Crystal structure prediction (CSP) methods have become essential tools in materials discovery. As the initial step in CSP, the quality of the generated structures critically determines efficiency. It has been increasingly recognized that incorporating symmetry during structure generation can significantly enhance efficiency, as most real materials crystallize in non-P1 symmetries. In this work, we present an open-source package for random symmetric structure generation under user-defined constraints. The program supports bulk, low-dimensional, and molecular crystal generation, with flexible control over parameters such as cell shape, bond length, conventional or primitive symmetry settings, Wyckoff position weighting, and density uniformity adjustment. Furthermore, it interfaces with prototype databases, enabling structure generation based on known prototypes. We demonstrate that its integration with CSP frameworks substantially improves search efficiency, offering strong potential for accelerating novel materials design and discovery.

Recently, electrides have received great attention because of their unique electronic, structural, and electron-phonon coupling behaviors, which are mainly attributed to the localizations of nonbound electrons at crystalline interstitial regions. Here, we propose several stable exotic Li-In compounds under pressures based on the crystal structure predictions and first-principles calculations. We identify a Li7In compound with electride characters, which transitions from a metallic state into an insulating state with increasing pressure due to the orbital overlapping and electron localization. Li7In is also calculated to have a superconducting transition temperature of 7.33 K at 60 GPa. Moreover, superionic states are found in Li4In and Li7In at high temperatures with diffused lithium atoms. It is remarkable to observe the coexistence behavior of superconducting, insulating, and superionic states within a single electride system. Our results enrich the high-pressure phase diagram of Li-In alloys and provide theoretical support for subsequent experiments.

Pressure is a powerful tool for tuning properties of materials, capable of inducing high-Tc superconductivity, topological phase transitions, and other novel states. Here, we systematically investigate the pressure-induced topological phase transition in the Lu2S3 system. Both the predicted P4/mbm phase (from 9 GPa to 57 GPa) and the I4/mmm phase (from 57 GPa to 200 GPa) feature cage-like structures, with Lu atoms centered within S poly hedra. Without spin-orbit coupling (SOC), the orbital-resolved band structures reveal band inversion between Lu-d and S-p dominated states, giving rise to a nodal square in the P4/mbm phase and a nodal crown in the I4/mmm phase. Once including SOC, the nodal square and nodal crown are fully gapped, leading to the strong topological insulator phase and weak topological insulator phase in the P4/mbm and I4/mmm phases, respec tively. Furthermore, we explore the evolution of these topological phases under various perturbations, indicating that they can serve as parent compounds for diverse topological states, including Dirac points, composite nodal lines and topological insulators. Our results reveal the rich topological physics in the Lu2S3 system under pressure and provide guidance for future experimental studies and potential electronic applications.

W & uuml;stite (FeO), silica (SiO2), and water (H2O) are highly abundant in the interior of planets. Given their extensive participation in most geochemical reactions within the mantle of Earth and other planets, it is important to investigate the high-pressure compounds of the ternary FeO-SiO2-H2O system. Here, taking advantage of machine learning assisted crystal structure predictions based on DFT+U calculations, we identified two thermodynamically stable iron hydrosilicate phases, the alpha-FeSiO4H2 and beta-FeSiO4H2 at high pressures of 50-150 GPa and above 150 GPa, respectively. Both these structures exhibit superionic behavior at pressure-temperature conditions corresponding to the Earth's interior. Most importantly, as a reservoir of water, the FeSiO4H2 can enter the lower mantle and release water through the disproportionation of ferrous iron, which occurs during the accretion process. Our findings provide a different perspective on the behavior of the Earth's interior and expose more possibilities for the evolution models of terrestrial planets in our solar system and beyond.

Electron correlation and electron-lattice interactions are two fundamental aspects of condensed-matter physics, which, combined with nonbound interstitial anionic electrons, can give rise to abundant physical phenomena. In this work, we combined crystal structure prediction with first-principles calculations to explore alkaline-earth halides as potential hosts of exotic electrides and physical properties. We identified nine unconventional stoichiometric phases, among which four exhibit pronounced electride characteristics. In particular, the P-6m2 CaI phase adopts a hexagonal structure, where interstitial electrons are localized within the calcium honeycomb layers. The strong interstitial-electron correlations drive a Mott metal-insulator transition, with an antiferromagnetic ground state. For the Ca3I compound, strong interactions between interstitial electrons and adjacent calcium lattices promote a structural transformation from the P63/mmc to the Cmcm phase, accompanied by the emergence of superconductivity with a transition temperature of 7.1 K at 70 GPa. Moreover, a metastable P4/mmm Ca3I electride is also predicted to exhibit superconductivity with a transition temperature of approximately 6.9 K. These findings highlight that interstitial electrons located near the Fermi level can induce strong electron correlations and enhance electron-phonon coupling, thereby giving rise to a rich spectrum of physical behaviors, including superconductivity and magnetism.

