Strong correlation between electronic bonding network and critical temperature in hydrogen-based superconductors

Structural transitions at the bilayer graphene-methanol interface from ab initio molecular dynamics

The precise tailoring of the atomic architecture of 2D carbon-based materials, which results in the modulation of their physical properties, promises to open new pathways for the design of technological devices in electronics, spintronics and energy storage. High-pressure conditions can lead to the synthesis of complex materials starting from multi-layer graphene, often relying on chemical transformations at the interface between carbon and pressure-transmitting media like water or alcohol. Unfortunately, the experimental characterization of molecular-scale mechanisms at interfaces is very challenging. On the other side, the sheer cost of ab initio simulations strongly limited, so far, the computational works in literature to simplified models that, often, do not capture the complexity of the materials and finite-temperature effects. In this work, we provide for the first time an extensive computational study of complex, realistic models of bilayer graphene-methanol interfaces at high pressure and finite temperature. Our simulations allow fundamental insight to be gained on several questions raised from previous experimental works about structural, electronic and reactivity properties of this challenging material. The exploitation of state-of-the-art enhanced sampling techniques combined with topological electronic descriptors allowed characterization of barrier-activated functionalization processes, unveiling a major catalytic effect of carbon defects and pressure towards sp3 formation.

Code dependence of calculated crystalline electron densities. Possible lessons for quantum crystallography

The use of electronic structure methods in crystallographic data analysis, the now well known field of quantum crystallography, aids in the solution of several problems in X-ray diffraction refinement, as well as opening new avenues to access a whole new set of experimentally available observables. A key ingredient in quantum crystallography is the theoretically derived electron density, ρ, obtained from standard electronic structure codes. Here, we introduce a factor that has not been carefully considered until now. As we demonstrate, theoretically derived ρ values depend not only on the set of computational conditions used to obtain them but also on the particular computational code selected for this task. We recommend that all quantum crystallographers carefully check the convergence of ρ before undertaking any serious study.

Ductile copper hydride Eliashberg superconductors with Tc in the liquid-nitrogen temperature range and band topology at ambient pressure

The engineering demands for superconductors require not only a high transition temperature (Tc) but also eco-friendliness, mechanical workability, and abundance. Currently, superconductors exhibiting both mechanical ductility and Tc above the liquid-nitrogen temperature are still lacking. Considering that copper is one of the most important conductive materials for power transmission, we investigate the synthetic routes, band topology, electron-phonon coupling (EPC) and anharmonic superconductivity of copper hydrides using first-principles calculations. Cubic-Cu4H3 remains stable at ambient pressure after kinetic simulations from its experimentally synthesized pressure state. The incorporation of hydrogen impacts the ductility of Cu4H3 negligibly compared to copper, while enabling high-Tc superconductivity up to 77 K and non-trivial band topology at ambient pressure. The novel properties arise from the strong EPC, Fermi surface nesting and hydrogen-induced band inversion. This discovery may fill the gap in the lack of ductile superconductors in the liquid-nitrogen temperature range and pave a new way for realizing high-temperature topological superconductivity at atmospheric pressure.

Molecular Hydride Superconductor BiH4 with Tc up to 91 K at 170 GPa

In pursuit of high-Tc hydride superconductors, the molecular hydrides have attracted less attention because the hydrogen quasimolecules are usually inactive for superconductivity. Here, we report on the successful synthesis of a novel bismuth hydride superconductor C2/c-BiH4 at pressures around 170-180 GPa. Its structure comprises bismuth atoms and elongated hydrogen molecules with a H-H bond length of 0.81 Å at 170 GPa, characterizing it as a typical molecular hydride. Transport measurements revealed the occurrence of superconductivity with Tc up to 91 K at 170 GPa, as evidenced by a sharp drop of resistivity to zero and a characteristic downward shift of Tc under magnetic fields. Calculations by density functional theory elucidate that both midfrequency H-derived phonons and low-frequency vibrations from Bi atoms are important for the strong electron-phonon coupling in BiH4, differentiating it from most high-Tc superconducting hydrides. Our work not only places C2/c-BiH4 among the molecular hydride superconductors with the highest Tc but also offers new directions for designing and synthesizing more high-Tc hydride superconductors.

