Anisotropic Migdal-Eliashberg Research Articles

Three-gap superconductivity with Tc above 80 K in hydrogenated 2D monolayer LiBC

Although the metallization of semiconductor bulk LiBC has been experimentally achieved, various flaws, including the strong lattice distortion, the uncontrollability of phase transition under pressure, usually appear. In this work, based on the first-principles calculations, we propose a new way of hydrogenation to realize metallization. Using the fully anisotropic Migdal-Eliashberg theory, we investigate the superconducting behaviors in the stable monolayers LiBCH and LiCBH, in which C and B atoms are hydrogenated, respectively. Our findings indicate that the monolayers possess the high Tc of 82.0 and 82.5 K, respectively, along with the interesting three-gap superconducting natures. The Fermi sheets showing the obvious three-region distribution characteristics and the abnormally strong electron-phonon coupling are responsible for the high-Tc three-gap superconductivity. Furthermore, the Tc can be dramatically boosted up to 120.0 K under 3.5% tensile strain. To a great extent, the high Tc is beyond the liquid nitrogen temperature (77 K), which is beneficial for the applications in future experiments. This study not only explores the superconducting properties of the monolayers LiBCH and LiCBH, but also offers practical insights into the search for high-Tc superconductors. Published by the American Physical Society 2024

Unraveling the evolution of multigap superconductivity in layered Na–B–C films: An additional energy gap induced by the internal B–C layer

Multigap superconductors provide a platform to confirm rich new physics such as time-reversal symmetry breaking, giant paramagnetic response, and hidden criticality. However, an obstacle hindering the experimental validation of these phenomena lies in the lack of superconductors with three or more gaps and critical temperatures higher than the liquid nitrogen temperature. In this work, we predicted NaB2C2 and Na2B3C3 films with high-temperature superconductivity (beyond 90 K) using the fully anisotropic Migdal-Eliashberg theory. The multigap behaviors of Na–B–C films with three and five atomic layers were analyzed in detail, revealing two typical configurations: three-gap (NaB2C2) and four-gap (Na2B3C3) superconductors. Compared with the NaB2C2 film, the additional gap observed in the Na2B3C3 film originates from the in-plane covalent state of the internal B–C layer. This research offers valuable insights into the evolution of multigap superconductivity in layered B–C films.

Efficient anisotropic Migdal-Eliashberg calculations with an intermediate representation basis and Wannier interpolation

Efficient anisotropic Migdal-Eliashberg calculations with an intermediate representation basis and Wannier interpolation

Strong electron-phonon coupling and multigap superconductivity in 2H/1T Janus MoSLi monolayer.

Two-dimensional (2D) Janus transition metal dichalcogenides MXY manifest novel physical properties owing to the breaking of out-of-plane mirror symmetry. Recently, the 2H phase of MoSH has been demonstrated to possess intrinsic superconductivity, whereas the 1T phase exhibits a charge density waves state. In this paper, we have systematically studied the stability and electron-phonon interaction characteristics of MoSLi. Our results have shown that both the 2H and 1T phases of MoSLi are stable, as indicated by the phonon spectrum and the abinitio molecular dynamics. However, the 1T phase exhibits an electron-phonon coupling constant that is twice as large as that of the 2H phase. In contrast to MoSH, the 1T phase of MoSLi exhibits intrinsic superconductivity. By employing the abinitio anisotropic Migdal-Eliashberg formalism, we have revealed the two-gap superconducting nature of 1T-MoSLi, with a transition temperature (Tc) of 14.8K. The detailed analysis indicates that the superconductivity in 1T-MoSLi primarily originates from the interplay between the vibration of the phonon modes in the low-frequency region and the dz2 orbital. These findings provide a fresh perspective on superconductivity within Janus structures.

Anomalous superconductivity in Li/F modified two-dimensional molybdenene

Anomalous superconductivity in Li/F modified two-dimensional molybdenene

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.

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.