Quantum phase transitions are crucial for understanding emergent phenomena in quantum many-body systems, especially at zero temperature, where quantum fluctuations dominate. Here, we utilized the crystal structure searching method in conjunction with first-principles calculations to investigate the lithium-lead system, leading to the discovery of three exotic phases. Notably, the P-62m Li7Pb emerges as an electride with distinct A-type and B-type interstitial anion electrons (IAEs). The bilayer Kagome lattice of Li7Pb accommodates weak itinerant ferromagnetism within the stable pressure range from 20 to 45 GPa, primarily attributed to the presence of B-type IAEs. On the contrary, A-type IAEs are sensitive to charge doping, impacting the modulation of ferromagnetism. Furthermore, electron doping led to the transition of Li7Pb into a superconductor as the magnetic moment diminished, and the transition temperature could be raised from 1.6 to 3.4 K as doping intensified. This transition was facilitated by the interaction between A-type IAEs and phonons from the surrounding lithium lattice, showcasing a unique quantum phase transition between itinerant ferromagnetism and superconductivity in electrides. Our study not only revealed novel structures in lithium-lead systems but also established a platform for exploring quantum phase transitions in electrides.

Magnesium fluoride (MgF2) serves as an important analog system to study the pressure-induced structural and electronic phase transitions in oxides relevant to geoscience and planetary science, such as SiO2 and GeO2. In this work, through first-principles calculations combined with synchrotron x-ray diffraction (XRD) and Ramanscattering measurements in laser-heated diamond anvil cells, we study the structural phase transition of MgF2 at high pressure. We confirm the existence of a mixed-coordinated rhombohedral phase with R3 & strns; symmetry in MgF2, which was previously predicted to be thermodynamically stable between 645 and 890 GPa in silica but has never been synthesized experimentally. This R3 & strns; phase is the ground state in the pressure range from 40 to 55 GPa in MgF2, in analogy to silica but at much lower pressure. The in situ high-pressure XRD measurements confirm the phase transition from the pyrite-type phase to the R3 & strns; phase after laser heating at around 51 GPa along with Raman modes well aligned with the calculated R3 & strns; phase. Furthermore, our extended calculations for GeO2 confirm the R3 & strns; phase as the ground state at 250-310 GPa. Considering the similar phase transition sequences of silica and magnesium fluoride, our findings provide a reference for the future experimental verification of the R & strns;3 phase of SiO2, which is of great significance in geoscience and planetary science.

Flexible electronic materials are essential for the development of next-generation devices that maintain reliable performance under mechanical deformation such as bending and stretching. In this work, we propose a novel monolayer compound, P4/mmm LaBr2 (denoted as "ML-P4/mmm-LaBr2"), discovered via high-pressure crystal structure prediction and characterized by first-principles and machine learning study, as a promising candidate for flexible electronics. The I4/mmm LaBr2 parent phase is thermodynamically stable at ambient pressure, and its monolayer can be exfoliated with a cleavage energy comparable to established 2D materials such as graphene, MoS2, and black phosphorus. The average Young's modulus E and shear modulus G of ML-P4/mmm-LaBr2 are calculated to be 55.8 and 23.0 N/m, respectively, indicating moderate mechanical flexibility. Electron-phonon coupling calculations reveal an exceptional electrical conductivity of 4.9 × 106 S/m (sheet conductance 3.1 mS) at 300 K, and a qualitative strain analysis indicates that this high conductivity is retained under small biaxial strains. Machine-learning molecular dynamics yields a low lattice thermal conductivity of 7.0 ± 0.2 W/(m·K). We further show that the monolayer tolerates moisture and intrinsic point defects, though oxygen sensitivity necessitates inert-atmosphere handling. These results suggest that ML-P4/mmm-LaBr2 is a promising candidate for flexible electronic applications, provided that appropriate encapsulation strategies are employed to mitigate its oxygen sensitivity.