TcESTIME: predicting high-temperature hydrogen-based superconductors

Superconductivity can be considered among the most exciting discoveries in material science of the 20th century. However, the hard conditions for the synthesis and the difficult characterization, make the statement of new high critical temperature (T c) complex from the experimental viewpoint and have recently led to several hot controversies in the literature. In this panorama, theory has become a trustworthy diagnosis. Nevertheless, this comes at an extremely high computational cost. A faster alternative would be to find cheap footprints of superconductivity from the electronic structure. Some of the authors have recently shown that a correlation exists between T c, the networking value [Nature Communications, 12, 5381 (2021)], and the molecularity index [arXiv:2403.07584v1 (2024)]. The networking value reflects the metallicity of the parent compound as a measure of its electron delocalization channels, by means of the Electron Localization Function topology (its bifurcation trees). Instead, the molecularity index quantifies the presence of H2 molecules within the system. All in all, these two quantities characterize bonding features that are related to high T c: high metallicity and low molecularity boost high T c states. However, the quantification or these bonding characteristics was initially made by a visual approach, which is not scalable for high throughput screening. We have developed a new code, TcESTIME, which allows to determine the networking value for a given hydrogen-based compound. In this contribution, we present such code and the underlying periodic algorithms we have developed. As a reference, the estimation of T c for LaH10 thanks to this new code amounts to 10 CPU minutes in a computer cluster equipped with Intel Xeon 2.4 GHz processor. Given the new potential for screening, we have applied it to a larger set including ternary hydrogen based superconductors, and have proposed new fits to estimate T c, leading to errors of ca. 33 K. We believe that this contribution settles the bases for an automatic high-throughput screening of hydrogen-based superconductors.

Introducing electron correlation in solid-state calculations for superconducting states

Analyzing the electronic localization of superconductors has been recently shown to be relevant for understanding their critical temperature [Nature Communications, 12, 5381, (2021)]. However, these relationships have only been shown at the Kohn-Sham density functional theory (DFT) level, where the onset of strong correlation linked to the superconducting state is missing. In this contribution, we approximate the superconducting gap in order to reconstruct the superconducting the one-reduced density matrix (1RDM) from a DFT calculation. This allows us to analyse the electron density and localization in the strong correlation regime. The method is applied to two well-known superconductors. Electron localization features along the electron-phonon coupling directions and hydrogen cluster formations are observed for different solids. However, in both cases we see that the overall localization channels are not affected by the onset of superconductivity, explaining the ability of DFT localization channels to characterize the superconducting ones.

Designing multicomponent hydrides with potential high Tc superconductivity

While hydrogen-rich materials have been demonstrated to exhibit high Tc superconductivity at high pressures, there is an ongoing search for ternary, quaternary, and more chemically complex hydrides that achieve such high critical temperatures at much lower pressures. First-principles searches are impeded by the computational complexity of solving the Eliashberg equations for large, complex crystal structures. Here, we adopt a simplified approach using electronic indicators previously established to be correlated with superconductivity in hydrides. This is used to study complex hydride structures, which are predicted to exhibit promisingly high critical temperatures for superconductivity. In particular, we propose three classes of hydrides inspired by the Fm[Formula: see text]m RH[Formula: see text] structures that exhibit strong hydrogen network connectivity, as defined through the electron localization function. The first class [RH[Formula: see text]X[Formula: see text]Y] is based on a Pm[Formula: see text]m structure showing moderately high Tc, where the Tc estimate from electronic properties is compared with direct Eliashberg calculations and found to be surprisingly accurate. The second class of structures [(RH[Formula: see text])[Formula: see text]X[Formula: see text]YZ] improves on this with promisingly high density of states with dominant hydrogen character at the Fermi energy, typically enhancing Tc. The third class [(R[Formula: see text]H[Formula: see text])(R[Formula: see text]H[Formula: see text])X[Formula: see text]YZ] improves the strong hydrogen network connectivity by introducing anisotropy in the hydrogen network through a specific doping pattern. These design principles and associated model structures provide flexibility to optimize both Tc and the structural stability of complex hydrides.