Superconductivity at 215 K in H3SM (M=Ne, Ar, Kr, Xe, Rn) ternary hydrides

The recent discovery of H3S attracts great attention due to the confirmed superconducting critical temperature (Tc) of 203 K. Following the previous structure prediction of H3SXe superconductors, the anisotropic Migdal-Eliashberg (ME) theory is carried out to study the superconducting properties of H3SM (M=Ne, Ar, Kr, Xe, Rn) under pressure. We identify a new H3SRn ternary hydride, with Tc of about 215 K under 240 GPa, belonging to two-gap superconductors with multi-band. H3SNe exhibits remarkable superconductivity with an anomalously low stabilization pressure (Ps) of about 60 GPa. With the motivation of discovering superconductors at the lowest possible pressure, the chemical pressure is quantified based on the same volume-strain effect of physical pressure and chemical pressure. In H3SM, the larger the chemical pressure of the central atom, the larger the physical pressure required for its stabilization. Away from the phase transition, decreasing pressure is beneficial to the superconductivity of the H3SM system. These findings open new avenues for designing and optimizing new high-Tc superconductors with low-Ps.

Full-bandwidth anisotropic Migdal-Eliashberg theory and its application to superhydrides

Migdal-Eliashberg theory is one of the state-of-the-art methods for describing conventional superconductors from first principles. However, widely used implementations assume a constant density of states around the Fermi level, which hinders a proper description of materials with distinct features in its vicinity. Here, we present an implementation of the Migdal-Eliashberg theory within the EPW code that considers the full electronic structure and accommodates scattering processes beyond the Fermi surface. To significantly reduce computational costs, we introduce a non-uniform sampling scheme along the imaginary axis. We demonstrate the power of our implementation by applying it to the sodalite-like clathrates YH6 and CaH6, and to the covalently-bonded H3S and D3S. Furthermore, we investigate the effect of maximizing the density of states at the Fermi level in doped H3S and BaSiH8 within the full-bandwidth treatment compared to the constant-density-of-states approximation. Our findings highlight the importance of this advanced treatment in such complex materials.

Phase diagram and superconductivity of calcium alanates under pressure

In this paper we present a first-principles study of the high-pressure superconducting phase diagram of calcium alanates (Ca–Al–H), based on ab-initio crystal structure prediction and anisotropic Migdal–Eliashberg Theory. Calcium alanates have been intensively studied at ambient pressure for their hydrogen-storage properties, but their high-pressure behavior is largely unknown. By performing a full scan of the ternary convex hull at several pressures between 0 and 300 GPa, we identify several new structural motifs, characterized by a high Al–H coordination, where Al d orbitals participate in the bonding. Among all new phases thus identified, we focus in particular on a phase with CaAlH7 composition, which lies on the convex hull at 300 GPa, and remains dynamically stable down to 50 GPa, with a predicted superconducting T c of 82 K, which likely represents a new promising template to achieve increase chemical precompression in ternary hydrides. Our findings reveal important insights into the structure-property relationships of calcium alanates under high pressure, and highlight a possible strategy to achieve conventional superconductivity at low pressures.

Interplay of charge ordering and superconductivity in two-dimensional 2H group V transition-metal dichalcogenides