The combinations of machine learning with ab initio methods have attracted much attention for their potential to resolve the accuracy-efficiency dilemma and facilitate calculations for large-scale systems. Recently, equivariant message passing neural networks (MPNNs) that explicitly incorporate symmetry constraints have demonstrated promise for interatomic potential and density functional theory (DFT) Hamiltonian predictions. However, the high-order tensors used to represent node and edge information are coupled through the Clebsch–Gordan tensor product, leading to steep increases in computational complexity and seriously hindering the performance of equivariant MPNNs. Here, we develop high-order tensor machine-learning Hamiltonian (Hot-Ham), an E (3) equivariant MPNN framework that combines two advanced technologies: local coordinate transformation and Gaunt tensor product to efficiently model DFT Hamiltonians. These two innovations significantly reduce the complexity of tensor products from O ( L 6 ) to O ( L 3 ) or O ( L 2 log 2 L ) for the max tensor order L , and enhance the performance of MPNNs. Benchmarks on several public datasets demonstrate its state-of-the-art accuracy with relatively few parameters, and applications to multilayer twisted moiré systems, heterostructures, and allotropes showcase its generalization ability and high efficiency. Our Hot-Ham method provides a new perspective for developing efficient equivariant neural networks and would be a promising approach for investigating the electronic properties of large-scale materials systems.

Using crystal structure prediction and first-principles calculations, we show that the Li-Xe system exhibits diverse structural, electronic, and dynamical behaviors under pressure. Lithium-rich phases display electride character, with interstitial electrons dominating the states at the Fermi level, leading to metallicity and phononmediated superconductivity with superconducting transition temperatures of approximately 9-14 K. In contrast, xenon-rich phases transition into a superionic state at elevated temperatures, characterized by Li ions becoming increasingly mobile within a rigid Xe lattice before melting at higher temperatures. These results reveal the dual nature of Li-Xe compounds, combining interstitial electron driven superconductivity at low temperatures with ion diffusion mediated superionicity at high temperatures, providing insights into noble-gas chemistry under extreme conditions and potential implications for planetary interiors.

Superionic materials have attracted considerable interest due to their unique electronic and thermal transporting properties, with far-reaching implications for solid-state electrolyte batteries and planetary science. Despite extensive studies, the physicochemical origin of superionic behavior remains insufficiently understood. In this work, we develop a generalized machine-learning descriptor for superionic materials by combining structural, elemental, and density-functional theory primary features with the Sure Independence Screening and Sparsifying Operator (SISSO) framework. We identify four key factors to recognize superionic materials: electronegativity, chemical hardness, density, and bond strength. The developed machine-learning descriptor applies well beyond conventional lithium- and sodium-based superionic systems and can be extended to high-pressure conditions. Based on our machine-learning descriptor, we conducted a high-throughput screening of 13 019 materials from the MATERIALS PROJECT database, and 353 potential superionic candidates were identified. This study not only sheds light on the underlying physical origin of the superionic state but also provides guidance and insights for the design and experimental synthesis of future superionic materials.

Confined gas and ionic hydrates play vital roles in energy storage, carbon capture, and water desalination. Yet, the fundamental interactions between water films and hydrophobic molecules remain poorly understood. Here, we investigated nanoconfined monolayer methane hydrates encapsulated within graphene capillaries, exploring their phase behavior through crystal structure prediction combined with a machine-learning force field. We identified a thermodynamically stable two-dimensional tetragonal compound CH4(H2O)4 under moderate pressures. Its hydrogen bonding network markedly differs from that of 2D pure or porous ice, giving rise to multiple plastic phases in which methane and water molecules rotate. Remarkably, 2D CH4(H2O)4 transitions into a superionic state featuring proton diffusion at pressures as low as ∼3 GPa, substantially lower than that required for 2D ice. The calculated phase diagram further reveals that CH4 molecule incorporation elevates the melting temperatures above 350 K while reducing the onset pressure for superionicity. These findings provide fundamental insight into hydrophobic gas hydrate under nanoscale confinement and open new avenues for applications in energy storage and hydrocarbon capture.