Discovery of novel materials through machine learning

Experimental exploration of new materials relies heavily on a laborious trial-and-error approach. In addition to substantial time and resource requirements, traditional experiments and computational modelling are typically limited in finding target materials within the enormous chemical space. Therefore, creating innovative techniques to expedite material discovery becomes essential. Recently, machine learning (ML) has emerged as a valuable tool for material discovery, garnering significant attention due to its remarkable advancements in prediction accuracy and time efficiency. This rapidly developing computational technique accelerates the search and optimization process and enables the prediction of material properties at a minimal computational cost, thereby facilitating the discovery of novel materials. We provide a comprehensive overview of recent studies on discovering new materials by predicting materials and their properties using ML techniques. Beginning with an introduction of the fundamental principles of ML methods, we subsequently examine the current research landscape on the applications of ML in predicting material properties that lead to the discovery of novel materials. Finally, we discuss challenges in employing ML within materials science, propose potential solutions, and outline future research directions.

Superconducting ternary hydrides: progress and challenges

Since the discovery of the high-temperature superconductors H3S and LaH10 under high pressure, compressed hydrides have received extensive attention as promising candidates for room-temperature superconductors. As a result of current high-pressure theoretical and experimental studies, it is now known that almost all the binary hydrides with a high superconducting transition temperature (T c) require extremely high pressure to remain stable, hindering any practical application. In order to further lower the stable pressure and improve superconductivity, researchers have started exploring ternary hydrides and had many achievements in recent years. Here, we discuss recent progress in ternary hydrides, aiming to deepen the understanding of the key factors regulating the structural stability and superconductivity of ternary hydrides, such as structural motifs, bonding features, electronic structures, electron-phonon coupling, etc. Furthermore, the current issues and challenges of superconducting ternary hydrides are presented, together with the prospects and opportunities for future research.

Layered Hydride LiH4 with a Pressure-Insensitive Superconductivity

For hydride superconductors, each significant advance is built upon the discovery of novel H-based structural units, which in turn push the understanding of the superconducting mechanism to new heights. Based on first-principles calculations, we propose a metastable LiH4 with a wavy H layer composed of the edge-sharing pea-like H18 rings at high pressures. Unexpectedly, it exhibits pressure-insensitive superconductivity manifested by an extremely small pressure coefficient (dTc/dP) of 0.04 K/GPa. This feature is attributed to the slightly weakened electron-phonon coupling with pressure, caused by the reduced charge transfer from Li atoms to wavy H layers, significantly suppressing the substantial increase in the contribution of phonons to Tc. Its superconductivity originates from the strong coupling between the H 1s electrons and the high-frequency phonons associated with the H layer. Our study extends the list of H-based structural units and enhances the in-depth understanding of pressure-related superconductivity.

Data-driven Design of High Pressure Hydride Superconductors using DFT and Deep Learning

The observation of superconductivity in hydride-based materials under ultrahigh pressures (for example, H3S and LaH10) has fueled the interest in a more data-driven approach to discovering new high-pressure hydride superconductors. In this work, we performed density functional theory (DFT) calculations to predict the critical temperature (Tc) of over 900 hydride materials under a pressure range of (0 to 500) GPa, where we found 122 dynamically stable structures with a Tc above MgB2 (39 K). To accelerate screening, we trained a graph neural network (GNN) model to predict Tc and demonstrated that a universal machine learned force-field can be used to relax hydride structures under arbitrary pressures, with significantly reduced cost. By combining DFT and GNNs, we can establish a more complete map of hydrides under pressure.

