Computational electron-phonon superconductivity: from theoretical physics to material science.

The search for room-temperature superconductors is a major challenge in modern physics. The discovery of copper-oxide superconductors in 1986 brought hope but also revealed complex mechanisms that are difficult to analyze and compute. In contrast, the traditional electron-phonon coupling (EPC) mechanism facilitated the practical realization of superconductivity in metallic hydrogen. Since 2015, the discovery of new hydrogen compounds has shown that EPC can enable room-temperature superconductivity under high pressures, driving extensive research. Advances in computational capabilities, especially exascale computing, now allow for the exploration of millions of materials. This paper reviews newly predicted superconducting systems in 2023-2024, focusing on hydrides, boron-carbon systems, and compounds with nitrogen, carbon, and pure metals. Although many computationally predicted high-Tc superconductors were not experimentally confirmed, some low-temperature superconductors were successfully synthesized. This paper provides a review of these developments and future research directions.

When van der Waals Met Kagome: A 2D Antimonide with a Vanadium-Kagome Network.

2D materials showcase unconventional properties emerging from quantum confinement effects. In this work, a "soft chemical" route allows for the deintercalation of K+ from the layered antimonide KV6Sb6, resulting in the discovery of a new metastable 2D-Kagome antimonide K0.1(1)V6Sb6 with a van der Waals gap of 3.2 Å. The structure of K0.1(1)V6Sb6 was determined via the synergistic techniques, including X-ray pair distribution function analysis, advanced transmission electron microscopy, and density functional theory calculations. The K0.1(1)V6Sb6 compound crystallizes in the monoclinic space group C2/m (a = 9.57(2) Å, b = 5.502(8) Å, c = 10.23(2) Å, ß = 97.6(2)°, Z = 2). The [V6Sb6] layers in K0.1(1)V6Sb6 are retained upon deintercalation and closely resemble the layers in the parent compound, yet deintercalation results in a relative shift of the adjacent [V6Sb6] layers. The magnetic properties of the K0.1(1)V6Sb6 phase in the 2-300 K range are comparable to those of KV6Sb6 and another Kagome antimonide KV3Sb5, consistent with nearly temperature-independent paramagnetism. Electronic band structure calculation suggests a nontrivial band topology with flat bands and opening of band crossing afforded by deintercalation. Transport property measurements reveal a metallic nature for K0.1(1)V6Sb6 and a low thermal conductivity of 0.6 W K-1 m-1 at 300 K. Additionally, ion exchange in KV6Sb6 via a solvothermal route leads to a successful partial exchange of K+ with A+ (A = Na, Rb, and Cs). This study highlights the tunability of the layered structure of the KV6Sb6 compound, providing a rich playground for the realization of new 2D materials.

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.

High-Throughput Screening for Boride Superconductors.

A high-throughput screening using density functional calculations is performed to search for stable boride superconductors from the existing materials database. The workflow employs the fast frozen-phonon method as the descriptor to evaluate the superconducting properties quickly. Twenty-three stable candidates were identified during the screening. The superconductivity was obtained earlier experimentally or computationally for almost all found binary compounds. Previous studies on ternary borides are very limited. Our extensive search among ternary systems confirmed superconductivity in known systems and found several new compounds. Among these discovered superconducting ternary borides, TaMo2B2 shows the highest superconducting temperature of ∼12 K. Most predicted compounds were synthesized previously; therefore, our predictions can be examined experimentally. Our work also demonstrates that the boride systems can have diverse structural motifs that lead to superconductivity.

Structure, bonding and electronic characteristics of amorphous Se.

Ovonic threshold switching (OTS) selectors can effectively improve the storage density and suppress the leakage current of advanced phase-change memory devices. As a prototypical OTS material, amorphous GeSe is widely investigated. But the attention paid to amorphous Se (i.e., the functional constituent in amorphous GeSe) has been very limited up to now. Here we have explored the structure, bonding and electronic characteristics of amorphous Se using ab initio molecular dynamics simulations. The results reveal that the Se atoms in amorphous Se tend to form 2-coordinated configurations, and they connect with each other to form long chains. The fraction of the vibrational density of state located in the high frequency range is relatively large, and the formation energy of the Se-Se bond is as large as 4.44 eV, hinting that the Se-Se bonds in chains possess high stability. In addition, the mid-gap state related to the OTS behavior is also found in amorphous Se despite the small proportion. Our findings enrich the knowledge of amorphous Se, which aids the applications of Se-based OTS selectors.

Unveiling the effect of Ni on the formation and structure of Earth's inner core.