Layered $2H\text{\ensuremath{-}}T{X}_{2}$ with $T=\mathrm{Nb}$, Ta and $X=\mathrm{S}$, Se exhibit rich dimensionality effects on charge density wave (CDW) order and superconductivity, but comprehensive understanding of these correlated quantum phases in the two-dimensional limit of $2H\text{\ensuremath{-}}T{X}_{2}$ is still lacking, hindering their practical applications. Here, I calculate from first principles the phonon linewidth and bare susceptibility to study the origin of CDW formation in ${\mathrm{NbSe}}_{2}$, ${\mathrm{TaS}}_{2}$, ${\mathrm{TaSe}}_{2}$, and ${\mathrm{NbS}}_{2}$ monolayers, analyze their relative CDW strength, and evaluate electron-phonon superconductivity within the fully anisotropic Migdal-Eliashberg theory. A peaked linewidth of the longitudinal acoustic branch and no Fermi-surface nesting around ${\mathbf{q}}_{\mathrm{CDW}}$ indicate CDW instability driven by the wave-vector-dependent electron-phonon coupling. The $3\ifmmode\times\else\texttimes\fi{}3$ CDW ground state favors a distinct hollow-centered clustering of transition-metal atoms, with larger distortion amplitude in ${\mathrm{NbSe}}_{2}$ and ${\mathrm{TaSe}}_{2}$ than in ${\mathrm{TaS}}_{2}$ and ${\mathrm{NbS}}_{2}$. Superconducting results of the monolayer CDW phase prove that strong spin-orbit coupling effects are dominant in determining the critical temperature ${T}_{\mathrm{c}}$ of each system via modifying both the strength and anisotropic extent of electron-phonon interactions. I also recapitulate measured opposite thickness dependencies of ${T}_{\mathrm{c}}$ in $\mathrm{Nb}{X}_{2}$ and $\mathrm{Ta}{X}_{2}$, and show that whether superconductivity is weakened or enhanced in monolayer limit relies on specific evolution of CDW-modulated Fermi-level density of states and electron-phonon matrix elements under reduced dimensionality. This work lays the foundation for applications of $2H$ group V transition-metal dichalcogenides in versatile nanoscale quantum devices.

Enhancement for phonon-mediated superconductivity up to 37 K in few-hydrogen metal-bonded layered magnesium hydride under atmospheric pressure.

The discovery of superconductivity in layered MgB2 has renewed interest in the search for high-temperature conventional superconductors, leading to the synthesis of numerous hydrogen-dominated materials with high critical temperatures (Tc) under high pressures. However, achieving a high-Tc superconductor under ambient pressure remains a challenging goal. In this study, we propose a novel approach to realize a high-temperature superconductor under ambient pressure by introducing a hexagonal H monolayer into the hexagonal close-packed magnesium lattice, resulting in a new and stable few-hydrogen metal-bonded layered magnesium hydride (Mg4)2H1. This compound exhibits superior ductility compared to multi-hydrogen, cuprate, and iron-based superconductors due to its metallic bonding. Our unconventional strategy diverges from the conventional design principles used in hydrogen-dominated covalent high-temperature superconductors. Using anisotropic Migdal-Eliashberg equations, we demonstrate that the stable (Mg4)2H1 compound is a typical phonon-mediated superconductor, characterized by strong electron-phonon coupling and an excellent Tc of 37 K under ambient conditions, comparable to that of MgB2. Our findings not only present a new pathway for exploring high-temperature superconductors but also provide valuable insights for future experimental synthesis endeavors.

Ternary superconducting hydrides stabilized via Th and Ce elements at mild pressures

The discovery of covalent H3S and clathrate structure LaH10 with excellent superconducting critical temperatures at high pressures has facilitated a multitude of research on compressed hydrides. However, their superconducting pressures are too high (generally above 150 GPa), thereby hindering their application. In addition, making room-temperature superconductivity close to ambient pressure in hydrogen-based superconductors is challenging. In this work, we calculated the chemically “pre-compressed” Be-H by heavy metals Th and Ce to stabilize the superconducting phase near ambient pressure. An unprecedented ThBeH8 (CeBeH8) with a “fluorite-type” structure was predicted to be thermodynamically stable above 69 GPa (76 GPa), yielding a Tc of 113 K (28 K) decompressed to 7 GPa (13 GPa) by solving the anisotropic Migdal–Eliashberg equations. Be-H vibrations play a vital role in electron–phonon coupling and structural stability of these ternary hydrides. Our results will guide further experiments toward synthesizing ternary hydride superconductors at mild pressures.

