Deep-Learning Density Functional Perturbation Theory.

Calculating perturbation response properties of materials from first principles provides a vital link between theory and experiment, but is bottlenecked by the high computational cost. Here, a general framework is proposed to perform density functional perturbation theory (DFPT) calculations by neural networks, greatly improving the computational efficiency. Automatic differentiation is applied on neural networks, facilitating accurate computation of derivatives. High efficiency and good accuracy of the approach are demonstrated by studying electron-phonon coupling and related physical quantities. This work brings deep-learning density functional theory and DFPT into a unified framework, creating opportunities for developing ab initio artificial intelligence.

Ubiquitous Topological States of Phonons in Solids: Silicon as a Model Material.

Research on topological physics of phonons has attracted enormous interest but demands appropriate model materials. Our ab initio calculations identify silicon as an ideal candidate material containing extraordinarily rich topological phonon states. In silicon, we identify various topological nodal lines characterized by quantized Berry phase π, which gives drumhead surface states observable from any surface orientations. Remarkably, a novel type of topological nexus phonon is discovered which is featured by double Fermi-arc-like surface states but requires neither inversion nor time-reversal symmetry breaking. Versatile topological states can be created from the nexus phonons, such as Hopf nodal links by strain. Furthermore, we generalize the symmetry analysis to other centrosymmetric systems and find numerous candidate materials, demonstrating the ubiquitous existence of topological phonons in solids. These findings open up new opportunities for studying topological phonons in realistic materials and their influence on surface physics.

Universal materials model of deep-learning density functional theory Hamiltonian.

Realizing large materials models has emerged as a critical endeavor for materials research in the new era of artificial intelligence, but how to achieve this fantastic and challenging objective remains elusive. Here, we propose a feasible pathway to address this paramount pursuit by developing universal materials models of deep-learning density functional theory Hamiltonian (DeepH), enabling computational modeling of the complicated structure-property relationship of materials in general. By constructing a large materials database and substantially improving the DeepH method, we obtain a universal materials model of DeepH capable of handling diverse elemental compositions and material structures, achieving remarkable accuracy in predicting material properties. We further showcase a promising application of fine-tuning universal materials models for enhancing specific materials models. This work not only demonstrates the concept of DeepH's universal materials model but also lays the groundwork for developing large materials models, opening up significant opportunities for advancing artificial intelligence-driven materials discovery.

General framework for E(3)-equivariant neural network representation of density functional theory Hamiltonian.

The combination of deep learning and ab initio calculation has shown great promise in revolutionizing future scientific research, but how to design neural network models incorporating a priori knowledge and symmetry requirements is a key challenging subject. Here we propose an E(3)-equivariant deep-learning framework to represent density functional theory (DFT) Hamiltonian as a function of material structure, which can naturally preserve the Euclidean symmetry even in the presence of spin-orbit coupling. Our DeepH-E3 method enables efficient electronic structure calculation at ab initio accuracy by learning from DFT data of small-sized structures, making the routine study of large-scale supercells (>104 atoms) feasible. The method can reach sub-meV prediction accuracy at high training efficiency, showing state-of-the-art performance in our experiments. The work is not only of general significance to deep-learning method development but also creates opportunities for materials research, such as building a Moiré-twisted material database.

Deep-learning electronic-structure calculation of magnetic superstructures.

Ab initio studies of magnetic superstructures are indispensable to research on emergent quantum materials, but are currently bottlenecked by the formidable computational cost. Here, to break this bottleneck, we have developed a deep equivariant neural network framework to represent the density functional theory Hamiltonian of magnetic materials for efficient electronic-structure calculation. A neural network architecture incorporating a priori knowledge of fundamental physical principles, especially the nearsightedness principle and the equivariance requirements of Euclidean and time-reversal symmetries ([Formula: see text]), is designed, which is critical to capture the subtle magnetic effects. Systematic experiments on spin-spiral, nanotube and moiré magnets were performed, making the challenging study of magnetic skyrmions feasible.

High-pressure synthesis of fully sp2-hybridized polymeric nitrogen layer in potassium supernitride.

Searching for fully sp2-hybridized layered structures is of fundamental importance because of their fascinating physical properties and potential to host topologically non-trivial electronic states. However, the synthesis of fully sp2-hybridized layered polymeric nitrogen structures remains a challenging work because of their low stability. Here, we report the synthesis of a fully sp2-hybridized layered polymeric nitrogen structure featuring fused 18-membered rings in potassium supernitride (K2N16) under high-pressure and high-temperature conditions. Bader charge analysis reveals that the potassium atomic layer stabilizes the unique sp2-hybridized polymeric nitrogen layers through the charge transfer effect in K2N16. The calculation of electronic structure indicates that K2N16 is a topological semimetal with multiple Dirac points and hosts higher-order Dirac fermions with cubic dispersion, which are contributed by the sp2-hybridized polymeric nitrogen layers arranged in P6/mcc symmetry. The high-pressure synthesis of the fully sp2-hybridized polymeric nitrogen layered structure provides promising prospects for exploring novel topological materials with effective stabilization routes.

Deep-learning density functional theory Hamiltonian for efficient ab initio electronic-structure calculation.

The marriage of density functional theory (DFT) and deep-learning methods has the potential to revolutionize modern computational materials science. Here we develop a deep neural network approach to represent the DFT Hamiltonian (DeepH) of crystalline materials, aiming to bypass the computationally demanding self-consistent field iterations of DFT and substantially improve the efficiency of ab initio electronic-structure calculations. A general framework is proposed to deal with the large dimensionality and gauge (or rotation) covariance of the DFT Hamiltonian matrix by virtue of locality, and this is realized by a message-passing neural network for deep learning. High accuracy, high efficiency and good transferability of the DeepH method are generally demonstrated for various kinds of material system and physical property. The method provides a solution to the accuracy-efficiency dilemma of DFT and opens opportunities to explore large-scale material systems, as evidenced by a promising application in the study of twisted van der Waals materials.

Dimensional Crossover and Topological Phase Transition in Dirac Semimetal Na3Bi Films.

Three-dimensional (3D) topological Dirac semimetal, when thinned down to 2D few layers, is expected to possess gapped Dirac nodes via quantum confinement effect and concomitantly display the intriguing quantum spin Hall (QSH) insulator phase. However, the 3D-to-2D crossover and the associated topological phase transition, which is valuable for understanding the topological quantum phases, remain unexplored. Here, we synthesize high-quality Na3Bi thin films with √3 × âˆš3 reconstruction on graphene and systematically characterize their thickness-dependent electronic and topological properties by scanning tunneling microscopy/spectroscopy in combination with first-principles calculations. We demonstrate that Dirac gaps emerge in Na3Bi films, providing spectroscopic evidence of dimensional crossover from a 3D semimetal to a 2D topological insulator. Importantly, the Dirac gaps are revealed to be of sizable magnitudes on three and four monolayers (72 and 65 meV, respectively) with topologically nontrivial edge states. Moreover, the Fermi energy of a Na3Bi film can be tuned via a certain growth process, thus offering a viable way for achieving charge neutrality in transport. The feasibility of controlling Dirac gap opening and charge neutrality enables realizing intrinsic high-temperature QSH effect in Na3Bi films and achieving potential applications in topological devices.