Ni is the second most abundant element in the Earth's core. Yet, its effects on the inner core's structure and formation process are usually disregarded because of its electronic and size similarity with Fe. Using ab initio molecular dynamics simulations, we find that the bcc phase can spontaneously crystallize in liquid Ni at temperatures above Fe's melting point at inner core pressures. The melting temperature of Ni is shown to be 700 to 800 K higher than that of Fe at 323 to 360 GPa. hcp, bcc, and liquid phase relations differ for Fe and Ni. Ni can be a bcc stabilizer for Fe at high temperatures and inner core pressures. A small amount of Ni can accelerate Fe's crystallization at core pressures. These results suggest that Ni may substantially impact the structure and formation process of the solid inner core.

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.

Ground and excited states of even-numbered Hubbard ring at half-filling: comparison of the extended Gutzwiller approach with exact diagonalization.

It remains a great challenge in condensed matter physics to develop a method to treat strongly correlated many-body systems with balanced accuracy and efficiency. We introduce an extended Gutzwiller (EG) method incorporating a manifold technique, which builds an effective manifold of the many-body Hilbert space, to describe the ground-state (GS) and excited-state (ES) properties of strongly correlated electrons. We systematically apply an EG projector onto the GS and ES of a non-interacting system. Diagonalization of the true Hamiltonian within the manifold formed by the resulting EG wavefunctions gives the approximate GS and ES of the correlated system. To validate this technique, we implement it on even-numbered fermionic Hubbard rings at half-filling with periodic boundary conditions, and compare the results with the exact diagonalization (ED) method. The EG method is capable of generating high-quality GS and low-lying ES wavefunctions, as evidenced by the high overlaps of wavefunctions between the EG and ED methods. Favorable comparisons are also achieved for other quantities including the total energy, the double occupancy, the total spin and the staggered magnetization. With the capability of accessing the ESs, the EG method can capture the essential features of the one-electron removal spectral function that contains contributions from states deep in the excited spectrum. Finally, we provide an outlook on the application of this method on large extended systems.

High-Throughput Screening of Strong Electron-Phonon Couplings in Ternary Metal Diborides.

We perform a high-throughput screening on phonon-mediated superconductivity in a ternary metal diboride structure with alkali, alkaline earth, and transition metals. We find 17 ground states and 78 low-energy metastable phases. From fast calculations of zone-center electron-phonon coupling, 43 compounds are revealed to show electron-phonon coupling strength higher than that of MgB2. An anticorrelation between the energetic stability and electron-phonon coupling strength is identified. We suggest two phases, i.e., Li3ZrB8 and Ca3YB8, to be synthesized, which show reasonable energetic stability and superconducting critical temperature.

Accelerating the discovery of novel magnetic materials using machine learning-guided adaptive feedback.

Magnetic materials are essential for energy generation and information devices, and they play an important role in advanced technologies and green energy economies. Currently, the most widely used magnets contain rare earth (RE) elements. An outstanding challenge of notable scientific interest is the discovery and synthesis of novel magnetic materials without RE elements that meet the performance and cost goals for advanced electromagnetic devices. Here, we report our discovery and synthesis of an RE-free magnetic compound, Fe3CoB2, through an efficient feedback framework by integrating machine learning (ML), an adaptive genetic algorithm, first-principles calculations, and experimental synthesis. Magnetic measurements show that Fe3CoB2 exhibits a high magnetic anisotropy (K1 = 1.2 MJ/m3) and saturation magnetic polarization (Js = 1.39 T), which is suitable for RE-free permanent-magnet applications. Our ML-guided approach presents a promising paradigm for efficient materials design and discovery and can also be applied to the search for other functional materials.

Machine Learning-Guided Discovery of Ternary Compounds Containing La, P, and Group 14 Elements.

We integrate a deep machine learning (ML) method with first-principles calculations to efficiently search for the energetically favorable ternary compounds. Using La-Si-P as a prototype system, we demonstrate that ML-guided first-principles calculations can efficiently explore crystal structures and their relative energetic stabilities, thus greatly accelerate the pace of material discovery. A number of new La-Si-P ternary compounds with formation energies less than 30 meV/atom above the known ternary convex hull are discovered. Among them, the formation energies of La5SiP3 and La2SiP phases are only 2 and 10 meV/atom, respectively, above the convex hull. These two compounds are dynamically stable with no imaginary phonon modes. Moreover, by replacing Si with heavier-group 14 elements in the eight lowest-energy La-Si-P structures from our ML-guided predictions, a number of low-energy La-X-P phases (X = Ge, Sn, Pb) are predicted.

A rotationally invariant approach based on Gutzwiller wave function for correlated electron systems.