Phonon mediated superconductivity in field-effect doped molybdenum dichalcogenides

Superconductivity occurs in electrochemically doped molybdenum dichalcogenides samples thicker than four layers. While the critical temperature (T c ) strongly depends on the field effect geometry (single or double gate) and on the sample (MoS2 or MoSe2), T c always saturates at high doping. The pairing mechanism and the complicated dependence of T c on doping, samples and field-effect geometry are currently not understood. Previous theoretical works assumed homogeneous doping of a single layer and attributed the T c saturation to a charge density wave instability, however the calculated values of the electron–phonon coupling in the harmonic approximation were one order of magnitude larger than the experimental estimates based on transport data. Here, by performing fully relativistic first principles calculations accounting for the sample thickness, the field-effect geometry and anharmonicity, we rule out the occurrence of charge density waves in the experimental doping range and demonstrate a suppression of one order of magnitude in the electron–phonon coupling, now in excellent agreement with transport data. By solving the anisotropic Migdal-Eliashberg equations, we explain the behavior of T c in different systems and geometries. As our first principles calculations show an ever increasing T c as a function of doping, we suggest that extrinsic mechanisms may be responsible for the experimentally observed saturating trend.

Superconductivity and topological aspects of two-dimensional transition-metal monohalides

Two-dimensional (2D) superconducting states have attracted much recent interest, especially when they coexist with nontrivial band topology which affords a promising approach towards Majorana fermions. Using first-principles calculations, we predict van der Waals monolayered transition-metal monohalides MX (M = Zr, Mo; X = F, Cl) as a class of 2D superconductors with remarkable transition temperature (5.9–12.4 K). Anisotropic Migdal-Eliashberg theory reveals that ZrCl have a single superconducting gap ∆ ~ 2.14 meV, while MoCl is a two-gap superconductor with ∆ ~ 1.96 and 1.37 meV. The Z2 band topology of 2D MX is further demonstrated that MoF and MoCl are candidates for realizing topological superconductivity. Moreover, the Dirac phonons of ZrCl and MoCl contribute w-shape phononic edge states, which are potential for an edge-enhanced electron-phonon coupling. These findings demonstrate that 2D MX offers an attractive platform for exploring the interplay between superconductivity, nontrivial electronic and phononic topology.

Ab initio study of Li-Mg-B superconductors

LiB, a predicted layered compound analogous to the ${\mathrm{MgB}}_{2}$ superconductor, has been recently synthesized via cold compression and quenched to ambient pressure, yet its superconducting properties have not been measured. According to prior isotropic superconductivity calculations, the critical temperature (${T}_{\mathrm{c}}$) was expected to be only 10--15 K. Using the anisotropic Migdal-Eliashberg formalism, we show that the ${T}_{\mathrm{c}}$ may actually exceed 32 K. Our analysis of the contribution from different electronic states helps explain the detrimental effect of pressure and doping on the compound's superconducting properties. In the search for related superconductors, we screened Li-Mg-B binary and ternary layered materials and found metastable phases with ${T}_{\mathrm{c}}$ close to or even 10--20% above the record 39 K value in ${\mathrm{MgB}}_{2}$. Our reexamination of the Li-B binary phase stability reveals a possible route to synthesize the LiB superconductor at lower pressures readily achievable in multianvil cells.

Superconducting Gap of Pressure Stabilized (Al0.5Zr0.5)H3 from Ab Initio Anisotropic Migdal-Eliashberg Theory.

Motivated by Matthias’ sixth rule for finding new superconducting materials in a cubic symmetry, we report the cluster expansion calculations, based on the density functional theory, of the superconducting properties of Al0.5Zr0.5H3. The Al0.5Zr0.5H3 structure is thermodynamically and dynamically stable up to at least 200 GPa. The structural properties suggest that the Al0.5Zr0.5H3 structure is a metallic. We calculate a superconducting transition temperature using the Allen–Dynes modified McMillan equation and anisotropic Migdal–Eliashberg equation. As result of this, the anisotropic Migdal–Eliashberg equation demonstrated that it exhibits superconductivity under high pressure with relatively high-Tc of 55.3 K at a pressure of 100 GPa among a family of simple cubic structures. Therefore, these findings suggest that superconductivity could be observed experimentally in Al0.5Zr0.5H3.