Magnetic materials exhibit an intricate coupling between atomic structure and spin degrees of freedom, posing a fundamental challenge for atomistic simulations across experimentally relevant length and time scales. Here we introduce HotPP-Spin, a spin-dependent extension of HotPP for magnetic machine learning interatomic potentials, built on Cartesian tensor equivariant message passing. Atomic magnetic moments are treated as explicit axial-vector degrees of freedom, while spatial-inversion and time-reversal parities are propagated through the tensor couplings. This construction provides a unified representation of exchange-dominated and spin-orbit-induced interactions without imposing predefined analytical interaction forms. A scalar spin-dependent potential energy surface yields energy-conserving atomic forces and magnetic effective fields through differentiation. Benchmarks spanning collinear magnetism, noncollinear magnetism, and spin-orbit-coupling-induced magnetic anisotropy show that HotPP-Spin accurately describes magnetic energy landscapes, magnetic forces, and magnetic-order-dependent energy-volume relations within the same general framework. For H-phase monolayer VSe_2, stochastic spin-dynamics simulations using the learned magnetic effective fields locate the finite-size magnetic ordering crossover at 415–435 K, in close numerical agreement with the reported experimental value of 418.5±7.8 K. These results establish Cartesian tensor message passing as a general route for connecting first-principles magnetic energetics with large-scale atomistic simulations of coupled structural and spin phenomena.

High-temperature conventional superconductivity at ambient conditions beyond MgB2 presents key challenges in the dynamic stabilization of compositional structures. However, the isostructural beryllium diboride (BeB2) phase lacks ambient-pressure dynamics stability, thus prohibiting superconductivity. Here, we predict a novel superconducting BeB2 phase with P63cm symmetry featuring distorted hexagonal boron layers. The Wurtzitic gauche boron framework favors thermodynamic stability at ambient pressure by modulating anharmonic beryllium displacements. Interestingly, mirror symmetry is observed to protect topological nodal lines in electronic states. Eliashberg function computations estimate strong electron-phonon coupling strength for the BeB2 phase beyond MgB2. High superconducting transition temperature achieves enhancement by mediating with broadened phonon modes attributed to atomic displacements. Our work can inspire wide interest in designing and modulating high-temperature superconducting structures with topology, especially offering potential exploration within meta-stable crystallographic databases.

Lithium-based compounds with interstitial anionic electrons(IAEs)exhibit unique electronic properties,including superconductivity and superionic behavior.The intrinsic connection between these properties offers valuable insights and potential applications in materials science.In this study,we employed machine-learning-accelerated crystal structure pre-diction and first-principles calculations to investigate the phase stability of various Li—B systems under high pressures.Our results indicate that the known R-3m Li6B compound is an electride.At 150 GPa,R-3m Li6B exhibits a superconduct-ing transition temperature of around 51 K and enters a superionic state at high temperatures.Additionally,a monoclinic compound,C2/m LiB6,which is metastable at ambient pressure,was found.More interestingly,an unpredicted cage-like metallic boron allotrope termed C2/m-B12 can be obtained by removing Li from LiB6.These findings open avenues for interdisciplinary research and highlight the potential of exotic boron allotropes in advanced device applications.

Near-room-temperature superconductivity has been achieved in hydrogen-rich materials under ultrahigh hydrostatic pressures, yet such extreme conditions remain a fundamental barrier to practical application. The search for ambient-pressure high-temperature superconductors has therefore increasingly turned to boron–carbon (B–C) and boron–nitrogen (B–N) clathrate systems, in which hydrogen is replaced by the light elements B, C, and N to form rigid covalent cage frameworks that retain the high phonon frequencies essential for elevated superconducting critical temperatures (Tc). Here, we present a systematic statistical analysis of reported B–C and B–N superconducting compounds and reveal the critical role of the interplay between the electron–phonon coupling constant λ and the logarithmic average phonon frequency ω log in determining Tc. Our statistical analysis reveals that the variation of Tc in B–C and B–N systems cannot be described by either λ or ω log alone but instead arises from their combined effects and intrinsic interplay. Extending the mass-ratio screening framework of binary hydrides to ternary B–C and B–N superconductors, we further identify two design descriptors for high Tc, namely, a low valence electron count and a small guest–host mass ratio MX/(MTotal−MX). These design rules provide a quantitative framework for the rational design and high-throughput discovery of ambient-pressure high-temperature superconductors.