We introduce a rotationally invariant approach combined with the Gutzwiller conjugate gradient minimization method to study correlated electron systems. In the approach, the Gutzwiller projector is parametrized based on the number of electrons occupying the onsite orbitals instead of the onsite configurations. The approach efficiently groups the onsite orbitals according to their symmetry and greatly reduces the computational complexity, which yields a speedup of20∼50×in the minimal basis energy calculation of dimers. The computationally efficient approach promotes more accurate calculations beyond the minimal basis that is inapplicable in the original approach. A large-basis energy calculation of F2demonstrates favorable agreements with standard quantum-chemical calculations Bytautaset al(2007J. Chem. Phys.127164317).

Path Less Traveled: A Contemporary Twist on Synthesis and Traditional Structure Solution of Metastable LiNi12B8.

Achieving kinetic control to synthesize metastable compounds is a challenging task, especially in solid-state reactions where the diffusion is slow. Another challenge is the unambiguous crystal structure determination for metastable compounds when high-quality single crystals suitable for single-crystal X-ray diffraction are inaccessible. In this work, we report an unconventional means of synthesis and an effective strategy to solve the crystal structure of an unprecedented metastable compound LiNi12B8. This compound can only be produced upon heating a metastable layered boride, HT-Li0.4NiB (HT: high temperature), in a sealed niobium container. A conventional heating and annealing of elements do not yield the title compound, which is consistent with the metastable nature of LiNi12B8. The process to crystallize this compound is sensitive to the annealing temperature and dwelling time, a testament to the complex kinetics involved in the formation of the product. The unavailability of crystals suitable for single-crystal X-ray diffraction experiments prompted solving the crystal structure from high-resolution synchrotron powder X-ray diffraction data. This compound crystallizes in a new structure type with space group I4/mmm (a = 10.55673(9) Å, c = 10.00982(8) Å, V = 1115.54(3) Å3, Z = 6). The resulting complex crystal structure of LiNi12B8 is confirmed by scanning transmission electron microscopy and solid-state 11B and 7Li NMR spectroscopy analyses. The extended Ni framework with Li/Ni disorder in its crystal structure resulted in the spin-glass or cluster glass type magnetic ordering below 24 K. This report illustrates a "contemporary twist" to traditional methodologies toward synthesizing a metastable compound and provides a recipe for solving structures by combining the complementary characterization techniques in the cases where the traditionally used single-crystal X-ray diffraction method is nonapplicable.

The Gutzwiller conjugate gradient minimization method for correlated electron systems.

We review our recent work on the Gutzwiller conjugate gradient minimization method, anab initioapproach developed for correlated electron systems. The complete formalism has been outlined that allows for a systematic understanding of the method, followed by a discussion of benchmark studies of dimers, one- and two-dimensional single-band Hubbard models. In the end, we present some preliminary results of multi-band Hubbard models and large-basis calculations of F2to illustrate our efforts to further reduce the computational complexity.

Two-step nucleation of the Earth's inner core.

The Earth's inner core started forming when molten iron cooled below the melting point. However, the nucleation mechanism, which is a necessary step of crystallization, has not been well understood. Recent studies have found that it requires an unrealistic degree of undercooling to nucleate the stable, hexagonal, close-packed (hcp) phase of iron that is unlikely to be reached under core conditions and age. This contradiction is referred to as the inner core nucleation paradox. Using a persistent embryo method and molecular dynamics simulations, we demonstrate that the metastable, body-centered, cubic (bcc) phase of iron has a much higher nucleation rate than does the hcp phase under inner core conditions. Thus, the bcc nucleation is likely to be the first step of inner core formation, instead of direct nucleation of the hcp phase. This mechanism reduces the required undercooling of iron nucleation, which provides a key factor in solving the inner core nucleation paradox. The two-step nucleation scenario of the inner core also opens an avenue for understanding the structure and anisotropy of the present inner core.

Lithium Diffusion in Silicon Encapsulated with Graphene.

The model of a graphene (Gr) sheet putting on a silicon (Si) substrate is used to simulate the structures of Si microparticles wrapped up in a graphene cage, which may be the anode of lithium-ion batteries (LIBS) to improve the high-volume expansion of Si anode materials. The common low-energy defective graphene (d-Gr) structures of DV5-8-5, DV555-777 and SV are studied and compared with perfect graphene (p-Gr). First-principles calculations are performed to confirm the stable structures before and after Li penetrating through the Gr sheet or graphene/Si-substrate (Gr/Si) slab. The climbing image nudged elastic band (CI-NEB) method is performed to evaluate the diffusion barrier and seek the saddle point. The calculation results reveal that the d-Gr greatly reduces the energy barriers for Li diffusion in Gr or Gr/Si. The energy stability, structural configuration, bond length between the atoms and layer distances of these structures are also discussed in detail.

