sensitive of superconductivity in these systems clearly demonstrate that they are potential candidates for applications in using as superconducting nanodevices. Our work will stimulate further searching of high-Tc superconductivity in low-dimensional materials.

Phonon-mediated superconductivity in {text{Mg}}_{{1 - x}} {text{Mo}}_{x} {text{B}}_{2} compounds: a crystal prediction via cluster expansion and particle-swarm optimization

Investigating superconductivity represents one of the most significant phenomena in the field of condensed matter physics. Our simulations aim to elucidate the structures in the metallic state of Mg1−xMoxB2, which is essential for predicting their superconducting properties. By employing a first-principle cluster expansion and particle-swarm optimization, we have predicted the structures of Mg1−xMoxB2 ternary alloys, including Mg0.667Mo0.333B2, Mg0.5Mo0.5B2, and Mg0.333Mo0.667B2, and have determined their thermodynamically stable configurations under both atmospheric and high-pressure conditions. To investigate the potential for superconductivity in these structures, we have conducted a detailed examination of electronic properties that are pertinent to determining the superconducting state. Regarding superconducting properties, Mg0.333Mo0.667B2 exhibits superconductivity with a critical temperature (Tc) of 7.4 K at ambient pressure. These findings suggest that the theoretically predicted structures in Mg/Mo-substituted metal borides could play a significant role in synthesis and offer valuable insights into superconducting materials.

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 (Zhou et al 2021 Science 373 801). Here, the 2D monolayer freestanding Mo4/3B2 is evidenced to be thermodynamically stable. Through electronic structure, phonon spectrum and EPC, monolayer Mo4/3B2 is 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, the Tc of monolayer Mo4/3B2 can 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 W4/3B2 is also a superconductor with the Tc of 2.37 K. Our research results enrich the database of 2D monolayer superconductors and boron-related formed materials science.

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.

Theoretical study of phonon-mediated superconductivity beyond Migdal-Eliashberg approximation and Coulomb pseudopotential

Theoretical study of phonon-mediated superconductivity beyond Migdal-Eliashberg approximation and Coulomb pseudopotential