Although equivariant neural networks have become a cornerstone for learning electronic Hamiltonians, the intrinsic non-orthogonality of linear combinations of atomic orbitals (LCAO) basis sets poses a fundamental challenge. The computational cost of Hamiltonian orthogonalization scales as O(N^3), which severely hinders electronic structure calculations for large-scale systems containing hundreds of thousands to millions of atoms. To address this issue, we develop GPUTB-2, a framework that learns implicitly orthogonality-preserving Hamiltonians by training directly on electronic band structures. Benefiting from an E(3)-equivariant network accelerated by Gaunt tensor product and SO(2) tensor product layers, GPUTB-2 achieves significantly higher accuracy than GPUTB across multiple benchmark systems. Moreover, GPUTB-2 accurately predicts large-scale electronic structures, including transport properties of temperature-perturbed SnSe and the band structures of magic-angle twisted bilayer graphene. By further integrating this framework with the linear-scaling quantum transport (LSQT) method, we investigate the electronic properties of million-atom amorphous graphene and uncover pressure-induced electronic structure transitions in more complex amorphous silicon. Together, these results establish GPUTB-2 as a high-accuracy and scalable approach for predicting orthogonal Hamiltonians.

We report a theoretical investigation into superconductivity within the MAX H 6 quaternary hydride system using first-principles calculations, where M and A denote alkali and alkaline earth elements, respectively, and X represents transition metal elements. Systematic analysis of electronic band structures, phonon dispersions, and electron-phonon coupling reveals that substitution of M A binary metal combinations and X metal atoms can create favorable conditions for superconductivity. Mapping of superconducting critical temperatures, combined with dynamical stability analysis through phonon calculations, identifies ten superconducting candidates at ambient pressure. Among these, LiNaAgH 6 exhibits nearly-free-electron behavior reminiscent of monovalent electron superconductors. It demonstrates exceptional superconducting properties with electron-phonon coupling λ = 2.707, which yields a superconducting transition temperature T c of 206.4 K using the Allen-Dynes formula. Its structural analogs MgNaPdH 6 , LiMgPdH 6 , LiMgAgH 6 , LiMgAuH 6 all exhibit superconducting transition temperatures above 110 K. These findings advance our fundamental understanding of superconductivity in quaternary hydrides and provide guidance for rational design of new high-temperature superconducting materials.

Group IV elements exhibit diverse bonding and crystalline structures, including carbon-based configurations such as graphene and diamond, and silicon-based porous structures. This diversity gives rise to intriguing physical phenomena and applications, such as magic-angle superconductivity and superhard materials. However, the potential configurations formed by germanium and their corresponding physical properties remain largely unexplored. In this study, we employ a crystal structure prediction method to investigate calcium germanide under high pressures, identifying 12 exotic thermodynamically stable phases. Notably, the CaGe systems display a variety of bonding types, with germanium forming zigzag, square ring, armchair, and ladder configurations. Additionally, we found that the known Ca2Ge system undergoes a metal-insulator phase transition, transforming into a hexagonal structure with nontrivial band topology. For calcium-rich compounds, we discovered several electride phases with distinct cavity shapes. Among these, the Ca4Ge Imma phase possesses one-dimensional interstitial electrons. It exhibits a superconducting transition temperature of approximately 10 K at 60 GPa, which is higher than other calcium-based electrides at moderate pressures. Our findings demonstrate that introducing metal atoms can induce diverse bonding characteristics in group IV elements, resulting in a wide range of physical properties, including superconducting and topological behaviors.

The high computational cost of ab-initio methods limits their application in predicting electronic properties at the device scale. Therefore, an efficient method is needed to map the atomic structure to the electronic structure quickly. Here, we develop GPUTB, a GPU-accelerated tight-binding (TB) machine learning framework. GPUTB employs atomic environment descriptors, enabling the model parameters to incorporate environmental dependence. This allows the model to transfer to different basis, xc-functionals, and allotropes easily. Combined with the linear scaling quantum transport method, we have calculated the electronic density of states for up to 100 million atoms in pristine graphene. Trained on finite-temperature structures, the model can be easily extended to millions of atom finite-temperature systems. Furthermore, GPUTB can also successfully describe h-BN/graphene heterojunction systems, demonstrating its capability to handle complex material with high precision. We accurately reproduce the relationship between carrier concentration and room temperature mobility in graphene to verify the framework's accuracy. Therefore, our GPUTB framework presents a delicate balance between computational accuracy and efficiency, providing a powerful computational tool for investigating electronic properties for large systems with millions of atoms.