Anisotropy and isotope effect in superconducting solid hydrogen

Elucidating the phase diagram of solid hydrogen is a key objective in condensed matter physics. Several decades ago, it was proposed that at low temperatures and high pressures, solid hydrogen would be a metal with a high superconducting transition temperature. This transition to a metallic state can happen through the closing of the energy gap in the molecular solid or through a transition to an atomic solid. Recent experiments have managed to reach pressures in the range of 400-500 GPa, providing valuable insights. There is strong evidence suggesting that metallization via either of these mechanisms occurs within this pressure range. Computational and experimental studies have identified multiple promising crystal phases, but the limited accuracy of calculations and the limited capabilities of experiments prevent us from determining unequivocally the observed phase or phases. Therefore, it is crucial to investigate the superconducting properties of all the candidate phases. Recently, we reported the superconducting properties of theC2/c-24,Cmca-12,Cmca-4 andI41/amd-2 phases, including anharmonic effects. Here, we report the effects of anisotropy on superconducting properties using Eliashberg theory. Then, we investigate the superconducting properties of deuterium and estimate the size of the isotope effect for each phase. We find that the isotope effect on superconductivity is diminished by anharmonicity in theC2/c-24 andCmca-12 phases and enlarged in theCmca-4 andI41/amd-2 phases. Our anharmonic calculations of theC2/c-24 phase of deuterium agree closely with the most recent experiment by Loubeyreet al(2022Phys. Rev. Lett.29035501), indicating that theC2/c-24 phase remains the leading candidate in this pressure range, and has a strong anharmonic character. These characteristics can serve to distinguish among crystal phases in experiment. Furthermore, expanding our understanding of superconductivity in pure hydrogen holds significance in the study of high-Tchydrides.

Composition and structural characteristics of compressed alkaline earth metal hydrides

The metallization of alkaline earth metal hydrides offers a way to achieve near-room temperature superconductivity. In order to explore the metallization mechanism of these hydrides under pressure, a detailed understanding of the property changes of alkaline earth metal hydrides is required. Based on first-principles calculations, we have systematically investigated the dihydrides (XH2, X = Be, Mg, Ca, Sr, Ba) and tetrahydrides (XH4, X = Mg, Ca, Sr, Ba) of alkaline earth metals, respectively. By applying external pressure, we show that the structures of these alkaline earth metal hydrides undergo a series of phase transitions. Moreover, we investigate how the size of the bandgap decreases and eventually closes and reveal the role of electronegativity of metal elements in the critical pressure of hydride metallization. Remarkably, the hydrogen units (H6 or H8) formed in XH4 can accelerate the metallization process. The increase of the energy level difference in hydrogen units promotes the electroacoustic coupling effect, which is conducive to realization of high superconducting transition temperature (Tc). Our theoretical findings identify MgH4-I4/mmm as having potential to be a high-temperature superconductor and provide unusual ideas for the search of unknown high-temperature superconducting materials.

Non-Fermi-Liquid Behavior of Superconducting SnH4

The chemical interaction of Sn with H2 by X-ray diffraction methods at pressures of 180-210 GPa is studied. A previously unknown tetrahydride SnH4 with a cubic structure (fcc) exhibiting superconducting properties below TC  = 72 K is obtained; the formation of a high molecular C2/m-SnH14 superhydride and several lower hydrides, fcc SnH2 , and C2-Sn12 H18 , is also detected. The temperature dependence of critical current density JC (T) in SnH4 yields the superconducting gap 2Δ(0) = 21.6 meV at 180 GPa. SnH4 has unusual behavior in strong magnetic fields: B,T-linear dependences of magnetoresistance and the upper critical magnetic field BC2 (T) ∝ (TC - T). The latter contradicts the Wertheimer-Helfand-Hohenberg model developed for conventional superconductors. Along with this, the temperature dependence of electrical resistance of fcc SnH4 in non-superconducting state exhibits a deviation from what is expected for phonon-mediated scattering described by the Bloch-Grüneisen model and is beyond the framework of the Fermi liquid theory. Such anomalies occur for many superhydrides, making them much closer to cuprates than previously believed.

H2 Chemical Bond in a High-Pressure Crystalline Environment

We show that the hydrogen in metal superhydride compounds can adopt two distinct states-atomic and molecular. At low pressures, the maximum number of atomic hydrogens is typically equal to the valency of the cation; additional hydrogens pair to form molecules with electronic states far below the Fermi energy causing low-symmetry structures with large unit cells. At high pressures, molecules become unstable, and all hydrogens become atomic. This study uses density functional theory, adopting BaH4 as a reference compound, which is compared with other stoichiometries and other cations. Increased temperature and zero-point motion also favor high-symmetry atomic states, and picosecond-timescale breaking and remaking of the bond permutations via intermediate H3- units.

