Phonon-mediated Superconductivity Research Articles

Discovery of PdHx compounds using genetic algorithms and first-principles calculations

Abstract In the present work, the variable-composition crystal structure prediction algorithm USPEX was combined with first-principles calculations to systematically explore stable PdHxcompounds in the pressure range from 0 to 100 GPa. The predicted structures are PdH, Pd4H5, Pd2H, and PdH4, of which PdH has previously been synthesized. The electronic structures show that these compounds can be metallic, with Pd states dominating at the Fermi level. However, the hydrogen atoms do not play a main role in the electronic properties; their vibrations do contribute to the electron-phonon coupling. The predicted Pd4H5has a superconducting transition temperature of ~13 K, which is higher than that of PdH (~8 K in the experiment). Additionally, PdH , Pd4H5, Pd2H, and PdH4can be classified as phonon-mediated superconductors, falling into the lowcoupling regime. Our results demonstrate that as the hydrogen concentration is increased in PdHx compounds, the superconducting transition temperature rises due to hydrogen vibrations, which is consistent with the experiment. Hence, the present study paves the way for discovering new PdHx compounds with promising superconducting transition temperatures.

Chemically tuning stability and superconductivity of Pd–H compounds: A routine to high temperature superconductivity under modest pressures

Motivated by searching room-temperature superconductors that could be realized near ambient conditions, palladium hydrides were chosen as the research subject considering that they can stably exist under ambient conditions, and Li as an electron donor for its outstanding performance in chemically tuning stability. A novel cubic phase structure of Li2PdH6 with a remarkably high estimated Tc of ∼165 K at 90 GPa was found using particle swarm optimization algorithm calculations. The superconducting behavior persists down to 10 GPa with a high Tc of 106.382 K. Even though the parent binary Pd–H system is not a good superconductor, the introduction of extra electrons breaks up the H2 molecules, inducing the increase of atomic hydrogen compared with parent hydride, which is necessary for outstanding superconducting behavior. The existence of relatively soft phonons associated with the H atoms in phonon dispersion curves is responsible for its high-Tc. Our results indicated that the doping of Li to binary hydrides, especially to binary hydrides with low-Tc that exist under ambient pressure, can produce robust phonon-mediated superconductivity. This may be a strategy to design and optimize room-temperature superconductors that can be synthesized under modest pressure. The findings may pave the way for realizing new high-Tc superconductors in experiments under lower pressure than recently documented superconducting hydrides.

High Temperature Phonon-Mediated Superconductivity with T c above 100 K in monolayer Na(BC)2 and K(BC)2

Abstract Two-dimensional (2D) materials have demonstrated promising prospects owing to their distinctive electronic properties and exceptional mechanical properties. Among them, 2D superconductors with T c above the boiling point of liquid nitrogen (77 K) will exhibit tremendous applicable value in the future. Here, we design two 2D superconductors Na(BC)2 and K(BC)2 with MgB2-like structure, which are theoretically predicted to host T c as high as 99 and 102 K, respectively. The origin of such high T c is ascribed to the presence of two σ-bonding bands and van Hove singularity at the Fermi level. Furthermore, the T c of Na(BC)2 is boosted up to 153 K with a biaxial strain of 5%, which set a new record among 2D superconductors. The predictions of Na(BC)2 and K(BC)2 open the door to explore 2D high temperature superconductors and provide a potential future for developing new applications in 2D materials.

Enhanced Superconductivity of Hydrogenated β12 Borophene.

Borophene stands out among elemental two-dimensional materials due to its extraordinary physical properties, including structural polymorphism, strong anisotropy, metallicity, and the potential for phonon-mediated superconductivity. However, confirming superconductivity in borophene experimentally has been evasive to date, mainly due to the detrimental effects of metallic substrates and its susceptibility to oxidation. In this study, we present an ab initio analysis of superconductivity in the experimentally synthesized hydrogenated β12 borophene, which has been proven to be less prone to oxidation. Our findings demonstrate that hydrogenation significantly enhances both the stability and superconducting properties of β12 borophene. Furthermore, we reveal that tensile strain and hole doping, achievable through various experimental methods, significantly enhance the critical temperature, reaching up to 29 K. These findings not only promote further fundamental research on superconducting borophene and its heterostructures, but also position hydrogenated borophene as a versatile platform for low-dimensional superconducting electronics.

Two-Gap Superconductivity and the Decisive Role of Rare-Earth d Electrons in Infinite-Layer Nickelates.

We present a theoretical prediction of a phonon-mediated two-gap superconductivity in infinite-layer nickelates Nd_{1-x}Sr_{x}NiO_{2} by performing abinitio GW and GW perturbation theory calculations. Electron GW self-energy effects significantly alter the characters of the two-band Fermi surface and enhance the electron-phonon coupling, compared with results based on density functional theory. Solutions of the fully k-dependent anisotropic Eliashberg equations yield two dominant s-wave superconducting gaps-a large gap on a band of rare-earth Nd d and interstitial orbital characters and a small gap on a band of transition-metal Ni d character. Increasing hole doping induces a non-rigid-band response in the electronic structure, leading to a rapid drop of the superconducting T_{c} in the overdoped regime in agreement with experiments.

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

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Pressurized hydrogen-based superconductors are phonon-mediated superconductors that exhibit high phonon frequencies. 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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.