In-silico synthesis of lowest-pressure high-Tc ternary superhydrides

We report the theoretical prediction of two high-performing hydride superconductors BaSiH8 and SrSiH8. They are thermodynamically stable above pressures of 130 and 174 GPa, respectively, and metastable below that. Employing anharmonic phonon calculations, we determine the minimum pressures of dynamical stability to be around 3 GPa for BaSiH8 and 27 GPa for SrSiH8, and using the fully anisotropic Migdal-Eliashberg theory, we predict Tc’s around 71 and 126 K, respectively. We also introduce a method to estimate the lowest pressure of synthesis, based on the calculation of the enthalpy barriers protecting the BaSiH8Fmbar{3}m structure from decomposition at various pressures. This kinetic pressure threshold is sensibly higher than the one based on dynamic stability, but gives a much more rigorous limit for synthesizability.

Intrinsic and doping-enhanced superconductivity in monolayer 1H−TaS2 : Critical role of charge ordering and spin-orbit coupling

The interplay of superconductivity with charge density wave (CDW) in metallic transition-metal dichalcogenides has been widely debated, and viable strategies manipulating these quantum states in the two-dimensional (2D) limit remain unclear. Using the ab initio anisotropic Migdal-Eliashberg theory, we successfully explain the superconductivity observed in monolayer $1H\text{\ensuremath{-}}{\mathrm{TaS}}_{2}$ by simultaneously determining its precise CDW structure and treating the marked modification of electron-phonon interaction and critical temperature ${T}_{\mathrm{c}}$ by spin-orbit coupling effects. With this paradigm, we further show that electron doping weakens the CDW order leading to increased ${T}_{\mathrm{c}}$ up to 11 K, along with a single-gap to two-gap superconductivity transition due to the suppression of the CDW gap. By contrast, a low hole doping barely affects the CDW but still yields a significantly enhanced superconducting order, implying their good coexistence. Combined with the synergistic behavior of CDW and superconductivity, which cooperate upon ${\mathrm{TaS}}_{2}$ thickness reduction causing an unusual rise of ${T}_{\mathrm{c}}$, our results unravel diversified interactions between the two collective orders in ultrathin ${\mathrm{TaS}}_{2}$, being competition, coexistence or cooperation depending on external stimuli, which provide key clues for controlling correlated states in devices based on 2D CDW superconductors.

Three-gap superconductivity in two-dimensional InB2/InB4 films

In recent years, multigap superconductors have attracted much attention since the discovery of novel two-gap superconductivity with transition temperature ${T}_{c}\ensuremath{\sim}39\phantom{\rule{4pt}{0ex}}\text{K}$ in bulk ${\mathrm{MgB}}_{2}$. Based on the first-principles calculation and anisotropic Migdal-Eliashberg theory, we conduct a study on a series of two-dimensional (2D) boron-based materials with doped metal atoms to search for multigap superconductors. We find that ${\mathrm{InB}}_{2}$ monolayer films and ${\mathrm{InB}}_{4}$ trilayer films are dynamically stable but not synthesized experimentally yet. An evident three-gap superconductor with high ${T}_{c}\ensuremath{\sim}$ 41.5 K is obtained in a ${\mathrm{InB}}_{2}$ monolayer film. Similarly, ${\mathrm{InB}}_{4}$ trilayer film is a novel superconductor with three distinct superconducting gaps and a high ${T}_{c}\ensuremath{\sim}$ 53 K. The superconductivity in both 2D films originates mainly from the covalent-state-driven metallization. In addition, the effect of biaxial strain on the superconducting behavior of $\mathrm{In}{\text{B}}_{4}$ trilayer films is also involved. The ${\mathrm{InB}}_{4}$ trilayer films stay dynamically stable under biaxial tensile strain of $\ensuremath{-}3%--6%$, and the highest ${T}_{c}$ boosts to 64 K under the biaxial tensile strain of $\ensuremath{\sim}4%$. Meanwhile, we also find that the ${\mathrm{GeB}}_{4}$ and ${\mathrm{ZnB}}_{4}$ trilayer films are two-gap superconductors with high ${T}_{c}\ensuremath{\sim}$ 48.5 and 32 K, respectively.