Pressure Stabilized Lithium-Aluminum Compounds with Both Superconducting and Superionic Behaviors

Superconducting and superionic behaviors have physically intriguing dynamic properties of electrons and ions, respectively, both of which are conceptually important and have great potential for practical applications. Whether these two phenomena can appear in the same system is an interesting and important question. Here, using crystal structure predictions and first-principle calculations combined with machine learning, we identify several stable Li-Al compounds with electride behavior under high pressure, and we find that the electronic density of states of some of the compounds has characteristics of the two-dimensional electron gas. Among them, we estimate that Li_{6}Al at 150 GPa has a superconducting transition temperature of around 29 K and enters a superionic state at a high temperature and wide pressure range. The diffusion in Li_{6}Al is found to be affected by an electride and attributed to the atomic collective motion. Our results indicate that alkali metal alloys can be effective platforms to study the abundant physical properties and their manipulation with pressure and temperature.

Effect of Pressure on the Distribution of Electrons in a Cluster of H2S

We carry out a theoretical study of the effect of pressure on the atomic and electronic distribution of a cluster made of 155 H₂S molecules. The pressure was modeled by bringing the cluster into a spherical container made of 500 helium atoms and reducing the diameter of the container. We did ab initio molecular calculations using DFT. At the lowest pressure, the S-H-S angle between two neighboring H₂S molecules has a distribution with a mean value of 167.1°. This angle will be shorter as pressure increases, reaching a distribution with a mean value of 125.5° at the highest pressure. Changes in this angle result from a strong S-S interaction, displacing the H atoms from the line joining the sulfur atoms. This rearrangement of the atomic distribution generates hydrogen-rich spatial regions. We analyzed the evolution of Mulliken charges on S and H atoms in the cluster with pressure, finding that electrons move from S to H atoms, suggesting that these hydrogen-rich regions should be responsible for the electrical conductivity and, consequently, also for the superconductivity in solid H₂S under pressure.

Carbon content drives high temperature superconductivity in a carbonaceous sulfur hydride below 100 GPa

We report a previously unobserved superconducting state of the photosynthesized carbonaceous sulfur hydride (C-S-H) system with a maximum TC of 191(1) K below 100 GPa. The properties of C-S-H are dependent on carbon content, and X-ray diffraction and simulations reveal the system remains molecular-like up to 100 GPa.

Superconducting hydrides on a quantum landscape

Reaching superconductivity at ambient conditions is one of the biggest scientific dreams. The discoveries in the last few years at high pressures place hydrogen-based compounds as the best candidates for making it true. As the recent history shows, first-principles calculations are expected to continue guiding the experimental quest in the right track in the coming years. Considering that ionic quantum fluctuations largely affect the crystal structure and the vibrational properties of superconducting hydrides, in many cases making them thermodynamically stable at much lower pressures than expected, it will be crucial to include such effects on the futureab initiopredictions. The prospects for low-pressure high critical-temperature compounds are wide open, even at ambient pressure.

High temperature superconductivity in the candidate phases of solid hydrogen

As the simplest element in nature, unraveling the phase diagram of hydrogen is a primary task for condensed matter physics. As conjectured many decades ago, in the low-temperature and high-pressure part of the phase diagram, solid hydrogen is expected to become metallic with a high superconducting transition temperature. The metallization may occur via band gap closure in the molecular solid or via a transition to the atomic solid. Recently, a few experimental studies pushed the achievable pressures into the 400-500 GPa range. There are strong indications that at some pressure in this range metallization via either of these mechanisms occurs, although there are disagreements between experimental reports. Furthermore, there are multiple good candidate crystal phases that have emerged from recent computational and experimental studies which may be realized in upcoming experiments. Therefore, it is crucial to determine the superconducting properties of these candidate phases. In a recent study, we reported the superconducting properties of theC2/c-24 phase, which we believe to be a strong candidate for metallization via band gap closure (Doganet al2022Phys. Rev. B105L020509). Here, we report the superconducting properties of theCmca-12,Cmca-4 andI4₁/amd-2 phases including the anharmonic effects using a Wannier function-based densek-point andq-point sampling. We find that theCmca-12 phase has a superconducting transition temperature that rises from 86 K at 400 GPa to 212 K at 500 GPa, whereas theCmca-4 andI4₁/amd-2 phases show a less pressure-dependent behavior with theirT_cin the 74-94 K and 307-343 K ranges, respectively. These properties can be used to distinguish between crystal phases in future experiments. Understanding superconductivity in pure hydrogen is also important in the study of high-T_chydrides.