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.

Quantum dot systems emerge as promising platforms for studying nanoscale thermoelectric effects and quantum fluctuation phenomena. In this work, we investigate the thermodynamic performance of a Coulomb-blockaded quantum dot operating as a quantum heat engine using the quantum master equation approach. By incorporating full counting statistics, we analyze both average transport properties and current fluctuations in this nanoscale system. We demonstrate that electron-electron interactions significantly enhance thermoelectric performance by increasing both the output power and energy conversion efficiency. Furthermore, we show that Coulomb interactions suppress current fluctuations while preserving the validity of the thermodynamic uncertainty relation. Our results provide important insights into the interplay between quantum effects and thermodynamic principles in nanoscale heat engines.

Bismuth's (Bi) unique high-pressure phase behavior has long attracted significant interest. Despite their significance in both technological applications and fundamental research, comprehensive and accurate modeling of these transitions remains challenging. To address this, we developed a neural equivariant potential machine learning potential for Bi with near first-principles accuracy. By integrating this potential with state-of-the-art computational techniques-including the MAGUS crystal structure search algorithm and GPUMD molecular dynamics simulations with enhanced sampling-we systematically explored the phase behavior of Bi under high-pressure and high-temperature conditions. The calculated solid-solid phase boundaries and solid-liquid coexistence line up to 4 GPa show good agreement with previous experimental results. Furthermore, we predict a new competitive phase of Bi with P42/mnm symmetry, which is dynamically stable around 2 GPa and competitive at free energy with the known phase C2/m near the melting line.

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.

Graphite intercalation compounds (GICs) serve as a highly tunable platform for exploring phonon-mediated superconductivity in lightweight materials. While theoretical models have long predicted that densely packed, first-stage (stage-1) sodium-intercalated graphite (Na-GIC) could host elevated critical temperatures (Tc), its experimental synthesis has remained a formidable challenge. Here, we report the realization of stage-1 Na-GIC that exhibits bulk superconductivity and achieves a maximum onset Tc of ∼31 K, setting a record for all known GIC systems. By employing a room-temperature mechanical synthesis with an excess sodium reservoir, followed by lattice compression, we force a sequential staging transition in Na-GIC─from an initial stage-8, through an intermediate stage-2, and ultimately to the densely intercalated stage-1 phase at 15.6 GPa. By correlating room-temperature in situ synchrotron X-ray diffraction with evolutionary structural searches, we identify the host of this high-Tc state as an orthorhombic NaC3 structure with Imma symmetry. First-principles calculations reveal a remarkably strong electron-phonon coupling (λ ∼ 2.0), dominated by interactions between out-of-plane carbon π electrons and low-frequency Na/C vibrations. Our findings not only capture the elusive stage-1 Na-GIC but also establish pressure-driven compositional tuning as a robust strategy to unlock high-Tc states in carbon-based superlattices.

Machine learning potentials (MLPs) achieve near first-principles accuracy but often fail for atomic environments outside the training distribution. Active learning can mitigate this limitation; however, its application to large-scale simulations is hindered by the prohibitive cost of labeling entire configurations. Here, we develop a D-optimality-driven active learning framework for the neuroevolution potential (NEP) implemented within the GPUMD package, named NEPMaker. Extrapolative atomic environments are identified on-the-fly and embedded into locally periodic structures, where boundary atoms are optimized to remain close to the training distribution. This strategy enables large-scale simulations to directly contribute to dataset construction, significantly reducing extrapolation errors while improving model robustness and transferability. The proposed framework provides a scalable route for constructing reliable machine learning potentials in complex materials systems, including those involving defects, interfaces, and phase transitions.

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.

Machine learning interatomic potentials (MLIPs) can approach quantum accuracy for short-range chemistry, but most architectures remain local and fail to capture the long-range electrostatic and polarization interactions essential for ionic, polar, and interfacial systems. Recent Ewald-based MLIPs show that locally predicted electrostatic variables can recover important long-range physics, including multipolar response. However, many energy-based implementations still compute reciprocal-space terms by direct summation over k vectors, leaving a gap with production molecular dynamics, where particle-mesh Ewald (PME) with O(NlogN) scaling is standard. Here we introduce a fully differentiable PME framework for learned charges and learned atomic dipoles within an E(n)-equivariant Cartesian tensor message passing network. Charges are predicted from scalar local features, while dipoles are predicted from equivariant vector features and enter the same particle-mesh solver as an effective bound charge density. This dipolar density is constructed using analytic real-space gradients of Hockney-Eastwood spline assignment weights, enabling charge-dipole and dipole-dipole long-range forces to be trained end-to-end through FFT-space electrostatics without direct charge or dipole supervision. On a charged-dimer test case, the differentiable PME module reproduces explicit Ewald energies and forces to numerical precision when assignment-kernel deconvolution is enabled. On molten NaCl, the charge and dipole long-range channel gives the lowest force RMSE among the tested models, while all energy RMSE values remain in the sub-meV per atom regime. Timing tests show the expected crossover from explicit Ewald summation to particle-mesh scaling. These results establish differentiable dipole PME as a scalable route toward polarization-aware MLIPs for condensed-phase and interfacial systems.

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.

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.

High harmonic generation (HHG) in solids offers a pathway to develop compact extreme ultraviolet (EUV) sources crucial for attosecond science and advanced spectroscopy. Here, we demonstrate theoretically that high pressure dramatically enhances HHG in superhard hexagonal tungsten nitride (h-WN6). Compared with solid-state systems at ambient pressure, the reshaped electronic environment under high pressure leads to a unique band-gap widening in h-WN6, which raises the material's damage threshold, allowing the use of stronger laser fields and enabling access to higher-energy bands. This pressure-induced band-gap widening offers a promising strategy to overcome the cutoff limitation of solid-state EUV light sources.

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.

Structure relaxation is important for the discovery of new materials, yet conventional ab initio optimization remains a major bottleneck in high-throughput screening workflows. Machine learning potentials have accelerated relaxation by orders of magnitude, but they still rely on iterative optimization and high-quality DFT force labels. Here, we present HotRelax, a high-order tensor message-passing neural network for one-shot, end-to-end prediction of relaxed structures. Trained directly on paired unrelaxed and relaxed structures, HotRelax requires no DFT force labels and predicts relaxed structures in a single forward pass, without iterative inference or post-processing. Across five diverse datasets spanning 3D bulk crystals, 2D layered materials and catalysts, HotRelax shows strong performance relative to state-of-the-art end-to-end relaxation models, achieving lower prediction errors on several benchmarks while maintaining a compact model size and efficient inference. Extensive DFT calculations further show that the predicted structures are close in energy to their DFT-relaxed counterparts. When integrated into catalytic workflows, HotRelax also improves the accuracy and generalization of relaxed-state energy prediction models. Together, these results support HotRelax as an efficient and widely applicable framework for end-to-end structure relaxation, with strong potential to accelerate high-throughput materials discovery.