Neural network potential for Zr-Rh system by machine learning.

Zr-Rh metallic glass has enabled its many applications in vehicle parts, sports equipment and so on due to its outstanding performance in mechanical property, but the knowledge of the microstructure determining the superb mechanical property remains yet insufficient. Here, we develop a deep neural network potential of Zr-Rh system by using machine learning, which breaks the dilemma between the accuracy and efficiency in molecular dynamics simulations, and greatly improves the simulation scale in both space and time. The results show that the structural features obtained from the neural network method are in good agreement with the cases inab initiomolecular dynamics simulations. Furthermore, we build a large model of 5400 atoms to explore the influences of simulated size and cooling rate on the melt-quenching process of Zr77Rh23. Our study lays a foundation for exploring the complex structures in amorphous Zr77Rh23, which is of great significance for the design and practical application.

How to Look for Compounds: Predictive Screening and in†situ Studies in Na-Zn-Bi System.

Here, the combination of theoretical computations followed by rapid experimental screening and in situ diffraction studies is demonstrated as a powerful strategy for novel compounds discovery. When applied for the previously "empty" Na-Zn-Bi system, such an approach led to four novel phases. The compositional space of this system was rapidly screened via the hydride route method and the theoretically predicted NaZnBi (PbClF type, P4/nmm) and Na11 Zn2 Bi5 (Na11 Cd2 Sb5 type, P 1 ‾ ) phases were successfully synthesized, while other computationally generated compounds on the list were rejected. In addition, single crystal X-ray diffraction studies of NaZnBi indicate minor deviations from the stoichiometric 1 : 1 : 1 molar ratio. As a result, two isostructural (PbClF type, P4/nmm) Zn-deficient phases with similar compositions, but distinctly different unit cell parameters were discovered. The vacancies on Zn sites and unit cell expansion were rationalized from bonding analysis using electronic structure calculations on stoichiometric "NaZnBi". In-situ synchrotron powder X-ray diffraction studies shed light on complex equilibria in the Na-Zn-Bi system at elevated temperatures. In particular, the high-temperature polymorph HT-Na3 Bi (BiF3 type, Fm 3 ‾ m) was obtained as a product of Na11 Zn2 Bi5 decomposition above 611 K. HT-Na3 Bi cannot be stabilized at room temperature by quenching, and this type of structure was earlier observed in the high-pressure polymorph HP-Na3 Bi above 0.5 GPa. The aforementioned approach of predictive synthesis can be extended to other multinary systems.

Ternary Zinc Antimonides Unlocked Using Hydride Synthesis.

Three new sodium zinc antimonides Na11Zn2Sb5, Na4Zn9Sb9, and NaZn3Sb3 were synthesized utilizing sodium hydride NaH as a reactive sodium source. In comparison to the synthesis using sodium metal, salt-like NaH can be ball-milled, leading to the easy and uniform mixing of precursors in the desired stoichiometric ratios. Such comprehensive compositional control enables a fast screening of the Na-Zn-Sb system and identification of new compounds, followed by their preparation in bulk with high purity. Na11Zn2Sb5 crystallizes in the triclinic P1 space group (No. 2, Z = 2, a = 8.8739(6) Å, b = 10.6407(7) Å, c = 11.4282(8) Å, α = 103.453(2)°, ß = 96.997(2)°, γ = 107.517(2)°) and features polyanionic [Zn2Sb5]11- clusters with unusual 3-coordinated Zn atoms. Both Na4Zn9Sb9 (Z = 4, a = 28.4794(4) Å, b = 4.47189(5) Å, c = 17.2704(2) Å, ß = 98.3363(6)°) and NaZn3Sb3 (Z = 8, a = 32.1790(1) Å, b = 4.51549(1) Å, c = 9.64569(2) Å, ß = 98.4618(1)°) crystallize in the monoclinic C2/m space group (No. 12) and have complex new structure types. For both compounds, their frameworks are built from ZnSb4 distorted tetrahedra, which are linked via edge-, vertex-sharing, or both, while Na cations fill in the framework channels. Due to the complex structures, Na4Zn9Sb9 and NaZn3Sb3 compounds exhibit low thermal conductivities (0.97-1.26 W·m-1 K-1) at room temperature, positive Seebeck coefficients (19-32 µV/K) suggestive of holes as charge carriers, and semimetallic electrical resistivities (∼1.0-2.3 × 10-4 Ω·m). Na4Zn9Sb9 and NaZn3Sb3 decompose into the equiatomic NaZnSb above ∼800 K, as determined by in situ synchrotron powder X-ray diffraction. The discovery of multiple ternary compounds highlights the importance of judicious choice of the synthetic method.